Description

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.

Solution

用matrix来记录最大square的边长，那么matrix[i][j] = min(matrix[i - 1][j - 1], matrix[i - 1][j], matrix[i][j - 1]) + 1

public class Solution {
    /*
     * @param matrix: a matrix of 0 and 1
     * @return: an integer
     */
    public int maxSquare(int[][] matrix) {
        // write your code here
        if (matrix == null || matrix.length == 0 || matrix[0] == null || matrix[0].length == 0) {
            return 0;
        }

        int n = matrix.length;
        int m = matrix[0].length;
        int max = 0;
        for (int i = 0; i < n; i++) {
            if (matrix[i][0] == 1) {
                max = 1;
                break;
            }
        }

        if (max == 0) {
            for (int j = 0; j < m; j++) {
                if (matrix[0][j] == 1) {
                    max = 1;
                    break;
                }
            }
        }

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

        return max * max;
    }
}