Maximum Side Length of a Square with Sum Less than or Equal to Threshold — LeetCode 1292 Python Solution

MediumArrayBinary SearchMatrixPrefix Sum

Problem: #1292
Pattern: 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

Python

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 l

Complexity

Measure	Complexity
Time	O(m \times n \times \log \min(m, n))
Space	O(m \times n) auxiliary

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.

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 \times n \times \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 \times 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.