Maximal Square

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

Example

For example, given the following matrix:

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

Return 4.

Analyse: Let dp[i][j] represents the maximum side of a square whose right bottom element is matrix[i][j]. 

dp[i][j] = min(dp[i][j - 1], min(dp[i - 1][j], dp[i - 1][j - 1])) + 1

Runtime: 124ms

class Solution {
public:
    /**
     * @param matrix: a matrix of 0 and 1
     * @return: an integer
     */
    int maxSquare(vector<vector<int> > &matrix) {
        // write your code here
        if (matrix.empty() || matrix[0].empty()) return 0;
        
        int m = matrix.size(), n = matrix[0].size();
        vector<vector<int> > dp(m, vector<int>(n, 0));
        
        int result = 0;
        // initialize the first row
        for (int i = 0; i < n; i++) {
            if (matrix[0][i]) {
                dp[0][i] = 1;
                result = 1;
            }
        }
        
        // initialize the first column
        for (int i = 0; i < m; i++) {
            if (matrix[i][0]) {
                dp[i][0] = 1;
                result = 1;
            }
        }
        
        // calculate the remaining part
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                if (matrix[i][j]) {
                    dp[i][j] = min(dp[i][j - 1], min(dp[i - 1][j], dp[i - 1][j - 1])) + 1;
                    result = max(result, dp[i][j]);
                }
                else dp[i][j] = 0;
            }
        }
        return result * result;
    }
};