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.

 1 public class Solution {
 2     public int maximalSquare(char[][] matrix) {
 3         if (matrix == null || matrix.length < 1)
 4             return 0;
 5         int row = matrix.length, column = matrix[0].length, max = 0;
 6         int[][] dp = new int[row][column];
 7         // Top Row
 8         for (int i = 0; i < column; i++) {
 9             if (matrix[0][i] == ‘0‘)
10                 dp[0][i] = 0;
11             else
12                 dp[0][i] = 1;
13         }
14         // Left Column
15         for (int i = 0; i < row; i++) {
16             if (matrix[i][0] == ‘0‘)
17                 dp[i][0] = 0;
18             else
19                 dp[i][0] = 1;
20         }
21         // Inside Filling
22         for (int i = 1; i < row; i++) {
23             for (int j = 1; j < column; j++) {
24                 if (matrix[i][j] == ‘0‘) {
25                     dp[i][j] = 0;
26                 } else {
27                     int tmp = Math.min(dp[i][j - 1], dp[i - 1][j]);
28                     dp[i][j] = Math.min(tmp, dp[i - 1][j - 1]) + 1;
29                 }
30             }
31         }
32         for (int i = 0; i < row; i++) {
33             for (int j = 0; j < column; j++)
34                 max = Math.max(max, dp[i][j]);
35         }
36         return max * max;
37     }
38 }