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.
解题思路：
dp问题，用一个dp[i][j]保存matrix[i][j]作为右下节点的时候的最大矩形的边长，JAVA实现如下：
public int maximalSquare(char[][] matrix) {
if (matrix.length == 0 || matrix[0].length == 0)
return 0;
int res = 0;
int[] dp = new int[matrix[0].length];
for (int i = 0; i < matrix[0].length; i++)
if (matrix[0][i] == '1'){
dp[i] = 1;
res=1;
}
for (int i = 1; i < matrix.length; i++) {
dp[0] = matrix[i][0] == '1' ? 1 : 0;
res=Math.max(res, dp[0]);
for (int j = 1; j < matrix[0].length; j++) {
if(matrix[i][j]=='0')
dp[j]=0;
else if (dp[j] == dp[j - 1]
&& matrix[i - dp[j]][j - dp[j]] == '0') {
dp[j] = Math.min(dp[j], dp[j - 1]);
} else
dp[j] = Math.min(dp[j], dp[j - 1]) + 1;
res=Math.max(res, dp[j]);
}
}
return res*res;
}