221. Maximal Square

Given a 2D binary matrix filled with 0's and 1's, find the largest square containing only 1's and return its area.

Example:

Input: 

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

Output: 4

Approach #1: DP. [C++]

class Solution {
public:
    int maximalSquare(vector<vector<char>>& matrix) {
        if (matrix.empty()) return 0;
        int m = matrix.size();
        int n = matrix[0].size();
        vector<vector<int>> dp(m+1, vector<int>(n+1, 0));
        
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                dp[i][j] = matrix[i-1][j-1] - '0'
                         + dp[i-1][j]
                         + dp[i][j-1]
                         - dp[i-1][j-1];
            }
        }
        
        int ans = 0;
        
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                for (int k = min(m-i+1, n-j+1); k > 0; --k) {
                    int sum = dp[i+k-1][j+k-1] 
                            - dp[i+k-1][j-1]
                            - dp[i-1][j+k-1]
                            + dp[i-1][j-1];
                    if (sum == k * k) {
                        ans = max(ans, sum);
                        break;
                    }
                }
            }
        }
        
        return ans;
    }
};

　　

Analysis:

http://zxi.mytechroad.com/blog/dynamic-programming/leetcode-221-maximal-square/