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Minimum Height Shelves Solution

Introduction

This README explains the implementation of a solution to find the minimum height required to place all books on a bookshelf with a fixed width. The solution uses dynamic programming to optimize the placement of books on shelves. Below are detailed step-by-step explanations for implementations in C++, Java, JavaScript, Python, and Go.

C++ Implementation

  1. Initialization: Define a class Solution with a public method minHeightShelves.
  2. Dynamic Programming Array: Create a vector dp to store the minimum height required to place the first i books. Initialize dp[0] to 0 (base case) and others to INT_MAX.
  3. Iterate Through Books: Use a nested loop to consider each book and try placing it on the current shelf.
    • Shelf Parameters: Track the current shelf's width and height.
    • Check Feasibility: For each possible starting book, add its width and check if it exceeds the shelf width. If it does, break the loop.
    • Update Shelf Height: Determine the maximum height for the current shelf.
    • Update DP Array: Update dp[i] with the minimum value of its current value and the new calculated height.
  4. Result: The last value in dp will give the minimum height required for all books.

Java Implementation

  1. Initialization: Define a class Solution with a public method minHeightShelves.
  2. Dynamic Programming Array: Create an integer array dp to store the minimum height for the first i books. Initialize dp[0] to 0 and others to Integer.MAX_VALUE.
  3. Iterate Through Books: Use a nested loop to consider each book and try placing it on the current shelf.
    • Shelf Parameters: Track the current shelf's width and height.
    • Check Feasibility: For each book, add its width and check if it exceeds the shelf width. If so, break the loop.
    • Update Shelf Height: Determine the maximum height for the current shelf.
    • Update DP Array: Update dp[i] with the minimum value of its current value and the new calculated height.
  4. Result: The last value in dp will give the minimum height required for all books.

JavaScript Implementation

  1. Function Definition: Define a function minHeightShelves that accepts books and shelfWidth as parameters.
  2. Dynamic Programming Array: Initialize an array dp with Infinity, setting dp[0] to 0.
  3. Iterate Through Books: Use a nested loop to iterate over each book and try placing it on the current shelf.
    • Shelf Parameters: Track the current shelf's width and height.
    • Check Feasibility: For each book, add its width and check if it exceeds the shelf width. If it does, break the loop.
    • Update Shelf Height: Determine the maximum height for the current shelf.
    • Update DP Array: Update dp[i] with the minimum value of its current value and the new calculated height.
  4. Result: The last value in dp will give the minimum height required for all books.

Python Implementation

  1. Class Definition: Define a class Solution with a method minHeightShelves.
  2. Dynamic Programming Array: Create a list dp initialized with float('inf'), setting dp[0] to 0.
  3. Iterate Through Books: Use a nested loop to iterate over each book and try placing it on the current shelf.
    • Shelf Parameters: Track the current shelf's width and height.
    • Check Feasibility: For each book, add its width and check if it exceeds the shelf width. If it does, break the loop.
    • Update Shelf Height: Determine the maximum height for the current shelf.
    • Update DP Array: Update dp[i] with the minimum value of its current value and the new calculated height.
  4. Result: The last value in dp will give the minimum height required for all books.

Go Implementation

  1. Function Definition: Define a function minHeightShelves that accepts books and shelfWidth.
  2. Dynamic Programming Array: Initialize an array dp with 1<<31 - 1 (representing infinity), setting dp[0] to 0.
  3. Iterate Through Books: Use a nested loop to iterate over each book and try placing it on the current shelf.
    • Shelf Parameters: Track the current shelf's width and height.
    • Check Feasibility: For each book, add its width and check if it exceeds the shelf width. If it does, break the loop.
    • Update Shelf Height: Determine the maximum height for the current shelf.
    • Update DP Array: Update dp[i] with the minimum value of its current value and the new calculated height.
  4. Result: The last value in dp will give the minimum height required for all books.

These implementations provide an efficient way to calculate the minimum height required to store books on a bookshelf with a fixed width. The use of dynamic programming helps optimize the solution by storing intermediate results, reducing the need for redundant calculations.