leetcode 221 Maximal Square
z
 2018-03-15 15:19:46  

Given a 2D binary matrix filled with 0’s and 1’s, find the largest square containing only 1’s and return its area.

For example, given the following matrix:

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1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

Return 4.

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class Solution {
    public int maximalSquare(char[][] matrix) {
        if(matrix.length == 0) return 0;
        if(matrix[0].length == 0) return 0;
        int m = matrix.length;
        int n = matrix[0].length;
        
        int[][] dp = new int[m+1][n+1];
        int size = 0;
        for(int i=1; i<=m; i++){
            for(int j=1; j<=n; j++){
                if(matrix[i-1][j-1] == '1'){
                    dp[i][j] = Math.min(dp[i-1][j-1], Math.min(dp[i-1][j], dp[i][j-1])) + 1;
                    size = Math.max(size, dp[i][j]);
                }
            }
        }
        return size*size;
    }
}
  • dp[i][j] = min(dp[i-1][j-1], dp[j-1][i], dp[i][j-1]) + 1 if(matrix[i-1][j-1] == 1)
  • 这里dp记录的是边长，只有当前点的左边，上边和左上角一般大时，当前点的值才加一
1 (dp = 1) 1 (dp = 1) 0 (dp = 0)
0 (dp = 0) 1 (dp = 1) 1 (dp = 1)
0 (dp = 0) 1 (dp = 1) 1 (dp = 2)
  • 要注意的是，如果最后一个位置的值为0的话，dp = 0 ，因此需要一个变量来保存整个过程中的最大值