MediumNo. 1105
Filling Bookcase Shelves — LeetCode 1105 Python Solution
- Pattern
- Dynamic Programming
- Topics
- Array, Dynamic Programming
- Reading time
- 2 min
- Source
- leetcode.com
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
- Time
- O(n2)
- Space · auxiliary
- O(n)
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.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0045 | Jump Game II | Medium |
| 0053 | Maximum Subarray | Medium |
| 0055 | Jump Game | Medium |
| 0063 | Unique Paths II | Medium |
| 0064 | Minimum Path Sum | Medium |
| 0085 | Maximal Rectangle | Hard |
Frequently asked questions
- How hard is LeetCode 1105. Filling Bookcase Shelves?
LeetCode 1105. Filling Bookcase Shelves is rated Medium on LeetCode.
- What is the time complexity of LeetCode 1105. Filling Bookcase Shelves?
The Python solution on this page runs in O(n2).
- What is the space complexity of LeetCode 1105. Filling Bookcase Shelves?
The Python solution on this page uses O(n) auxiliary space.
- What topics does LeetCode 1105. Filling Bookcase Shelves cover?
LeetCode 1105. Filling Bookcase Shelves is tagged Array and Dynamic Programming on LeetCode.