MediumNo. 1292
Maximum Side Length of a Square with Sum Less than or Equal to Threshold — LeetCode 1292 Python Solution
- Pattern
- Prefix Sum
- Topics
- Array, Binary Search, Matrix, Prefix Sum
- Reading time
- 4 min
- Source
- leetcode.com
The problem
Given a m x n matrix mat and an integer threshold, return the maximum side-length of a square with a sum less than or equal to threshold or return 0 if there is no such square.
Example
- Input
- mat = [[1,1,3,2,4,3,2],[1,1,3,2,4,3,2],[1,1,3,2,4,3,2]], threshold = 4
- Output
- 2
- Explanation
- The maximum side length of square with sum less than 4 is 2 as shown.
Python solution
class Solution:
def maxSideLength(self, mat: List[List[int]], threshold: int) -> int:
def check(k: int) -> bool:
for i in range(m - k + 1):
for j in range(n - k + 1):
v = s[i + k][j + k] - s[i][j + k] - s[i + k][j] + s[i][j]
if v <= threshold:
return True
return False
m, n = len(mat), len(mat[0])
s = [[0] * (n + 1) for _ in range(m + 1)]
for i, row in enumerate(mat, 1):
for j, x in enumerate(row, 1):
s[i][j] = s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1] + x
l, r = 0, min(m, n)
while l < r:
mid = (l + r + 1) >> 1
if check(mid):
l = mid
else:
r = mid - 1
return lComplexity
- Time
- O(m × n × log min(m, n))
- Space · auxiliary
- O(m × n)
Pattern: Prefix Sum
Precompute running totals once so any range query becomes a single subtraction. LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold is filed here because LeetCode tags it Prefix Sum, which is the vocabulary this hub collects.
The prefix sum guide has the Python template for the pattern and the 157 LeetCode problems that use it.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0363 | Max Sum of Rectangle No Larger Than K | Hard |
| 0074 | Search a 2D Matrix | Medium |
| 0240 | Search a 2D Matrix II | Medium |
| 0378 | Kth Smallest Element in a Sorted Matrix | Medium |
| 0410 | Split Array Largest Sum | Hard |
| 0497 | Random Point in Non-overlapping Rectangles | Medium |
Frequently asked questions
- How hard is LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold?
LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold is rated Medium on LeetCode.
- What is the time complexity of LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold?
The Python solution on this page runs in O(m × n × log min(m, n)).
- What is the space complexity of LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold?
The Python solution on this page uses O(m × n) auxiliary space.
- What topics does LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold cover?
LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold is tagged Array, Binary Search, Matrix and Prefix Sum on LeetCode.