1292

1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold (Medium)

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 1:

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.

Example 2:

Input: mat = [[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2]], threshold = 1
Output: 0

Example 3:

Input: mat = [[1,1,1,1],[1,0,0,0],[1,0,0,0],[1,0,0,0]], threshold = 6
Output: 3

Example 4:

Input: mat = [[18,70],[61,1],[25,85],[14,40],[11,96],[97,96],[63,45]], threshold = 40184
Output: 2

 

Constraints:

• 1 <= m, n <= 300
• m == mat.length
• n == mat[i].length
• 0 <= mat[i][j] <= 10000
• 0 <= threshold <= 10^5

Related Topics:
Array, Binary Search

Solution 1. Prefix Sum

// OJ: https://leetcode.com/problems/maximum-side-length-of-a-square-with-sum-less-than-or-equal-to-threshold/
// Author: github.com/lzl124631x
// Time: O(MN)
// Space: O(MN)
class Solution {
public:
    int maxSideLength(vector<vector<int>>& A, int threshold) {
        int M = A.size(), N = A[0].size(), ans = 0;
        vector<vector<int>> sum(M + 1, vector<int>(N + 1));
        for (int i = 0; i < M; ++i) {
            int s = 0;
            for (int j = 0; j < N; ++j) sum[i + 1][j + 1] = sum[i][j + 1] + (s += A[i][j]);
        }
        for (int i = 0; ans <= min(M, N) && i <= M - ans; ++i) {
            for (int j = 0; ans <= min(M, N) && j <= N - ans; ++j) {
                for (; ans <= min(M - i, N - j) && sum[i + ans][j + ans] - sum[i + ans][j] - sum[i][j + ans] + sum[i][j] <= threshold; ++ans);
            }
        }
        return ans - 1;
    }
};

Solution 2. Binary Answer

// OJ: https://leetcode.com/problems/maximum-side-length-of-a-square-with-sum-less-than-or-equal-to-threshold/
// Author: github.com/lzl124631x
// Time: O(MN * log(min(M, N)))
// Space: O(MN)
class Solution {
    bool valid(vector<vector<int>> &sum, int len, int threshold) {
        for (int i = 0; i < sum.size() - len; ++i) {
            for (int j = 0; j < sum[0].size() - len; ++j) {
                if (sum[i + len][j + len] - sum[i + len][j] - sum[i][j + len] + sum[i][j] <= threshold) return true;
            }
        }
        return false;
    }
public:
    int maxSideLength(vector<vector<int>>& A, int threshold) {
        int M = A.size(), N = A[0].size(), L = 0, R = min(M, N);
        vector<vector<int>> sum(M + 1, vector<int>(N + 1));
        for (int i = 0; i < M; ++i) {
            int s = 0;
            for (int j = 0; j < N; ++j) sum[i + 1][j + 1] = sum[i][j + 1] + (s += A[i][j]);
        }
        while (L <= R) {
            int M = (L + R) / 2;
            if (valid(sum, M, threshold)) L = M + 1;
            else R = M - 1;
        }
        return R;
    }
};