[LeetCode 221] 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.

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.

solution:

DP, f(x,y) represents length of the right-bottom node of square,

ifmatrix[i][j] == 1, f(x,y) = Math.min(f(x-1,y), f(x,y-1),f(x-1,y-1))+1;

public int maximalSquare(char[][] matrix) {
        int n = matrix.length;
        if(n<=0) return 0;
        int m = matrix[0].length;
        int max = 0;
        int[][] mat = new int[n][m];
        for(int i=0;i<n;i++){
            if(matrix[i][0] == '1'){
                mat[i][0] = 1;
                max = 1;
            }
        }
        for(int i=0;i<m;i++){
            if(matrix[0][i] == '1'){
                mat[0][i] = 1;
                max = 1;
            }
        }
        for(int i=1;i<n;i++){
            for(int j=1;j<m;j++){
                if(matrix[i][j] == '1'){
                    mat[i][j] = Math.min(Math.min(mat[i-1][j], mat[i][j-1]), mat[i-1][j-1])+1;
                    max = Math.max(max, mat[i][j]);
                }else {
                    mat[i][j] = 0;
                }
            }
        }
        return max*max;
    }