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Max Points Problem Solution

This document provides step-by-step explanations for solving the "Max Points" problem in C++, Java, JavaScript, Python, and Go. The goal is to maximize the points collected while traversing a matrix with specific constraints.

C++ Solution

  1. Initialize Dimensions: Determine the number of rows (m) and columns (n) from the input matrix points.

  2. Setup DP Array: Create a dp array to store the maximum points collectible for each column in the current row. Initialize it with the values from the first row of the matrix.

  3. Process Rows:

    • Left and Right Max Arrays: Use two additional arrays (leftMax and rightMax) to keep track of the maximum points collectible when moving from left to right and right to left, respectively.
    • Update DP Values: For each row, calculate new values for the dp array using leftMax and rightMax adjusted by column indices, and add the points from the current cell.

  4. Compute Result: After processing all rows, the maximum value in the dp array represents the maximum points that can be collected.

Java Solution

  1. Determine Dimensions: Get the number of rows (m) and columns (n) from the points array.

  2. Initialize DP Array: Create and populate a dp array with the values from the first row.

  3. Iterate Through Rows:

    • Calculate Left Max Values: Fill the leftMax array with maximum points collectible from left to right.
    • Calculate Right Max Values: Fill the rightMax array with maximum points collectible from right to left.
    • Update DP Values: Calculate new dp values for the current row using leftMax and rightMax and update the dp array.

  4. Find Maximum Points: Determine the maximum value in the dp array after processing all rows.

JavaScript Solution

  1. Determine Matrix Size: Extract the number of rows (m) and columns (n) from the points matrix.

  2. Initialize DP Array: Set up the dp array with the values from the first row of the matrix.

  3. Process Each Row:

    • Compute Left Max Array: Calculate maximum points when moving from left to right and store in leftMax.
    • Compute Right Max Array: Calculate maximum points when moving from right to left and store in rightMax.
    • Update New DP Values: For each cell in the row, compute the new dp value using leftMax and rightMax and update the dp array.

  4. Return Maximum Points: The highest value in the dp array after processing all rows is the result.

Python Solution

  1. Extract Matrix Size: Determine the number of rows (m) and columns (n) from the points matrix.

  2. Initialize DP Array: Set up the dp array with the values from the first row.

  3. Process Rows:

    • Calculate Left Max Array: Fill the leftMax array with maximum values when traversing from left to right.
    • Calculate Right Max Array: Fill the rightMax array with maximum values when traversing from right to left.
    • Update DP Values: Compute new dp values for the current row using leftMax and rightMax, and update the dp array.

  4. Return Maximum Points: Find and return the maximum value in the dp array after processing all rows.

Go Solution

  1. Determine Matrix Dimensions: Identify the number of rows (m) and columns (n) from the points matrix.

  2. Setup DP Array: Initialize a dp array with values from the first row.

  3. Iterate Through Rows:

    • Compute Left Max: Calculate maximum values from left to right and store in leftMax.
    • Compute Right Max: Calculate maximum values from right to left and store in rightMax.
    • Update DP Values: Compute new values for the dp array using leftMax and rightMax.

  4. Compute Final Result: Find the maximum value in the dp array after processing all rows and return it.