Leetcode | 1105. Filling Bookcase Shelves | question with solution

Описание: 📝Code Description:
This Java code solves the “Minimum Height Shelves” problem using Dynamic Programming. Each book has a width and height, and the goal is to arrange the books in order onto shelves such that the total height of all shelves is minimized, while ensuring the total width of books on each shelf does not exceed shelfWidth.
The algorithm uses a 1D DP array where dp[i] represents the minimum height needed to place the first i books. For each book, it tries to group it with previous books on the same shelf as long as the width constraint is satisfied, keeping track of the tallest book on that shelf. It calculates the optimal combination to update the minimum total height.
This approach ensures an optimal solution with O(n²) complexity by exploring all valid ways of placing books on shelves.


🏷Tags:
Dynamic Programming
Optimization
1D DP
Greedy and DP
Array Processing
Bookshelf Arrangement Problem
Algorithmic Problem Solving


🔑 Keywords:
Minimum Height Shelves
DP recurrence
Book arrangement
Shelf width constraint
Height minimization
dp[i] computation
Nested dynamic programming
Bookshelf optimization


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