notebooks/7-algos-and-data-structures.ipynb

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        "<a href=\"https://colab.research.google.com/github/jonkrohn/ML-foundations/blob/master/notebooks/7-algos-and-data-structures.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aTOLgsbN69-P"
      },
      "source": [
        "# Algorithms & Data Structures"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yqUB9FTRAxd-"
      },
      "source": [
        "This class, *Algorithms & Data Structures*, introduces the most important computer science topics for machine learning, enabling you to design and deploy computationally efficient data models.\n",
        "\n",
        "Through the measured exposition of theory paired with interactive examples, you’ll develop a working understanding of all of the essential data structures across the list, dictionary, tree, and graph families. You’ll also learn the key algorithms for working with these structures, including those for searching, sorting, hashing, and traversing data.\n",
        "\n",
        "The content covered in this class is itself foundational for the *Optimization* class of the *Machine Learning Foundations* series."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d4tBvI88BheF"
      },
      "source": [
        "Over the course of studying this topic, you'll:\n",
        "\n",
        "* Use “Big O” notation to characterize the time efficiency and space efficiency of a given algorithm, enabling you to select or devise the most sensible approach for tackling a particular machine learning problem with the hardware resources available to you.\n",
        "* Get acquainted with the entire range of the most widely-used Python data structures, including list-, dictionary-, tree-, and graph-based structures.\n",
        "* Develop an understanding of all of the essential algorithms for working with data, including those for searching, sorting, hashing, and traversing.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z68nQ0ekCYhF"
      },
      "source": [
        "**Note that this Jupyter notebook is not intended to stand alone. It is the companion code to a lecture or to videos from Jon Krohn's [Machine Learning Foundations](https://github.com/jonkrohn/ML-foundations) series, which offer detail on the following:**\n",
        "\n",
        "*Segment 1: Introduction to Data Structures and Algorithms*\n",
        "* A Brief History of Data\n",
        "* A Brief History of Algorithms\n",
        "* “Big O” Notation for Time and Space Complexity\n",
        "\n",
        "*Segment 2: Lists and Dictionaries*\n",
        "* List-Based Data Structures: Arrays, Linked Lists, Stacks, Queues, and Deques\n",
        "* Searching and Sorting: Binary, Bubble, Merge, and Quick\n",
        "* Set-Based Data Structures: Maps and Dictionaries\n",
        "* Hashing: Hash Tables, Load Factors, and Hash Maps\n",
        "\n",
        "*Segment 3: Trees and Graphs*\n",
        "* Trees: Decision Trees, Random Forests, and Gradient-Boosting (XGBoost)\n",
        "* Graphs: Terminology, Directed Acyclic Graphs (DAGs)\n",
        "* Resources for Further Study of Data Structures & Algorithms\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "US_XIfDtbQ97"
      },
      "source": [
        "# Segment 1: Intro to Data Structures & Algorithms"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ovp27r5XbQ98"
      },
      "source": [
        "### \"Big O\" Notation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H9P5M6chbQ98"
      },
      "source": [
        "import numpy as np\n",
        "import tensorflow as tf\n",
        "import torch\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import time # for timing processes\n",
        "import random # for generating random values"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rG1p0sPTbQ9_"
      },
      "source": [
        "#### Constant Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vjkFiJxCbQ-A"
      },
      "source": [
        "def take_first(my_list):\n",
        "    return my_list[0]"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HgiIJRe0bQ-C"
      },
      "source": [
        "short_list = [13, 25, 42]"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GV9YDEMSbQ-F"
      },
      "source": [
        "tic = time.process_time() # if using a version of Python older than 3.3, you can use time.clock() here\n",
        "first = take_first(short_list)\n",
        "toc = time.process_time()"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rK1UsYwgbQ-H",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d8272a25-1ad4-4fa3-a379-81798c6e723c"
      },
      "source": [
        "first"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "13"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q4Ek1NZXbQ-L",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bfac30e7-9cc5-41ea-b6b2-6d282c9383f1"
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0001363100000002504"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
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    {
      "cell_type": "code",
      "metadata": {
        "id": "7gOQ5YsDbQ-N"
      },
      "source": [
        "long_list = [42] * 10**8 # one hundred million items"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mvlDw_QubQ-Q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b38e2f03-e9f3-4e00-b017-6e55c82ebe84"
      },
      "source": [
        "len(long_list)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "100000000"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "atHBBvjUbQ-S"
      },
      "source": [
        "tic = time.process_time()\n",
        "first = take_first(long_list)\n",
        "toc = time.process_time()"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c5-RorglbQ-V",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9ae73c25-e19e-4af7-86e0-382d4788a51e"
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7.197999999952742e-05"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VOzWLc7hbQ-Y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2a62fabd-64e0-407d-94fa-c6cd0d37105f"
      },
      "source": [
        "list_lengths = [10**l for l in range(1, 8)]\n",
        "list_lengths"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000, 100000, 1000000, 10000000]"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P_cblOS1bQ-b"
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      "source": [
        "constant_times = []\n",
        "\n",
        "for l in list_lengths:\n",
        "    lst = [42]*l\n",
        "\n",
        "    tic = time.process_time()\n",
        "    x = take_first(lst)\n",
        "    toc = time.process_time()\n",
        "\n",
        "    constant_times.append(toc-tic)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
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      "source": [
        "constant_df = pd.DataFrame(list(zip(list_lengths, constant_times)), columns=['n', 'time'])\n",
        "constant_df"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
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            "text/plain": [
              "          n      time\n",
              "0        10  0.000008\n",
              "1       100  0.000001\n",
              "2      1000  0.000001\n",
              "3     10000  0.000001\n",
              "4    100000  0.000004\n",
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              "  <div id=\"id_5d1d2960-cd8b-41ef-b793-06d589f7ec10\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('constant_df')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
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              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_5d1d2960-cd8b-41ef-b793-06d589f7ec10 button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('constant_df');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "constant_df",
              "summary": "{\n  \"name\": \"constant_df\",\n  \"rows\": 7,\n  \"fields\": [\n    {\n      \"column\": \"n\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 3727676,\n        \"min\": 10,\n        \"max\": 10000000,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          10,\n          100,\n          1000000\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"time\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.00022884825934905054,\n        \"min\": 1.2429999998175845e-06,\n        \"max\": 0.0006102339999998208,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          7.812999999856629e-06,\n          1.2619999996132947e-06,\n          1.3633000000012885e-05\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OuN_BT2cbQ-h"
      },
      "source": [
        "#### Linear Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FZL22BUebQ-i"
      },
      "source": [
        "def find_max(my_list):\n",
        "    max_value = my_list[0]\n",
        "    for i in range(len(my_list)):\n",
        "        if my_list[i] > max_value:\n",
        "            max_value = my_list[i]\n",
        "    return max_value"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gcN1QkRMbQ-l"
      },
      "source": [
        "tic = time.process_time()\n",
        "largest = find_max(short_list)\n",
        "toc = time.process_time()"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8lMMH3ckbQ-o",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1c731a4b-0436-4ecc-b887-8680c029fe72"
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.00010972199999947918"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z6wEKdTVbQ-q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d068d1fd-ff8e-44d2-98cd-b58a9fec0792"
      },
      "source": [
        "largest"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "42"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aWCO7ykabQ-s"
      },
      "source": [
        "tic = time.process_time()\n",
        "largest = find_max(long_list)\n",
        "toc = time.process_time()"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ml1ymMSdbQ-u",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "932d86f9-5af3-43f1-cca7-0d5a1f32a2b0"
      },
      "source": [
        "toc-tic"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12.221527860000002"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tNNuyd8vbQ-w",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3b09602e-a755-4dc1-b956-b3674cfa5804"
      },
      "source": [
        "largest"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "42"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M8CH9iVqbQ-y"
      },
      "source": [
        "linear_times = []\n",
        "\n",
        "for l in list_lengths:\n",
        "    lst = [42]*l\n",
        "\n",
        "    tic = time.process_time()\n",
        "    x = find_max(lst)\n",
        "    toc = time.process_time()\n",
        "\n",
        "    linear_times.append(toc-tic)"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WdH0rse1bQ-0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "bd081373-28f6-4f3c-8f4c-1042de828af3"
      },
      "source": [
        "linear_df = pd.DataFrame(list(zip(list_lengths, linear_times)), columns=['n', 'time'])\n",
        "linear_df"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          n      time\n",
              "0        10  0.000010\n",
              "1       100  0.000012\n",
              "2      1000  0.000135\n",
              "3     10000  0.001169\n",
              "4    100000  0.011611\n",
              "5   1000000  0.157893\n",
              "6  10000000  1.258876"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-30e409cd-b1b9-4100-b024-e33268342df1\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "      <td>0.001169</td>\n",
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              "      <td>1000000</td>\n",
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              "      <td>1.258876</td>\n",
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              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
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              "    .colab-df-container {\n",
              "      display:flex;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
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              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
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              "        document.querySelector('#df-30e409cd-b1b9-4100-b024-e33268342df1 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-30e409cd-b1b9-4100-b024-e33268342df1');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "\n",
              "  .colab-df-quickchart {\n",
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              "\n",
              "  .colab-df-quickchart:hover {\n",
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              "    fill: var(--button-hover-fill-color);\n",
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              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "\n",
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              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
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              "\n",
              "  <div id=\"id_dc508388-7b5a-41dd-93bb-51e8c3819f8d\">\n",
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              "\n",
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              "\n",
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              "\n",
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              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('linear_df')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_dc508388-7b5a-41dd-93bb-51e8c3819f8d button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('linear_df');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "linear_df",
              "summary": "{\n  \"name\": \"linear_df\",\n  \"rows\": 7,\n  \"fields\": [\n    {\n      \"column\": \"n\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 3727676,\n        \"min\": 10,\n        \"max\": 10000000,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          10,\n          100,\n          1000000\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"time\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.46865513260850444,\n        \"min\": 9.911999999445698e-06,\n        \"max\": 1.2588756080000003,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          9.911999999445698e-06,\n          1.1519000000959068e-05,\n          0.15789314699999935\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NcAT8vylbQ-2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "outputId": "5b33c47d-b5b1-4033-e07e-d86a3d1e66cf"
      },
      "source": [
        "_ = sns.lmplot(x='n', y='time', data=linear_df, ci=None) # linear model (regression) plot"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yDkSjD7QbQ-4"
      },
      "source": [
        "#### Polynomial Time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GDU07KttbQ-5"
      },
      "source": [
        "def element_multiplier(my_list):\n",
        "    for i in range(len(my_list)):\n",
        "        for j in range(len(my_list)):\n",
        "            x = my_list[i] * my_list[j]"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gKJhMq94bQ-7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "abc359c5-18c5-40ee-cb17-515460744722"
      },
      "source": [
        "list_lengths"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000, 100000, 1000000, 10000000]"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8POGVlk_bQ-9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "70bfb3b6-a93c-433b-9f47-86f8fc24a11a"
      },
      "source": [
        "list_lengths[:4] # compute time gets annoyingly long from list_lengths[5] onward"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000]"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HSTNVTA1bQ_A",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fb8da31e-b2b5-417a-f10f-36594f44014d"
      },
      "source": [
        "granular_list_lengths = list_lengths[:4] + [50, 500, 5000]\n",
        "granular_list_lengths.sort()\n",
        "granular_list_lengths"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 50, 100, 500, 1000, 5000, 10000]"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "luWZPfGkbQ_B"
      },
      "source": [
        "poly_times = []\n",
        "\n",
        "for l in granular_list_lengths:\n",
        "    lst = [42]*l\n",
        "\n",
        "    tic = time.process_time()\n",
        "    x = element_multiplier(lst)\n",
        "    toc = time.process_time()\n",
        "\n",
        "    poly_times.append(toc-tic)"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LuIgiv79bQ_E",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "8ecb6b48-cca6-472d-f8f2-cfb66138d294"
      },
      "source": [
        "poly_df = pd.DataFrame(list(zip(granular_list_lengths, poly_times)), columns=['n', 'time'])\n",
        "poly_df"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       n       time\n",
              "0     10   0.000028\n",
              "1     50   0.000383\n",
              "2    100   0.001468\n",
              "3    500   0.035158\n",
              "4   1000   0.182454\n",
              "5   5000   3.122360\n",
              "6  10000  11.175045"
            ],
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              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "  @keyframes spin {\n",
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              "      border-bottom-color: var(--fill-color);\n",
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              "  }\n",
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              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "</div>\n",
              "\n",
              "  <div id=\"id_53a66988-fd0f-48e2-b7e1-81d29c94ad3e\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('poly_df')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
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              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_53a66988-fd0f-48e2-b7e1-81d29c94ad3e button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('poly_df');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "poly_df",
              "summary": "{\n  \"name\": \"poly_df\",\n  \"rows\": 7,\n  \"fields\": [\n    {\n      \"column\": \"n\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 3799,\n        \"min\": 10,\n        \"max\": 10000,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          10,\n          50,\n          5000\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"time\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4.174516652387147,\n        \"min\": 2.7741000000247595e-05,\n        \"max\": 11.175044654000004,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          2.7741000000247595e-05,\n          0.00038312199999879226,\n          3.1223600790000035\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YRPtWuObbQ_G",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "outputId": "1ce80f17-dbe5-4da1-e7f3-59c6dc8d60e3"
      },
      "source": [
        "_ = sns.lmplot(x='n', y='time', data=poly_df, ci=None, order=2)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mBOSI7RgbQ_I"
      },
      "source": [
        "**In Big O notation**:\n",
        "\n",
        "* Constant: O(1)\n",
        "* Linear: O($n$)\n",
        "* Polynomial: O($n^2$)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S-Iu9v9pbQ_I"
      },
      "source": [
        "**Other common runtimes**:\n",
        "\n",
        "* Logarithmic: O(log $n$)\n",
        "* Exponential: O($2^n$)\n",
        "* O($n$ log $n$)\n",
        "* O($n!$)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yEmvHfjDbQ_I"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uwkFwWfGbQ_J"
      },
      "source": [
        "## Segment 2: Lists and Dictionaries"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "75kQx0StbQ_J"
      },
      "source": [
        "### List-Based Data Structures"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LMZUkiBzbQ_K"
      },
      "source": [
        "#### Lists"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bYjn-LUvbQ_K",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "21c39513-3770-4651-b001-3d03a5008f3c"
      },
      "source": [
        "t = [25, 2, 5]\n",
        "t"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[25, 2, 5]"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_9ue0FJzbQ_M"
      },
      "source": [
        "Lists in Python are **extensible** by default:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BxLoVg9LbQ_N",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "637768c1-8c16-4395-c681-effe26cbea9f"
      },
      "source": [
        "t.append(26)\n",
        "t"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[25, 2, 5, 26]"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nn0mjz8IbQ_P",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c1815f6f-e983-4947-ca44-4b9475bc3613"
      },
      "source": [
        "t[2]"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pNCGZLPibQ_Q"
      },
      "source": [
        "Cannot apply mathematical operators, e.g., try uncommenting:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UYOXE7t3bQ_R"
      },
      "source": [
        "# t/2"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3bqqZduEbQ_T"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IO1j-BB3bQ_T"
      },
      "source": [
        "#### Arrays"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T9Wufa8ZbQ_U",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "32422b8b-381e-49b8-d25f-b16056d00da6"
      },
      "source": [
        "x = np.array([25, 2, 5])\n",
        "x"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ILAFgARTbQ_W",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6976a962-02c8-43a8-e27e-4682572c63e4"
      },
      "source": [
        "x[2]"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eaQZXwGYbQ_Y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a41d46b4-48dd-4f77-cde0-728268feb394"
      },
      "source": [
        "x/2."
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([12.5,  1. ,  2.5])"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O2njtLKPbQ_b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "92f5c4fa-a7cb-4b01-f2f4-a65596138c3c"
      },
      "source": [
        "y = torch.tensor([[25, 2, 5], [26, 1, 4]])\n",
        "y"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[25,  2,  5],\n",
              "        [26,  1,  4]])"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lO4Fp87RbQ_d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1bb8676e-adf1-49fe-82c4-7cb5d7ef91f2"
      },
      "source": [
        "y[0, 2]"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(5)"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WVmPPyNybQ_g",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "86c3abeb-f872-4b36-9a03-635dc2328777"
      },
      "source": [
        "y/2."
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[12.5000,  1.0000,  2.5000],\n",
              "        [13.0000,  0.5000,  2.0000]])"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XLGc3ZLNbQ_i",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "46e34b2a-39c0-4205-98d8-1615a9785306"
      },
      "source": [
        "z = tf.Variable([[[0, 1], [2, 3]], [[25, 26], [7, 9]]], dtype=tf.float16)\n",
        "z"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=(2, 2, 2) dtype=float16, numpy=\n",
              "array([[[ 0.,  1.],\n",
              "        [ 2.,  3.]],\n",
              "\n",
              "       [[25., 26.],\n",
              "        [ 7.,  9.]]], dtype=float16)>"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b-mBUUXSbQ_l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "593e00d8-96c0-45b6-8705-b35d3a30b443"
      },
      "source": [
        "z[1, 0, 0]"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=float16, numpy=25.0>"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vF_Vx6kUbQ_n",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "24b6d87b-bb4c-4f9f-c112-2c068b7c4e63"
      },
      "source": [
        "z/2."
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(2, 2, 2), dtype=float16, numpy=\n",
              "array([[[ 0. ,  0.5],\n",
              "        [ 1. ,  1.5]],\n",
              "\n",
              "       [[12.5, 13. ],\n",
              "        [ 3.5,  4.5]]], dtype=float16)>"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "grLMKTA9bQ_p"
      },
      "source": [
        "Arrays in Python are also typically extensible by default.\n",
        "\n",
        "Note that it's very efficient (O(1)) to append items to end of list..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yw0vxB1wbQ_p",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aa17ec59-2e14-46c5-c646-060a2beb6ed9"
      },
      "source": [
        "np.append(x, 26)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5, 26])"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3VVvEmDcbQ_r"
      },
      "source": [
        "...but time inefficient to add at start or middle of long list as later items will need to be shifted to later in list. Worst case is insert at beginning of list, which has O($n$) complexity.\n",
        "\n",
        "Note that as well as appending, accessing an array element by index or finding the array's length are O(1)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eAMI_JhobQ_s"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ux7X2TtObQ_t"
      },
      "source": [
        "#### Stacks"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mfUpv9mmbQ_t"
      },
      "source": [
        "Can be implemented in Python with lists:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ox6jmYt1bQ_t",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f0363de6-ca9a-41f9-c708-ec4eb0be9782"
      },
      "source": [
        "s = []\n",
        "s"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aO62dJ7mbQ_v",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8e41ca5f-20c9-4616-f3cf-72c6487058e6"
      },
      "source": [
        "s.append('five_of_diamonds') # push\n",
        "s"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['five_of_diamonds']"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6xL9EVlEbQ_x",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0e80af28-96e2-4634-cda6-0578ebdfe2c4"
      },
      "source": [
        "s.append('queen_of_hearts')\n",
        "s"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['five_of_diamonds', 'queen_of_hearts']"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mp3FWjIAbQ_1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ed3f8f6f-2649-44ed-9180-17a3d9822f39"
      },
      "source": [
        "s.append('ace_of_spades')\n",
        "s"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['five_of_diamonds', 'queen_of_hearts', 'ace_of_spades']"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yj7R5DypbQ_3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "fa0a46b1-e400-48e6-a30d-48734f0ebb01"
      },
      "source": [
        "s.pop()"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'ace_of_spades'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PRJMSEi6bQ_6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c39c8692-35e9-47e2-8e9e-893d954e1754"
      },
      "source": [
        "s"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['five_of_diamonds', 'queen_of_hearts']"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1h5Jn3sNbQ_8"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sW1P2RYgbQ_8"
      },
      "source": [
        "### Searching and Sorting"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MOGhRGE7bQ_-"
      },
      "source": [
        "Topics in this section:\n",
        "* Binary search\n",
        "* Bubble sort\n",
        "* Merge sort\n",
        "* Quick sort"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "926iDawVbQ__"
      },
      "source": [
        "#### Binary Search"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vh4b6rjibQ__"
      },
      "source": [
        "Let's say we have an array, `b`:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AqihwZaBbRAA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4a08f7bd-62c4-47f2-e4d2-d56091a37850"
      },
      "source": [
        "b = np.array([25, 2, 5, 14, 22, 11, 96, 1, 101])\n",
        "b"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 25,   2,   5,  14,  22,  11,  96,   1, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ILRfUWW8bRAB"
      },
      "source": [
        "Under normal circumstances, the only way to search for a value (e.g., `25`) is to search element by element. In the worse-case, this has O($n$) time complexity (e.g., if we were to search `b` for `25` from its end).\n",
        "\n",
        "If `b` already happens to be sorted, however..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H3kijg5DbRAB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b428fb63-dba4-4b27-e599-0a4b6767d412"
      },
      "source": [
        "b.sort() # FYI: uses quick sort\n",
        "b"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  1,   2,   5,  11,  14,  22,  25,  96, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jUNwtC9VbRAD"
      },
      "source": [
        "...we can use the **binary search** algorithm, which has O(log $n$) time complexity:\n",
        "\n",
        "* Start at the midpoint (`b` is nine elements long, so midpoint is 5th: `14`).\n",
        "* Since `25` is larger than `14`, we need only search the top half of `b`...\n",
        "* So we find the midpoint between the 5th element and the 9th, which is the 7th, and which happens to be `25`.\n",
        "* Done! And in only two steps instead of seven (if we were to search elementwise from first onward).\n",
        "* If we were searching for `22`, then our next search would be halfway between 5th and 7th elements, which is 6th element and voilà!\n",
        "* With our nine-element array, worst case is four steps (for `1` or `101`) to find any value (or determine value *isn't* in array).\n",
        "\n",
        "(Note: called *binary* because at each step we either search upward or downward.)\n",
        "\n",
        "Doubling $n$ results in only one extra step in worst case:\n",
        "* One step with array of length 1($= 2^0$)\n",
        "* Two steps with length 2($= 2^1$) up to length 3\n",
        "* Three steps with $n = 4 (= 2^2$) up to $n = 7$\n",
        "* Four steps with $n = 8 (= 2^3$) up to $n = 15$\n",
        "* Five steps with $n = 16 (= 2^4$) up to $n = 31$\n",
        "\n",
        "Hence O(log $n$) where, as is typical in CS, we use $\\text{log}_2$ (because of binary bits and frequently doubling/halving quantities). E.g.:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aMCXLkATbRAD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0c146167-f05b-4204-8f67-f32f7e044345"
      },
      "source": [
        "np.log2(4) + 1"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.0"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GkKU00_jbRAF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5c0e0492-58fa-4b8d-d782-4e6a2a1bae94"
      },
      "source": [
        "np.log2(8) + 1"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4.0"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lem_1CFEbRAH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3e52aff5-edbe-44e7-f71c-f1a1c2aefb8b"
      },
      "source": [
        "np.log2(16) + 1"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5.0"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qw_uflkYbRAJ"
      },
      "source": [
        "Recall that we retain only the dominant term, so O(log $n$ + 1) becomes O(log $n$)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uKR2g6w-bRAK"
      },
      "source": [
        "Here's an implementation of binary search, for your reference, that *iterates* over binary search steps with a `while` loop:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eSnow5fBbRAK"
      },
      "source": [
        "def binary_search(array, value):\n",
        "\n",
        "    low = 0\n",
        "    high = len(array)-1\n",
        "\n",
        "    while low <= high:\n",
        "        midpoint = (low + high) // 2 # rounds down to nearest integer after division\n",
        "        if value < array[midpoint]:\n",
        "            high = midpoint-1\n",
        "        elif value > array[midpoint]:\n",
        "            low = midpoint+1\n",
        "        else:\n",
        "            return midpoint\n",
        "    return -1"
      ],
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KVLvfQyMbRAL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "23b60faf-079f-4980-83db-3a7a201e785e"
      },
      "source": [
        "binary_search(b, 25)"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vlIy86McbRAO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0c7ad906-626d-43d5-db80-e928c8f6bfb0"
      },
      "source": [
        "binary_search(b, 255)"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-1"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QgWnRKYMbRAP"
      },
      "source": [
        "Alternatively, you could implement binary search with *recursion* instead of iteration:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CGW08COgbRAQ"
      },
      "source": [
        "def recursive_binary_search(array, value, low, high):\n",
        "\n",
        "    if low <= high:\n",
        "\n",
        "        midpoint = (low + high) // 2\n",
        "\n",
        "        if array[midpoint] == value:\n",
        "            return midpoint\n",
        "        elif array[midpoint] > value:\n",
        "            return recursive_binary_search(array, value, low, midpoint-1)\n",
        "        else:\n",
        "            return recursive_binary_search(array, value, midpoint+1, high)\n",
        "    else:\n",
        "        return -1"
      ],
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KCybEoSTbRAR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "95614adc-2b45-42fd-df59-00823de0545e"
      },
      "source": [
        "recursive_binary_search(b, 25, 0, len(b)-1)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rHNqJWZFbRAS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b483ec5b-b362-4ad7-c823-760964f1bb5d"
      },
      "source": [
        "recursive_binary_search(b, 255, 0, len(b)-1)"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-1"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-4qFVG7wbRAV"
      },
      "source": [
        "#### Bubble Sort"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xXl97ruDbRAV"
      },
      "source": [
        "Binary search required a sorted list. To sort a list (e.g., from smallest to largest value), the most naïve (and computationally complex) approach would be to compare every given element with all other elements.\n",
        "\n",
        "A common naïve implementation is the **bubble sort**, which allows the largest values to gradually \"bubble up\" toward the \"top\" (typically the end) of the array:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Si7_TCUBbRAW"
      },
      "source": [
        "def bubble_sort(array):\n",
        "\n",
        "    n = len(array)\n",
        "\n",
        "    for i in range(n-1):\n",
        "        for j in range(0, n-1): # could be n-i-1 as, e.g., top value is guaranteed to have bubbled up in 1st iteration\n",
        "            if array[j] > array[j+1]:\n",
        "                array[j], array[j+1] = array[j+1], array[j]\n",
        "\n",
        "    return array"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bHJXYGoWbRAX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "76ae1215-7856-400a-f6a6-82bd26c696e6"
      },
      "source": [
        "b = np.array([25, 2, 5, 14, 22, 11, 96, 1, 101])\n",
        "b"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 25,   2,   5,  14,  22,  11,  96,   1, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dRG0hcs8bRAa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6e08ca11-cfac-4e93-f666-7a8e0548a3b7"
      },
      "source": [
        "bubble_sort(b)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  1,   2,   5,  11,  14,  22,  25,  96, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SeEwGoyhbRAb"
      },
      "source": [
        "* During each iteration, we make $n-1$ comparisons\n",
        "* A total of $n-1$ iterations need to be made\n",
        "\n",
        "$$ (n-1)(n-1) = n^2 -2n + 1 $$\n",
        "\n",
        "Since we drop all terms but the dominant one, this leaves us with polynomial O($n^2$) time complexity for the worst case and the average case. (For more clever implementations, best case is O($n$) because array would already be sorted.)\n",
        "\n",
        "In contrast, as is typical in algos, there is a time- vs memory-complexity trade-off: Memory complexity is constant, O(1)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XaVyDNNEbRAb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "77f35ab7-e96b-464b-f79a-b724cf472108"
      },
      "source": [
        "granular_list_lengths"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 50, 100, 500, 1000, 5000, 10000]"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5VCZfbt5bRAd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "db13f3dd-f08d-4240-f8e7-daa8a67cd3f4"
      },
      "source": [
        "max(granular_list_lengths)"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10000"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KF3yROSObRAf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3193e75d-bd79-4231-b49c-8342e7f689d6"
      },
      "source": [
        "random.sample(range(0, max(granular_list_lengths)), 5) # samples 5 integers w/o replacement from uniform distribution"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[7906, 8845, 8249, 6160, 3448]"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BH-e63O-bRAg"
      },
      "source": [
        "bubble_times = []\n",
        "\n",
        "for l in granular_list_lengths[0:7]:\n",
        "    lst = random.sample(range(0, max(granular_list_lengths)), l)\n",
        "\n",
        "    tic = time.process_time()\n",
        "    x = bubble_sort(lst)\n",
        "    toc = time.process_time()\n",
        "\n",
        "    bubble_times.append(toc-tic)"
      ],
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sc7PYo7rbRAi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "72735fdd-015a-420b-edbd-7b310e53ddfd"
      },
      "source": [
        "bubble_df = pd.DataFrame(list(zip(granular_list_lengths, bubble_times)), columns=['n', 'time'])\n",
        "bubble_df"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       n       time\n",
              "0     10   0.000033\n",
              "1     50   0.000578\n",
              "2    100   0.002153\n",
              "3    500   0.057291\n",
              "4   1000   0.260174\n",
              "5   5000   6.131653\n",
              "6  10000  16.825840"
            ],
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              "type": "dataframe",
              "variable_name": "bubble_df",
              "summary": "{\n  \"name\": \"bubble_df\",\n  \"rows\": 7,\n  \"fields\": [\n    {\n      \"column\": \"n\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 3799,\n        \"min\": 10,\n        \"max\": 10000,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          10,\n          50,\n          5000\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"time\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 6.368798532331655,\n        \"min\": 3.328000000379916e-05,\n        \"max\": 16.825840375,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          3.328000000379916e-05,\n          0.0005783920000013154,\n          6.131653374999999\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ylF8L9ZRbRAk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "outputId": "f0bc880d-7ece-440e-f0b9-b9645a406ae7"
      },
      "source": [
        "_ = sns.lmplot(x='n', y='time', data=bubble_df, ci=None, order=2)"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BaIYCE7CbRAl"
      },
      "source": [
        "#### Merge Sort"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3ebEOGvNbRAm"
      },
      "source": [
        "* General idea is to \"divide and conquer\"; specifically:\n",
        "    1. Halve the array into smaller arrays\n",
        "    2. Sort the smaller arrays\n",
        "    3. Merge them back into full array\n",
        "* The above steps are carried out recursively so ultimately sort arrays of max length 2, then merge back up to full length."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rwJEeUdTbRAm"
      },
      "source": [
        "def merge_sort(my_list): # using list instead of array so we can .pop() (np arrays don't pop with built-in method)\n",
        "\n",
        "    if len(my_list) > 1: # if length is 1, no need to sort (at deepest recursion, some will have len 1, others len 2)\n",
        "\n",
        "        # 1. Halve:\n",
        "        midpoint = len(my_list) // 2 # Note: This is ~O(log n) behavior\n",
        "        left_half = my_list[:midpoint]\n",
        "        right_half = my_list[midpoint:]\n",
        "\n",
        "        # 2. Sort (recursively):\n",
        "        left_half = merge_sort(left_half)\n",
        "        right_half = merge_sort(right_half)\n",
        "\n",
        "        my_list = []\n",
        "\n",
        "        # 3. Merge:\n",
        "        while len(left_half)>0 and len(right_half)>0: # Note: This inner loop exhibits ~O(n) behavior\n",
        "\n",
        "            if left_half[0] < right_half[0]:\n",
        "                my_list.append(left_half.pop(0)) # pop first element\n",
        "\n",
        "            else: # 1st element of right half < 1st element of left\n",
        "                my_list.append(right_half.pop(0))\n",
        "\n",
        "        # If any elements remain from either half, they must be the largest value:\n",
        "        for i in left_half:\n",
        "            my_list.append(i)\n",
        "        for i in right_half:\n",
        "            my_list.append(i)\n",
        "\n",
        "    return my_list"
      ],
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yu0POqD4bRAo"
      },
      "source": [
        "m = [25, 2, 5, 14, 22, 11, 96, 1, 101]"
      ],
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yb5kYBRNbRAq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7f19abcd-a95d-47d6-81f0-0a89550f340b"
      },
      "source": [
        "merge_sort(m)"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1, 2, 5, 11, 14, 22, 25, 96, 101]"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wft09yAQbRAr"
      },
      "source": [
        "Because of the O($n$) loop performing comparisons inside of the function halving list sizes (which we'll need to call O(log $n$) times), merge sort time complexity is the product, i.e., O($n$ log $n$)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UsiZJrrobRAs",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d1b741e3-b9da-44df-d018-6b29924ad11a"
      },
      "source": [
        "granular_list_lengths"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 50, 100, 500, 1000, 5000, 10000]"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O2bhlTkgbRAw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f226a63f-046b-4f5d-c70a-21fecfff30ec"
      },
      "source": [
        "ext_granular_lengths = granular_list_lengths + [50000, 100000] # extended\n",
        "ext_granular_lengths"
      ],
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000]"
            ]
          },
          "metadata": {},
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y174TTjwbRAx"
      },
      "source": [
        "merge_times = []\n",
        "\n",
        "for l in ext_granular_lengths:\n",
        "    lst = random.sample(range(0, max(ext_granular_lengths)), l)\n",
        "\n",
        "    tic = time.process_time()\n",
        "    x = merge_sort(lst)\n",
        "    toc = time.process_time()\n",
        "\n",
        "    merge_times.append(toc-tic)"
      ],
      "execution_count": 76,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pNQfPAy7bRAz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "outputId": "f1b8a15f-5c04-4585-b2d6-eadd4da4c0f1"
      },
      "source": [
        "merge_df = pd.DataFrame(list(zip(ext_granular_lengths, merge_times)), columns=['n', 'time'])\n",
        "merge_df"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "        n      time\n",
              "0      10  0.000045\n",
              "1      50  0.000226\n",
              "2     100  0.000287\n",
              "3     500  0.001795\n",
              "4    1000  0.003506\n",
              "5    5000  0.026664\n",
              "6   10000  0.065815\n",
              "7   50000  0.482626\n",
              "8  100000  1.500227"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-ca30ae26-7bfc-4973-8820-adc5080de0ce\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>10</td>\n",
              "      <td>0.000045</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>50</td>\n",
              "      <td>0.000226</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>100</td>\n",
              "      <td>0.000287</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>500</td>\n",
              "      <td>0.001795</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1000</td>\n",
              "      <td>0.003506</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5000</td>\n",
              "      <td>0.026664</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>10000</td>\n",
              "      <td>0.065815</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>50000</td>\n",
              "      <td>0.482626</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>100000</td>\n",
              "      <td>1.500227</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ca30ae26-7bfc-4973-8820-adc5080de0ce')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
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              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-ca30ae26-7bfc-4973-8820-adc5080de0ce button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-ca30ae26-7bfc-4973-8820-adc5080de0ce');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
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              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-d8699c59-4ce7-4b31-9e4d-d12fa3399466')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-d8699c59-4ce7-4b31-9e4d-d12fa3399466 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "  <div id=\"id_ffdd325f-4cf7-4dff-9d37-eeccdddc5048\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('merge_df')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_ffdd325f-4cf7-4dff-9d37-eeccdddc5048 button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('merge_df');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "merge_df",
              "summary": "{\n  \"name\": \"merge_df\",\n  \"rows\": 9,\n  \"fields\": [\n    {\n      \"column\": \"n\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 34532,\n        \"min\": 10,\n        \"max\": 100000,\n        \"num_unique_values\": 9,\n        \"samples\": [\n          50000,\n          50,\n          5000\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"time\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.5009248094656548,\n        \"min\": 4.515000000537839e-05,\n        \"max\": 1.5002269559999917,\n        \"num_unique_values\": 9,\n        \"samples\": [\n          0.4826260260000055,\n          0.00022582500000112304,\n          0.026663675999998304\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TxbDpaXUbRA1"
      },
      "source": [
        "On local laptop, $n=10000$ took ~0.05s with merge sort compared to ~10.5s with bubble sort: a ~200x speedup."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_vNv29-3bRA1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "outputId": "8f505f5c-5674-4b19-b829-374578313aeb"
      },
      "source": [
        "_ = sns.lmplot(x='n', y='time', data=merge_df, ci=None, order=2)"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j09sAT9ubRA3"
      },
      "source": [
        "In contrast, while memory complexity for bubble sort was O(1) because we were sorting \"in place\" (not storing any values in memory), memory complexity is O($n$) for merge sort.\n",
        "\n",
        "(We need at least two array copies (2$n$) for the most space-efficient merge sort implementations, but we drop constants so this becomes O($n$). Our recursive merge sort implementation would require more as it stores several copies in memory; one more copy of size $n$ would be used for every time the array length doubles (log $n$) resulting in O($n$ log $n$) memory complexity.)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QgsX2oJNbRA3"
      },
      "source": [
        "#### Quick Sort"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "liGs0XOabRA3"
      },
      "source": [
        "Under many common conditions, the aptly-named **quick sort** is at least as time-efficient as merge sort while also being more space-efficient.\n",
        "\n",
        "Like merge sort, quick sort uses the \"divide and conquer\" principle:\n",
        "1. Pick a *pivot* point (often the final element, though it could be any element, e.g., first, random, median)\n",
        "2. Move pivot within array such that all elements above pivot are larger (though randomly ordered) and all elements below pivot are smaller (though likewise randomly ordered)\n",
        "    * Movement occurs element-by-element (and \"in place\", thus retaining O(1) memory complexity)\n",
        "3. Recursively, perform quick sort both below and above pivot"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k0oYCHi0bRA3"
      },
      "source": [
        "def quick_sort(array):\n",
        "    _quick_sort(array, 0, len(array)-1) # to start, low is index of first element in array; high is final element\n",
        "    return array"
      ],
      "execution_count": 79,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VW6wpvafbRA4"
      },
      "source": [
        "def _quick_sort(array, low, high):\n",
        "\n",
        "    if low < high: # when low reaches high, we know all elements in array must be in order\n",
        "\n",
        "        # Result of 2.: Element at \"partitioning index\" has been pivoted to its correct position\n",
        "        p_index = partition(array, low, high)\n",
        "\n",
        "        # 3. Recursively sort the elements below the partitioning index...\n",
        "        _quick_sort(array, low, p_index-1)\n",
        "        # ...and, separately, above the partitioning index:\n",
        "        _quick_sort(array, p_index+1, high)\n",
        "\n",
        "    return array"
      ],
      "execution_count": 80,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c4vF29ylbRA6"
      },
      "source": [
        "def partition(array, low, high):\n",
        "\n",
        "    # 1. Use the final element as the pivot:\n",
        "    pivot = array[high]\n",
        "\n",
        "    i = (low-1) # index of element on small side\n",
        "    for j in range(low, high): # like a bubble swap, we compare pivot to all elements between low and high\n",
        "        if array[j] < pivot: # if value < pivot, it's correctly on left so increment the smaller element's index...\n",
        "            i = i+1\n",
        "            array[i], array[j] = array[j], array[i]\n",
        "    array[i+1], array[high] = array[high], array[i+1] # ...otherwise, swap greater value to right of pivot (now what we want)\n",
        "    return(i+1) # return index of correctly positioned pivot"
      ],
      "execution_count": 81,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TGbYfXozbRA7"
      },
      "source": [
        "b = np.array([25, 2, 5, 14, 22, 11, 96, 1, 101])"
      ],
      "execution_count": 82,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eUwabel3bRA9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d2a2c9d8-268c-415d-ebe6-5ec992fce92e"
      },
      "source": [
        "quick_sort(b)"
      ],
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  1,   2,   5,  11,  14,  22,  25,  96, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pgrhXuTSbRA-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aad429c4-5acf-443a-ec30-5d139f423bc0"
      },
      "source": [
        "list_lengths"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000, 100000, 1000000, 10000000]"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3Zw2sLRDbRBA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8d16a07b-fa58-4c2f-d872-4a5f81ce6d74"
      },
      "source": [
        "list_lengths[:6]"
      ],
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[10, 100, 1000, 10000, 100000, 1000000]"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WMkykWEjbRBB"
      },
      "source": [
        "quick_times = []\n",
        "\n",
        "for l in list_lengths[:6]:\n",
        "    lst = random.sample(range(0, max(list_lengths[:6])), l)\n",
        "\n",
        "    tic = time.process_time()\n",
        "    x = quick_sort(lst)\n",
        "    toc = time.process_time()\n",
        "\n",
        "    quick_times.append(toc-tic)"
      ],
      "execution_count": 86,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aA3pD0GEbRBC",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        },
        "outputId": "17d1d571-4243-4d66-aebb-df4697df7d51"
      },
      "source": [
        "quick_df = pd.DataFrame(list(zip(list_lengths[:6], quick_times)), columns=['n', 'time'])\n",
        "quick_df"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         n      time\n",
              "0       10  0.000024\n",
              "1      100  0.000143\n",
              "2     1000  0.002078\n",
              "3    10000  0.034235\n",
              "4   100000  0.422946\n",
              "5  1000000  5.986721"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-e34e0109-82f8-44e2-b225-f21ddd68695b\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>n</th>\n",
              "      <th>time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>10</td>\n",
              "      <td>0.000024</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>100</td>\n",
              "      <td>0.000143</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1000</td>\n",
              "      <td>0.002078</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>10000</td>\n",
              "      <td>0.034235</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>100000</td>\n",
              "      <td>0.422946</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1000000</td>\n",
              "      <td>5.986721</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-e34e0109-82f8-44e2-b225-f21ddd68695b')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-e34e0109-82f8-44e2-b225-f21ddd68695b button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-e34e0109-82f8-44e2-b225-f21ddd68695b');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-badf229a-3761-4c0a-a6eb-b66bd58b26b1\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-badf229a-3761-4c0a-a6eb-b66bd58b26b1')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-badf229a-3761-4c0a-a6eb-b66bd58b26b1 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "  <div id=\"id_b8d7195b-2e2e-47bd-b6a8-2d5188ee641a\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('quick_df')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_b8d7195b-2e2e-47bd-b6a8-2d5188ee641a button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('quick_df');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "quick_df",
              "summary": "{\n  \"name\": \"quick_df\",\n  \"rows\": 6,\n  \"fields\": [\n    {\n      \"column\": \"n\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 401083,\n        \"min\": 10,\n        \"max\": 1000000,\n        \"num_unique_values\": 6,\n        \"samples\": [\n          10,\n          100,\n          1000000\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"time\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.4122775673650505,\n        \"min\": 2.4358000004554015e-05,\n        \"max\": 5.986720657999996,\n        \"num_unique_values\": 6,\n        \"samples\": [\n          2.4358000004554015e-05,\n          0.00014324100000351336,\n          5.986720657999996\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 87
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WEWln2HPbRBF"
      },
      "source": [
        "At $n=$ 10k, about a 2x speed-up relative to merge sort (so ~400 relative to bubble sort).\n",
        "\n",
        "At $n=$ 100k, about a 5x speed-up relative to merge sort."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yMG5f6hwbRBG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "outputId": "8e9fdcef-3881-49d6-bc49-f2e780bd06b0"
      },
      "source": [
        "_ = sns.lmplot(x='n', y='time', data=quick_df, ci=None, order=2)"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "svDy0tGRbRBH"
      },
      "source": [
        "**Average-case time**: The efficiency of quick sort comes from moving lower-valued pivots toward the front (ideally to the midpoint) of the array then \"dividing and conquering\" on either side of the pivot. In which case (the average case), quick sort behaves like a merge sort (thereby it has O($n$ log $n$) time complexity), but in a manner that requires only a single copy of the array in memory.\n",
        "\n",
        "**Worst-case time**: With the pivot starting at the final element, if the array is already sorted, this is the worst case. There will be as many calls to `quick_sort()` as there are elements in the array (i.e., $n$ calls) and quick sort will perform a full round of bubble sorting (as per the `for j in range` loop) during each of those (i.e., $n-1$ comparisons); the product of these resulting in O($n^2$) time complexity. So, don't use quick sort if the array is nearly in order!\n",
        "\n",
        "**Best-case time**: If all values in the array are equal, quick sort will scan over them all once to confirm this, in which case it has O($n$) time complexity. The more values that are equal in the array, the closer to O($n$) performance will be."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wGql4D1WbRBH"
      },
      "source": [
        "Those are the most frequently covered sorting algos. They're relatively straightforward to implement and illustrate time/space complexity trade-offs clearly. There are, however, many more ways to sort, with pros and cons related to time/space complexity as well as implementation difficulty. See the [Big O Cheat Sheet here](https://www.bigocheatsheet.com)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ceTsWVKgbRBH"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LQOPQyUxbRBI"
      },
      "source": [
        "### Set-Based Data Structures: Maps/Dictionaries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-iUBoFZEbRBI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4a4cbb80-eefe-472a-815f-d32460861b2f"
      },
      "source": [
        "inventory = {}\n",
        "inventory"
      ],
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{}"
            ]
          },
          "metadata": {},
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k9ThSSP7bRBK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5ba52415-4c00-46ae-e373-b6c964315c6a"
      },
      "source": [
        "inventory['hammer'] = [17]\n",
        "inventory"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'hammer': [17]}"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CHAlpCLgbRBL"
      },
      "source": [
        "inventory['nail'] = [2552]\n",
        "inventory['unicorn'] = [2]\n",
        "inventory['dolphin'] = ['none']"
      ],
      "execution_count": 91,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GJvRhipdbRBM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "39e392e2-d142-4680-9b5d-599946a774d7"
      },
      "source": [
        "inventory"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'hammer': [17], 'nail': [2552], 'unicorn': [2], 'dolphin': ['none']}"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iJElGR-VbRBO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e28eb177-dd2c-4abf-fa2f-5cf35e5a8824"
      },
      "source": [
        "inventory['dolphin'] = [0]\n",
        "inventory"
      ],
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'hammer': [17], 'nail': [2552], 'unicorn': [2], 'dolphin': [0]}"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kl1avvQAbRBP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ac55264b-5205-43b3-b384-4e5a460d997b"
      },
      "source": [
        "inventory['unicorn'].append(3)\n",
        "inventory"
      ],
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'hammer': [17], 'nail': [2552], 'unicorn': [2, 3], 'dolphin': [0]}"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8EQa-WNwbRBQ"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QeJeTpTUbRBR"
      },
      "source": [
        "### Hashing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EZuRS1k8bRBR"
      },
      "source": [
        "Let's say we have some value:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qaEqWADrbRBR"
      },
      "source": [
        "value = 5551234567 # a phone number from any American '90s sitcom"
      ],
      "execution_count": 95,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SYNQv_GgbRBS"
      },
      "source": [
        "A common hash function approach is to use the modulo operator on the last few digits of the value..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NdQHebyabRBT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3f28dfc1-d975-4e90-9c66-a65588caa9d1"
      },
      "source": [
        "split_value = [digit for digit in str(value)]\n",
        "split_value"
      ],
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['5', '5', '5', '1', '2', '3', '4', '5', '6', '7']"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9ElRrr1obRBU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1ce07765-80dc-45eb-c95b-b994aa8d510b"
      },
      "source": [
        "final_digits = int(''.join(split_value[-2:])) # final digits typically used b/c they tend to vary more than first ones\n",
        "final_digits"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "67"
            ]
          },
          "metadata": {},
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z8Z9NUsTbRBV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2b5a0970-0d45-41a4-c7eb-f01df6fc288c"
      },
      "source": [
        "hash_value = final_digits % 10 # 10 is arbitrary, but would be used consistently across values to be hashed\n",
        "hash_value"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XEBGAP0FbRBW"
      },
      "source": [
        "def simple_hash(v):\n",
        "    split_v = [digit for digit in str(v)]\n",
        "    final_2 = int(''.join(split_v[-2:]))\n",
        "    return final_2 % 10"
      ],
      "execution_count": 99,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FTtuf6sJbRBZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "98023ee5-23a4-4d3e-b15a-33a6152e6dc6"
      },
      "source": [
        "simple_hash(value)"
      ],
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {},
          "execution_count": 100
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sNdnyNMkbRBb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aa6a4de3-da8d-4b83-96e2-d71419bdbcb3"
      },
      "source": [
        "simple_hash(5557654321)"
      ],
      "execution_count": 101,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 101
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bPfLF9b4bRBd"
      },
      "source": [
        "These hash values (`7` and `1`) could be used in a sequential, small-integer index, i.e., a *hash table*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pmpE8IHfbRBe"
      },
      "source": [
        "#### Collisions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lus6EYZhbRBe"
      },
      "source": [
        "Major problem with the `simple_hash()` function:\n",
        "* The hash table has at most ten indices\n",
        "* Ergo, many input values will result in **collisions**, e.g.:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2ylVWx8jbRBe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dcc65f41-d502-4069-d906-76411a9a9f06"
      },
      "source": [
        "simple_hash(555)"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rSIkIOMtbRBf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "21a04b1d-68e8-441d-f48b-4828d2a18d1b"
      },
      "source": [
        "simple_hash(125)"
      ],
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jeVzqmMsbRBg"
      },
      "source": [
        "Three common ways to resolve collisions:\n",
        "1. Change the modulus denominator (e.g., `10` --> `11`); this adds procedural (and thus time) complexity to hash algo\n",
        "2. Change the hash function entirely; ditto w.r.t. procedural complexity\n",
        "3. Store a list (or similar) at the index, e.g.:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZxBjBwmcbRBg"
      },
      "source": [
        "hash_table = {}"
      ],
      "execution_count": 104,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vNyDE65wbRBh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "018248dc-836d-456a-e4fd-1bb693f65663"
      },
      "source": [
        "hash_table[simple_hash(555)] = [555]\n",
        "hash_table"
      ],
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{5: [555]}"
            ]
          },
          "metadata": {},
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x4ztIzo4bRBi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d2cdadee-a510-49a7-c13d-5a18f5dec7ce"
      },
      "source": [
        "hash_table[simple_hash(125)].append(125)\n",
        "hash_table"
      ],
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{5: [555, 125]}"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nE4V0Qq4bRBk"
      },
      "source": [
        "Such a list is called a **bucket**.\n",
        "\n",
        "Worst case:\n",
        "* All of the values hash to the same hash value (e.g., `5`)\n",
        "* Thus, all of the values are stored in a single bucket\n",
        "* Searching through the bucket has linear O($n$) time complexity\n",
        "\n",
        "Alternatively, we can increase memory complexity instead of time complexity:\n",
        "* Use very large modulus denominator\n",
        "* Reduces probability of collisions\n",
        "* If use denominator of `1e9`, we have a hash table with a billion buckets\n",
        "\n",
        "Could also have a second hash function *inside* of the bucket (e.g., if we know we'll have a few very large buckets).\n",
        "\n",
        "There is no \"perfect hash\". It depends on the values you're working with. There are many options to consider with various trade-offs."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "98fmN7hBbRBk"
      },
      "source": [
        "**Load Factor**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GOG4oYkAbRBk"
      },
      "source": [
        "Metric that guides hashing decisions:\n",
        "$$ \\text{load factor} = \\frac{n_\\text{values}}{n_\\text{buckets}} $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HfnftH3VbRBk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cb3c14b0-5e84-44d4-ecbf-e5becf9ef194"
      },
      "source": [
        "10/1e9"
      ],
      "execution_count": 107,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1e-08"
            ]
          },
          "metadata": {},
          "execution_count": 107
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PXphCIwvbRBl"
      },
      "source": [
        "If we have ten values to store, but a billion buckets...\n",
        "$$ \\text{load factor} = \\frac{10}{10^9} = 10^{-8}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YtgP2bP2bRBl"
      },
      "source": [
        "...we are probably using much more memory than we need to. This is the case whenever load factor $\\approx 0$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xD6_09uwbRBm"
      },
      "source": [
        "As a general rule of thumb, the \"Goldilocks\" sweet spot would be to maintain a load factor between 0.6 and 0.75, providing a balance between memory and time complexity.\n",
        "\n",
        "Below 0.6, you're potentially wasting memory with too many empty buckets.\n",
        "\n",
        "Above 0.75, you risk having too many collisions, which degrades performance."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f6CRWlNrbRBm"
      },
      "source": [
        "#### Hash Maps"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rfdnZtvZbRBm"
      },
      "source": [
        "In all of the above examples, we were hashing \"values\", but these \"values\" could in fact be the *keys* of a key-value pair, allowing us to have a **hash map**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DrsTrapabRBm"
      },
      "source": [
        "Let's say `Jane Dough` has receipt number `5551234567`, where we're using the receipt numbers as keys to look up customers.\n",
        "\n",
        "We can add this as an entry in a hash table for quick lookup later (once we have many more receipts...):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hJWypGfybRBm"
      },
      "source": [
        "hash_map = {}"
      ],
      "execution_count": 108,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-WE0_Lu3bRBn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cbeb3ef8-e836-4799-98d8-99f82f5948bd"
      },
      "source": [
        "hash_map[simple_hash(5551234567)] = [(5551234567, 'Jane Dough')]\n",
        "hash_map"
      ],
      "execution_count": 109,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{7: [(5551234567, 'Jane Dough')]}"
            ]
          },
          "metadata": {},
          "execution_count": 109
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J6uw0CTbbRBo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8b22aafc-cb14-4c94-99a0-6d3b678058c0"
      },
      "source": [
        "hash_map[simple_hash(5551234568)] = [(5551234568, 'Johnny Dochevski')]\n",
        "hash_map"
      ],
      "execution_count": 110,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{7: [(5551234567, 'Jane Dough')], 8: [(5551234568, 'Johnny Dochevski')]}"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "hash_map[simple_hash(5551234578)].append((5551234578, 'Jon Krohn'))\n",
        "hash_map"
      ],
      "metadata": {
        "id": "Sic22vTZVle2",
        "outputId": "7eb5d999-bf37-420d-916f-15aa2b728920",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{7: [(5551234567, 'Jane Dough')],\n",
              " 8: [(5551234568, 'Johnny Dochevski'), (5551234578, 'Jon Krohn')]}"
            ]
          },
          "metadata": {},
          "execution_count": 111
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D2EcE46ubRBq"
      },
      "source": [
        "**FYI**: In Python, dictionaries are hash maps."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "31sAGRifbRBq"
      },
      "source": [
        "#### String Keys"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h7jhtFxvbRBr"
      },
      "source": [
        "If our keys are character strings, we can still make use of hashing by converting the character string into an integer.\n",
        "\n",
        "For example, we could use the [ASCII table](http://www.asciitable.com) to convert `Jon` to `112157156`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L4WA71uvKYm8"
      },
      "source": [
        "**Exercises**\n",
        "\n",
        "1. Use the `simple_hash()` function to add a customer named Jean d'Eau, who has receipt number `5551234569`, to `hash_map`.\n",
        "\n",
        "1. You have a hash table with a million buckets and two million values to store in the table. What is your load factor? Are collisions likely? If so, how can the probability of collisions be reduced?\n",
        "\n",
        "1. Use the octal standard of the ASCII table to convert the string `Llama` into an integer representation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zZMONjCZbRBr"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CP9-bZ3XbRBr"
      },
      "source": [
        "## Segment 3: Trees and Graphs"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4I1ClWo7bRBr"
      },
      "source": [
        "### Decision Trees"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_AQ6Eo8qbRBr"
      },
      "source": [
        "titanic = sns.load_dataset('titanic')"
      ],
      "execution_count": 112,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4r5mwCPWbRBs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 443
        },
        "outputId": "505eb766-2029-4cc9-ba0a-183d30b52da5"
      },
      "source": [
        "titanic"
      ],
      "execution_count": 113,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     survived  pclass     sex   age  sibsp  parch     fare embarked   class  \\\n",
              "0           0       3    male  22.0      1      0   7.2500        S   Third   \n",
              "1           1       1  female  38.0      1      0  71.2833        C   First   \n",
              "2           1       3  female  26.0      0      0   7.9250        S   Third   \n",
              "3           1       1  female  35.0      1      0  53.1000        S   First   \n",
              "4           0       3    male  35.0      0      0   8.0500        S   Third   \n",
              "..        ...     ...     ...   ...    ...    ...      ...      ...     ...   \n",
              "886         0       2    male  27.0      0      0  13.0000        S  Second   \n",
              "887         1       1  female  19.0      0      0  30.0000        S   First   \n",
              "888         0       3  female   NaN      1      2  23.4500        S   Third   \n",
              "889         1       1    male  26.0      0      0  30.0000        C   First   \n",
              "890         0       3    male  32.0      0      0   7.7500        Q   Third   \n",
              "\n",
              "       who  adult_male deck  embark_town alive  alone  \n",
              "0      man        True  NaN  Southampton    no  False  \n",
              "1    woman       False    C    Cherbourg   yes  False  \n",
              "2    woman       False  NaN  Southampton   yes   True  \n",
              "3    woman       False    C  Southampton   yes  False  \n",
              "4      man        True  NaN  Southampton    no   True  \n",
              "..     ...         ...  ...          ...   ...    ...  \n",
              "886    man        True  NaN  Southampton    no   True  \n",
              "887  woman       False    B  Southampton   yes   True  \n",
              "888  woman       False  NaN  Southampton    no  False  \n",
              "889    man        True    C    Cherbourg   yes   True  \n",
              "890    man        True  NaN   Queenstown    no   True  \n",
              "\n",
              "[891 rows x 15 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-2c34dad6-14e6-4d29-a530-32eceba79359\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>survived</th>\n",
              "      <th>pclass</th>\n",
              "      <th>sex</th>\n",
              "      <th>age</th>\n",
              "      <th>sibsp</th>\n",
              "      <th>parch</th>\n",
              "      <th>fare</th>\n",
              "      <th>embarked</th>\n",
              "      <th>class</th>\n",
              "      <th>who</th>\n",
              "      <th>adult_male</th>\n",
              "      <th>deck</th>\n",
              "      <th>embark_town</th>\n",
              "      <th>alive</th>\n",
              "      <th>alone</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>male</td>\n",
              "      <td>22.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>7.2500</td>\n",
              "      <td>S</td>\n",
              "      <td>Third</td>\n",
              "      <td>man</td>\n",
              "      <td>True</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Southampton</td>\n",
              "      <td>no</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>female</td>\n",
              "      <td>38.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>71.2833</td>\n",
              "      <td>C</td>\n",
              "      <td>First</td>\n",
              "      <td>woman</td>\n",
              "      <td>False</td>\n",
              "      <td>C</td>\n",
              "      <td>Cherbourg</td>\n",
              "      <td>yes</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>female</td>\n",
              "      <td>26.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>7.9250</td>\n",
              "      <td>S</td>\n",
              "      <td>Third</td>\n",
              "      <td>woman</td>\n",
              "      <td>False</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Southampton</td>\n",
              "      <td>yes</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>female</td>\n",
              "      <td>35.0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>53.1000</td>\n",
              "      <td>S</td>\n",
              "      <td>First</td>\n",
              "      <td>woman</td>\n",
              "      <td>False</td>\n",
              "      <td>C</td>\n",
              "      <td>Southampton</td>\n",
              "      <td>yes</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>male</td>\n",
              "      <td>35.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8.0500</td>\n",
              "      <td>S</td>\n",
              "      <td>Third</td>\n",
              "      <td>man</td>\n",
              "      <td>True</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Southampton</td>\n",
              "      <td>no</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>886</th>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>male</td>\n",
              "      <td>27.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>13.0000</td>\n",
              "      <td>S</td>\n",
              "      <td>Second</td>\n",
              "      <td>man</td>\n",
              "      <td>True</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Southampton</td>\n",
              "      <td>no</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>887</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>female</td>\n",
              "      <td>19.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>S</td>\n",
              "      <td>First</td>\n",
              "      <td>woman</td>\n",
              "      <td>False</td>\n",
              "      <td>B</td>\n",
              "      <td>Southampton</td>\n",
              "      <td>yes</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>888</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>female</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>23.4500</td>\n",
              "      <td>S</td>\n",
              "      <td>Third</td>\n",
              "      <td>woman</td>\n",
              "      <td>False</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Southampton</td>\n",
              "      <td>no</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>889</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>male</td>\n",
              "      <td>26.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>30.0000</td>\n",
              "      <td>C</td>\n",
              "      <td>First</td>\n",
              "      <td>man</td>\n",
              "      <td>True</td>\n",
              "      <td>C</td>\n",
              "      <td>Cherbourg</td>\n",
              "      <td>yes</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>890</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>male</td>\n",
              "      <td>32.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>7.7500</td>\n",
              "      <td>Q</td>\n",
              "      <td>Third</td>\n",
              "      <td>man</td>\n",
              "      <td>True</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Queenstown</td>\n",
              "      <td>no</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>891 rows × 15 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
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              "                                                    [key], {});\n",
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              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
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              "\n",
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              "      const quickchartButtonEl =\n",
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              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
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              "        const charts = await google.colab.kernel.invokeFunction(\n",
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              "type": "dataframe",
              "variable_name": "titanic",
              "summary": "{\n  \"name\": \"titanic\",\n  \"rows\": 891,\n  \"fields\": [\n    {\n      \"column\": \"survived\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 0,\n        \"max\": 1,\n        \"num_unique_values\": 2,\n        \"samples\": [\n          1,\n          0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"pclass\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 1,\n        \"max\": 3,\n        \"num_unique_values\": 3,\n        \"samples\": [\n          3,\n          1\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sex\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"female\",\n          \"male\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"age\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 14.526497332334044,\n        \"min\": 0.42,\n        \"max\": 80.0,\n        \"num_unique_values\": 88,\n        \"samples\": [\n          0.75,\n          22.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sibsp\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 0,\n        \"max\": 8,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          1,\n          0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"parch\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 0,\n        \"max\": 6,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          0,\n          1\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"fare\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49.693428597180905,\n        \"min\": 0.0,\n        \"max\": 512.3292,\n        \"num_unique_values\": 248,\n        \"samples\": [\n          11.2417,\n          51.8625\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"embarked\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 3,\n        \"samples\": [\n          \"S\",\n          \"C\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"class\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 3,\n        \"samples\": [\n          \"Third\",\n          \"First\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"who\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 3,\n        \"samples\": [\n          \"man\",\n          \"woman\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"adult_male\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          false,\n          true\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"deck\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 7,\n        \"samples\": [\n          \"C\",\n          \"E\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"embark_town\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 3,\n        \"samples\": [\n          \"Southampton\",\n          \"Cherbourg\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"alive\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"yes\",\n          \"no\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"alone\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 113
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ybcAVekXbRBt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9d1421a2-65ea-4ab6-b34b-bdea42935508"
      },
      "source": [
        "np.unique(titanic['survived'], return_counts=True)"
      ],
      "execution_count": 114,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0, 1]), array([549, 342]))"
            ]
          },
          "metadata": {},
          "execution_count": 114
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iRMcgJsMbRBu",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fc7e8f0e-c594-4695-e12e-f80267751352"
      },
      "source": [
        "np.unique(titanic['sex'], return_counts=True)"
      ],
      "execution_count": 115,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array(['female', 'male'], dtype=object), array([314, 577]))"
            ]
          },
          "metadata": {},
          "execution_count": 115
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ypbFKoWYbRBw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eb877976-37da-42e9-b419-25bda2d31b25"
      },
      "source": [
        "np.unique(titanic['class'], return_counts=True)"
      ],
      "execution_count": 116,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array(['First', 'Second', 'Third'], dtype=object), array([216, 184, 491]))"
            ]
          },
          "metadata": {},
          "execution_count": 116
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c7fhfdfjbRBx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "outputId": "947aecd5-7b36-4529-f27c-4bb9f708ac57"
      },
      "source": [
        "gender = pd.get_dummies(titanic['sex'])\n",
        "gender"
      ],
      "execution_count": 117,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     female   male\n",
              "0     False   True\n",
              "1      True  False\n",
              "2      True  False\n",
              "3      True  False\n",
              "4     False   True\n",
              "..      ...    ...\n",
              "886   False   True\n",
              "887    True  False\n",
              "888    True  False\n",
              "889   False   True\n",
              "890   False   True\n",
              "\n",
              "[891 rows x 2 columns]"
            ],
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
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              "        google.colab.notebook.generateWithVariable('gender');\n",
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              "\n",
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            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "gender",
              "summary": "{\n  \"name\": \"gender\",\n  \"rows\": 891,\n  \"fields\": [\n    {\n      \"column\": \"female\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"male\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          false,\n          true\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
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          },
          "metadata": {},
          "execution_count": 117
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          "height": 423
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        "outputId": "9a0190d3-7540-40f0-8c97-dc1c0d458ae2"
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      "source": [
        "clas = pd.get_dummies(titanic['class'])\n",
        "clas"
      ],
      "execution_count": 118,
      "outputs": [
        {
          "output_type": "execute_result",
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              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
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              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
              "      [theme=dark] .colab-df-generate {\n",
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              "\n",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('clas');\n",
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              "\n",
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            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "clas",
              "summary": "{\n  \"name\": \"clas\",\n  \"rows\": 891,\n  \"fields\": [\n    {\n      \"column\": \"First\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Second\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Third\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          false,\n          true\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 118
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iyu7ditFbRBz"
      },
      "source": [
        "y = titanic.survived"
      ],
      "execution_count": 119,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RxhDwnjFbRB2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "outputId": "d8bb192b-3126-47f5-c020-6565468b8773"
      },
      "source": [
        "X = pd.concat([clas.First, clas.Second, gender.female], axis=1)\n",
        "X"
      ],
      "execution_count": 120,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     First  Second  female\n",
              "0    False   False   False\n",
              "1     True   False    True\n",
              "2    False   False    True\n",
              "3     True   False    True\n",
              "4    False   False   False\n",
              "..     ...     ...     ...\n",
              "886  False    True   False\n",
              "887   True   False    True\n",
              "888  False   False    True\n",
              "889   True   False   False\n",
              "890  False   False   False\n",
              "\n",
              "[891 rows x 3 columns]"
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              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>886</th>\n",
              "      <td>False</td>\n",
              "      <td>True</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>887</th>\n",
              "      <td>True</td>\n",
              "      <td>False</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>888</th>\n",
              "      <td>False</td>\n",
              "      <td>False</td>\n",
              "      <td>True</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>889</th>\n",
              "      <td>True</td>\n",
              "      <td>False</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>890</th>\n",
              "      <td>False</td>\n",
              "      <td>False</td>\n",
              "      <td>False</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>891 rows × 3 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-cdd71e13-d7c3-4055-88a5-7c7cd06f45af')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
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              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-cdd71e13-d7c3-4055-88a5-7c7cd06f45af button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-cdd71e13-d7c3-4055-88a5-7c7cd06f45af');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-37d75b55-7ae1-406a-869e-262bfc5de157\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-37d75b55-7ae1-406a-869e-262bfc5de157')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-37d75b55-7ae1-406a-869e-262bfc5de157 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "  <div id=\"id_4335ba0f-aa59-441e-95e4-02fc412ecd25\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('X')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_4335ba0f-aa59-441e-95e4-02fc412ecd25 button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('X');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "X",
              "summary": "{\n  \"name\": \"X\",\n  \"rows\": 891,\n  \"fields\": [\n    {\n      \"column\": \"First\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Second\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"female\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 120
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zsJ5YtrdbRB3"
      },
      "source": [
        "from sklearn.model_selection import train_test_split"
      ],
      "execution_count": 121,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WuqGw1-ZbRB5"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)"
      ],
      "execution_count": 122,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U-NyY2qTbRB6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d936282b-1bc7-4118-e929-98161dd7e40f"
      },
      "source": [
        "X_train.shape"
      ],
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(596, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9YOgdtp3bRB7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "326ba558-4098-4014-8a80-4d6033902e9b"
      },
      "source": [
        "y_train.shape"
      ],
      "execution_count": 124,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(596,)"
            ]
          },
          "metadata": {},
          "execution_count": 124
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jjc8dNehbRB9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6877e50b-f7e2-4b00-a5bf-8d663ec7065e"
      },
      "source": [
        "X_test.shape"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(295, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AQn0vfiLbRCA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6300e5e4-72fb-4dad-ef8e-69c968751b0b"
      },
      "source": [
        "y_test.shape"
      ],
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(295,)"
            ]
          },
          "metadata": {},
          "execution_count": 126
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_qqzwlHWbRCB"
      },
      "source": [
        "from sklearn.tree import DecisionTreeClassifier, plot_tree"
      ],
      "execution_count": 127,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6rQcNwcgbRCC"
      },
      "source": [
        "dt_model = DecisionTreeClassifier()"
      ],
      "execution_count": 128,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5qy2a1RKbRCE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "outputId": "f11fc376-6b6e-478a-8317-c393b0b84c32"
      },
      "source": [
        "dt_model.fit(X_train, y_train)"
      ],
      "execution_count": 129,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeClassifier()"
            ],
            "text/html": [
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              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
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              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
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              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
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              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
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              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
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              "  border: 1px dashed var(--sklearn-color-line);\n",
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              "  box-sizing: border-box;\n",
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              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-1 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-1 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-1 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-1 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeClassifier()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;DecisionTreeClassifier<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.tree.DecisionTreeClassifier.html\">?<span>Documentation for DecisionTreeClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>DecisionTreeClassifier()</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 129
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rwU0_o7tbRCG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 632
        },
        "outputId": "f251dd56-aa54-4f9e-9bc0-f9fe6f7caae0"
      },
      "source": [
        "plot_tree(dt_model) # can read about Gini here: en.wikipedia.org/wiki/Decision_tree_learning#Gini_impurity"
      ],
      "execution_count": 130,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Text(0.5555555555555556, 0.875, 'x[2] <= 0.5\\ngini = 0.467\\nsamples = 596\\nvalue = [374, 222]'),\n",
              " Text(0.3333333333333333, 0.625, 'x[0] <= 0.5\\ngini = 0.304\\nsamples = 390\\nvalue = [317, 73]'),\n",
              " Text(0.4444444444444444, 0.75, 'True  '),\n",
              " Text(0.2222222222222222, 0.375, 'x[1] <= 0.5\\ngini = 0.263\\nsamples = 314\\nvalue = [265, 49]'),\n",
              " Text(0.1111111111111111, 0.125, 'gini = 0.252\\nsamples = 237\\nvalue = [202, 35]'),\n",
              " Text(0.3333333333333333, 0.125, 'gini = 0.298\\nsamples = 77\\nvalue = [63.0, 14.0]'),\n",
              " Text(0.4444444444444444, 0.375, 'gini = 0.432\\nsamples = 76\\nvalue = [52, 24]'),\n",
              " Text(0.7777777777777778, 0.625, 'x[0] <= 0.5\\ngini = 0.4\\nsamples = 206\\nvalue = [57, 149]'),\n",
              " Text(0.6666666666666667, 0.75, '  False'),\n",
              " Text(0.6666666666666666, 0.375, 'x[1] <= 0.5\\ngini = 0.465\\nsamples = 147\\nvalue = [54, 93]'),\n",
              " Text(0.5555555555555556, 0.125, 'gini = 0.498\\nsamples = 99\\nvalue = [53, 46]'),\n",
              " Text(0.7777777777777778, 0.125, 'gini = 0.041\\nsamples = 48\\nvalue = [1, 47]'),\n",
              " Text(0.8888888888888888, 0.375, 'gini = 0.097\\nsamples = 59\\nvalue = [3, 56]')]"
            ]
          },
          "metadata": {},
          "execution_count": 130
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h11i69csbRCH"
      },
      "source": [
        "rose = np.array([[1, 0, 1]]) # must be matrix format\n",
        "jack = np.array([[0, 0, 0]])"
      ],
      "execution_count": 131,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ij3pgICEbRCI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0b152020-eb1b-4c17-e73d-30dcc682c388"
      },
      "source": [
        "dt_model.predict(rose)"
      ],
      "execution_count": 132,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:493: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1])"
            ]
          },
          "metadata": {},
          "execution_count": 132
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XShTUGbPu1Pl",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3578b8f8-928c-4a99-d842-5e8a7df7f31a"
      },
      "source": [
        "dt_model.predict_proba(rose)"
      ],
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:493: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.05084746, 0.94915254]])"
            ]
          },
          "metadata": {},
          "execution_count": 133
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VO3j3_T8bRCJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a6bc3300-28da-4e88-95ee-c82ab1a74d3e"
      },
      "source": [
        "dt_model.predict(jack)"
      ],
      "execution_count": 134,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:493: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0])"
            ]
          },
          "metadata": {},
          "execution_count": 134
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mnjuDxEou-1e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ad31fd5f-486d-4dd5-b16f-4cbfa31598e1"
      },
      "source": [
        "dt_model.predict_proba(jack)"
      ],
      "execution_count": 135,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:493: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.85232068, 0.14767932]])"
            ]
          },
          "metadata": {},
          "execution_count": 135
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P3OSLifkbRCK"
      },
      "source": [
        "dt_yhat = dt_model.predict(X_test) # decision trees are prone to overfitting training data"
      ],
      "execution_count": 136,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GmSFtkv6tgr1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8680896f-1ae8-4afb-a580-947dc530d9a2"
      },
      "source": [
        "dt_yhat[0:6]"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 0, 1, 0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 137
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "45DfyRL9bRCM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "4d31a5af-d8d9-4341-8991-766848fd6bea"
      },
      "source": [
        "y_test[0:6]"
      ],
      "execution_count": 138,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "709    1\n",
              "439    0\n",
              "840    0\n",
              "720    1\n",
              "39     1\n",
              "290    1\n",
              "Name: survived, dtype: int64"
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>survived</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>709</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>439</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>840</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>720</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>290</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div><br><label><b>dtype:</b> int64</label>"
            ]
          },
          "metadata": {},
          "execution_count": 138
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rkjgiymJbRCN"
      },
      "source": [
        "from sklearn.metrics import accuracy_score, roc_auc_score"
      ],
      "execution_count": 139,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MsahEJR2bRCP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ff537e2d-3ff9-4410-893e-4c6ba9a8552c"
      },
      "source": [
        "accuracy_score(y_test, dt_yhat)"
      ],
      "execution_count": 140,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7728813559322034"
            ]
          },
          "metadata": {},
          "execution_count": 140
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "beXofak0bRCQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1020d996-fcb8-4433-f8d0-134abe2c5642"
      },
      "source": [
        "roc_auc_score(y_test, dt_yhat)"
      ],
      "execution_count": 141,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7273809523809524"
            ]
          },
          "metadata": {},
          "execution_count": 141
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DvjgUHJxbRCT"
      },
      "source": [
        "**Exercises**:\n",
        "\n",
        "1. Create more features ([here are some ideas for creating them](https://towardsdatascience.com/predicting-the-survival-of-titanic-passengers-30870ccc7e8)) with an eye to improving model fit on the test data.\n",
        "\n",
        "2. Re-train the decision tree on the training data and evaluate its accuracy and ROC AUC on the test data. How does the tree compare with an ordinary-least-squares regression model (from [*Intro to Stats*](https://github.com/jonkrohn/ML-foundations/blob/master/notebooks/6-statistics.ipynb)) trained on the same data?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7qiPS5IjbRCT"
      },
      "source": [
        "**Return to slides here.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EGl67nVMbRCT"
      },
      "source": [
        "### Random Forests"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y--kKV7DbRCT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "outputId": "9889e47b-4dd6-4ab0-84be-894cdde1c1d9"
      },
      "source": [
        "iris = sns.load_dataset('iris')\n",
        "iris"
      ],
      "execution_count": 142,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     sepal_length  sepal_width  petal_length  petal_width    species\n",
              "0             5.1          3.5           1.4          0.2     setosa\n",
              "1             4.9          3.0           1.4          0.2     setosa\n",
              "2             4.7          3.2           1.3          0.2     setosa\n",
              "3             4.6          3.1           1.5          0.2     setosa\n",
              "4             5.0          3.6           1.4          0.2     setosa\n",
              "..            ...          ...           ...          ...        ...\n",
              "145           6.7          3.0           5.2          2.3  virginica\n",
              "146           6.3          2.5           5.0          1.9  virginica\n",
              "147           6.5          3.0           5.2          2.0  virginica\n",
              "148           6.2          3.4           5.4          2.3  virginica\n",
              "149           5.9          3.0           5.1          1.8  virginica\n",
              "\n",
              "[150 rows x 5 columns]"
            ],
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              "<table border=\"1\" class=\"dataframe\">\n",
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sepal_length</th>\n",
              "      <th>sepal_width</th>\n",
              "      <th>petal_length</th>\n",
              "      <th>petal_width</th>\n",
              "      <th>species</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>6.7</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.2</td>\n",
              "      <td>2.3</td>\n",
              "      <td>virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>6.3</td>\n",
              "      <td>2.5</td>\n",
              "      <td>5.0</td>\n",
              "      <td>1.9</td>\n",
              "      <td>virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>6.5</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.2</td>\n",
              "      <td>2.0</td>\n",
              "      <td>virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>6.2</td>\n",
              "      <td>3.4</td>\n",
              "      <td>5.4</td>\n",
              "      <td>2.3</td>\n",
              "      <td>virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>149</th>\n",
              "      <td>5.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.1</td>\n",
              "      <td>1.8</td>\n",
              "      <td>virginica</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>150 rows × 5 columns</p>\n",
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              "    async function quickchart(key) {\n",
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              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
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              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
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              "\n",
              "  <div id=\"id_c4d636c7-1027-4e5a-ae2f-e80c018df1b4\">\n",
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              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
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              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
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              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
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              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "            title=\"Generate code using this dataframe.\"\n",
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              "\n",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('iris');\n",
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              "\n",
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              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "iris",
              "summary": "{\n  \"name\": \"iris\",\n  \"rows\": 150,\n  \"fields\": [\n    {\n      \"column\": \"sepal_length\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.8280661279778629,\n        \"min\": 4.3,\n        \"max\": 7.9,\n        \"num_unique_values\": 35,\n        \"samples\": [\n          6.2,\n          4.5,\n          5.6\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sepal_width\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.435866284936698,\n        \"min\": 2.0,\n        \"max\": 4.4,\n        \"num_unique_values\": 23,\n        \"samples\": [\n          2.3,\n          4.0,\n          3.5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal_length\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.7652982332594667,\n        \"min\": 1.0,\n        \"max\": 6.9,\n        \"num_unique_values\": 43,\n        \"samples\": [\n          6.7,\n          3.8,\n          3.7\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal_width\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.7622376689603465,\n        \"min\": 0.1,\n        \"max\": 2.5,\n        \"num_unique_values\": 22,\n        \"samples\": [\n          0.2,\n          1.2,\n          1.3\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"species\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 3,\n        \"samples\": [\n          \"setosa\",\n          \"versicolor\",\n          \"virginica\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 142
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mvehRZ4vbRCU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 450
        },
        "outputId": "cc67eb69-3bef-43c8-b8cf-e5a46abd6930"
      },
      "source": [
        "_ = sns.scatterplot(x='sepal_width', y='petal_length', hue='species', data=iris)"
      ],
      "execution_count": 143,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b2r2B8f6bRCV"
      },
      "source": [
        "X = iris[['sepal_width', 'petal_length']]"
      ],
      "execution_count": 144,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9YFi_xu7bRCW"
      },
      "source": [
        "y = iris.species"
      ],
      "execution_count": 145,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qaAe_OmMbRCX"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)"
      ],
      "execution_count": 146,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c6gOK1YAbRCY"
      },
      "source": [
        "iris_dt = DecisionTreeClassifier().fit(X_train, y_train)"
      ],
      "execution_count": 147,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8VN61N39bRCZ"
      },
      "source": [
        "iris_dt_yhat = iris_dt.predict(X_test)"
      ],
      "execution_count": 148,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MKdjKFzMbRCa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8cada902-7ba2-4326-edca-19602ba97d2a"
      },
      "source": [
        "accuracy_score(iris_dt_yhat, y_test) # ROC AUC is for binary classifier"
      ],
      "execution_count": 149,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9"
            ]
          },
          "metadata": {},
          "execution_count": 149
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LSbCHSDSbRCa"
      },
      "source": [
        "from sklearn.ensemble import RandomForestClassifier"
      ],
      "execution_count": 150,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XM4PnPhBbRCb"
      },
      "source": [
        "rf_model = RandomForestClassifier(n_estimators=100) # n decision trees in forest"
      ],
      "execution_count": 151,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZdH728GebRCc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "outputId": "98062ea9-41dd-47f9-fa2d-31d9f5258c37"
      },
      "source": [
        "rf_model.fit(X_train, y_train)"
      ],
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "RandomForestClassifier()"
            ],
            "text/html": [
              "<style>#sk-container-id-2 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-2 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-2 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-2 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-2 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-2 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-2 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-2 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-2 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestClassifier()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;RandomForestClassifier<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.ensemble.RandomForestClassifier.html\">?<span>Documentation for RandomForestClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>RandomForestClassifier()</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 152
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gj0UdpKsbRCd"
      },
      "source": [
        "rf_yhat = rf_model.predict(X_test)"
      ],
      "execution_count": 153,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hhjVA9z_bRCe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "33ea8956-4d86-410f-931c-83c0a7acf595"
      },
      "source": [
        "accuracy_score(rf_yhat, y_test)"
      ],
      "execution_count": 154,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.96"
            ]
          },
          "metadata": {},
          "execution_count": 154
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lzm9A7bwbRCf"
      },
      "source": [
        "**Return to slides.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jpu53mFkbRCg"
      },
      "source": [
        "### Gradient-Boosted Trees"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lgfz5kkabRCi"
      },
      "source": [
        "import xgboost as xgb"
      ],
      "execution_count": 155,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y_1twJezbRCj"
      },
      "source": [
        "XGBoost `DMatrix()` method requires numeric inputs, not strings:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9_r4ulQObRCj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "0288dd5e-891b-4527-e468-c7b40b7bf7bb"
      },
      "source": [
        "y_train[0:6]"
      ],
      "execution_count": 156,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "96     versicolor\n",
              "105     virginica\n",
              "66     versicolor\n",
              "0          setosa\n",
              "122     virginica\n",
              "67     versicolor\n",
              "Name: species, dtype: object"
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>species</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>versicolor</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>105</th>\n",
              "      <td>virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>66</th>\n",
              "      <td>versicolor</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>setosa</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>122</th>\n",
              "      <td>virginica</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>67</th>\n",
              "      <td>versicolor</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div><br><label><b>dtype:</b> object</label>"
            ]
          },
          "metadata": {},
          "execution_count": 156
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FDbSz7u0bRCk"
      },
      "source": [
        "mapping = {'setosa': 0, 'versicolor': 1, 'virginica': 2}\n",
        "y_train_int = y_train.map(mapping)\n",
        "y_test_int = y_test.map(mapping)"
      ],
      "execution_count": 157,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jKzJ2WBpbRCl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "6944e629-6916-4cc5-dc8d-370f6ca6053b"
      },
      "source": [
        "y_train_int[0:6]"
      ],
      "execution_count": 158,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "96     1\n",
              "105    2\n",
              "66     1\n",
              "0      0\n",
              "122    2\n",
              "67     1\n",
              "Name: species, dtype: int64"
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>species</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>105</th>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>66</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>122</th>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>67</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div><br><label><b>dtype:</b> int64</label>"
            ]
          },
          "metadata": {},
          "execution_count": 158
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ntrQLtLgbRCn"
      },
      "source": [
        "D_train = xgb.DMatrix(X_train, label=y_train_int)\n",
        "D_test = xgb.DMatrix(X_test, label=y_test_int)"
      ],
      "execution_count": 159,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pf1YBYMjbRCn"
      },
      "source": [
        "param = {\n",
        "    'eta': 0.1, # learning rate (0.1 to 0.3 are common)\n",
        "    'max_depth': 2, # I mean, we only have two features...\n",
        "    'objective': 'multi:softprob',\n",
        "    'num_class': 3\n",
        "}\n",
        "steps = 10"
      ],
      "execution_count": 160,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sr1liohYbRCo"
      },
      "source": [
        "xg_model = xgb.train(param, D_train, steps)"
      ],
      "execution_count": 161,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kSbjrMI2bRCp"
      },
      "source": [
        "xg_yhats = xg_model.predict(D_test)"
      ],
      "execution_count": 162,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nuiLEGs-bRCq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "77a1959d-06b5-41e0-8119-aebade0bfa7d"
      },
      "source": [
        "xg_yhats[0] # supports >2 classes"
      ],
      "execution_count": 163,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.14787205, 0.6481497 , 0.20397826], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 163
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gLdW2QDebRCs"
      },
      "source": [
        "xg_yhat = np.asarray([np.argmax(line) for line in xg_yhats])"
      ],
      "execution_count": 164,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n8KSTQSAbRCt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dde5c953-a0ba-4647-ac8c-d72dea669664"
      },
      "source": [
        "xg_yhat[0]"
      ],
      "execution_count": 165,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 165
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bapU-nE4bRCv",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "35ebdbca-55fe-4c27-e5f0-7b09ceecccb8"
      },
      "source": [
        "accuracy_score(xg_yhat, y_test_int)"
      ],
      "execution_count": 166,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.98"
            ]
          },
          "metadata": {},
          "execution_count": 166
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fzs6y3UcLlYI"
      },
      "source": [
        "**Exercise**:\n",
        "\n",
        "1. Try training random forest and XGBoost models with additional iris features. Can you attain 100% accuracy on the test data set?\n",
        "2. Explore [CatBoost](https://catboost.ai/en/docs/concepts/python-quickstart) for situations where you have categorical *features* in the model (CatBoost works for both classification and regression problems)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hcMPnX4z7_R7"
      },
      "source": [
        "**Return to slides.**"
      ]
    }
  ]
}