Maximal Square 解答

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.

Solution

2-D array. The changing condition is:

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

public class Solution {
    public int maximalSquare(char[][] matrix) {
        if (matrix == null || matrix.length < 1)
            return 0;
        int row = matrix.length, column = matrix[0].length, max = 0;
        int[][] dp = new int[row][column];
        // Top Row
        for (int i = 0; i < column; i++) {
            if (matrix[0][i] == '0')
                dp[0][i] = 0;
            else
                dp[0][i] = 1;
        }
        // Left Column
        for (int i = 0; i < row; i++) {
            if (matrix[i][0] == '0')
                dp[i][0] = 0;
            else
                dp[i][0] = 1;
        }
        // Inside Filling
        for (int i = 1; i < row; i++) {
            for (int j = 1; j < column; j++) {
                if (matrix[i][j] == '0') {
                    dp[i][j] = 0;
                } else {
                    int tmp = Math.min(dp[i][j - 1], dp[i - 1][j]);
                    dp[i][j] = Math.min(tmp, dp[i - 1][j - 1]) + 1;
                }
            }
        }
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++)
                max = Math.max(max, dp[i][j]);
        }
        return max * max;
    }
}