Question:

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.

Thinking:

IIf the [i-1][j], [i][j-1] and [i-1][j-1] all have the same length of ‘1’ edge and the [i][j] is ‘1’, the length of the square can increase.

Solution:

public int maximalSquare(char[][] matrix) {
    int m = matrix.length;
    if (m == 0)    return 0;
    int n = matrix[0].length;
    int res = 0;
    int[][] opt = new int[m+1][n+1];

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

    return res * res;
}