题目：Maximal 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.

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Yes

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样例

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

.

标签 Expand

动态规划

根据题意可用动态规划去求解，先求解出最大的正方形边长
若a[m,n] = 1
a[m,n] = min(a[m-1,n-1],min(a[m-1,n],a[m,n-1]))+1；
比如
10100
10111
11111
10010
求解后
10100
10111
11122
10010
求出最大的边长，面积=边长*边长

public class Solution {
/**
* @param matrix: a matrix of 0 and 1
* @return: an integer
*/
public int maxSquare(int[][] matrix) {
// write your code here
if(null==matrix||0==matrix.length) return 0;
int m = matrix.length;
int n = matrix[0].length;
int squareArr[][] = new int[m]
;
int res = 0;
for(int i=0;i<m;i++){
if(matrix[i][0]==1){
squareArr[i][0] = 1;
res = 1;
}
}
for(int j=0;j<n;j++){
if(matrix[0][j]==1){
squareArr[0][j]=1;
res = 1;
}
}

for(int i=1;i<m;i++){
for(int j=1;j<n;j++){
if(matrix[i][j]==1){
squareArr[i][j] = min(squareArr[i-1][j-1], min(squareArr[i][j-1],squareArr[i-1][j]))+1;
res = max(res, squareArr[i][j]*squareArr[i][j]);
}
}
}
return res;
}
public int min(int a,int b){
return a>b?b:a;
}
public int max(int a, int b){
return a>b?a:b;
}

}