# Max 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[x][y] = min(dp[x - 1][y - 1], dp[x][y - 1], dp[x - 1][y]) + 1
``````

## Code

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

int[][] dp = new int[matrix.length][matrix[0].length];
int max = 0;

for (int i = 0; i < matrix.length; i++) {
dp[i][0] = matrix[i][0] == 1 ? 1 : 0;
max = Math.max(max, dp[i][0]);
}

for (int j = 0; j < matrix[0].length; j++) {
dp[0][j] = matrix[0][j] == 1 ? 1 : 0;
max = Math.max(max, dp[0][j]);
}

for (int i = 1; i < matrix.length; i++) {
for (int j = 1; j < matrix[0].length; j++) {
dp[i][j] = matrix[i][j] == 1 ?
Math.min(Math.min(dp[i - 1][j], dp[i][j - 1]), dp[i - 1][j - 1]) + 1 : 0;
max = Math.max(max, dp[i][j]);
}
}

return (int)Math.pow(max, 2);
}
}

``````