Filling Bookcase Shelves — LeetCode 1105 Python Solution

The problem

You are given an array books where books[i] = [thicknessi, heighti] indicates the thickness and height of the ith book. You are also given an integer shelfWidth.

Example

Input

books = [[1,1],[2,3],[2,3],[1,1],[1,1],[1,1],[1,2]], shelfWidth = 4

Output

6

Explanation

The sum of the heights of the 3 shelves is 1 + 3 + 2 = 6.

Python solution

class Solution:
    def minHeightShelves(self, books: List[List[int]], shelfWidth: int) -> int:
        n = len(books)
        f = [0] * (n + 1)
        for i, (w, h) in enumerate(books, 1):
            f[i] = f[i - 1] + h
            for j in range(i - 1, 0, -1):
                w += books[j - 1][0]
                if w > shelfWidth:
                    break
                h = max(h, books[j - 1][1])
                f[i] = min(f[i], f[j - 1] + h)
        return f[n]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1105. Filling Bookcase Shelves is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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