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.

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.

画图即可找到规律

这是错误的图

黑色的大小是前几个的最小的 + 1

// dp(i, j) represents the length of the square 
// whose lower-right corner is located at (i, j)
// dp(i, j) = min{ dp(i-1, j-1), dp(i-1, j), dp(i, j-1) }


public class Solution {
    public int maximalSquare(char[][] matrix) {

        if(matrix.length == 0) return 0;

        int m = matrix.length;
        int n = matrix[0].length;

        int[][] dp = new int[m + 1][n + 1];

        int max = 0;
        for(int i = 1; i <= m; i ++){
            for(int j = 1; j <= n; j ++){
                if(matrix[i - 1][j - 1] == '1')
                    dp[i][j] = Math.min(dp[i-1][j-1], Math.min(dp[i-1][j], dp[i][j-1])) + 1;

                max = Math.max(max, dp[i][j]);
            }
        }

        return max * max;
    }
}