【刷题-LeetCode】221. Maximal Square

1. Maximal Square

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

Example:

Input: 

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

Output: 4

解 动态规划，设\(dp[i][j]\)表示下标为(i, j)的左上角区域的最大正方形面积，当\(\mathrm{matrix}[i][j]\neq '0'\)时：

\[dp[i][j] = \min\{dp[i-1][j], dp[i][j-1], dp[i-1][j-1]\}
\]

class Solution {
public:
    int maximalSquare(vector<vector<char>>& matrix) {
        if(matrix.size() == 0)return 0;
        int m = matrix.size(), n = matrix[0].size();
        int *dp = new int[n+1];
        memset(dp, 0, (n+1)*sizeof(int));
        int ans = 0, prev = 0;
        for(int i = 1; i <= m; ++i){
            prev = dp[0];
            for(int j = 1; j <= n; ++j){
                int tmp = dp[j];
                if(matrix[i-1][j-1] == '1'){
                    dp[j]=min(dp[j], min(prev, dp[j-1]))+1;
                    ans = max(ans, dp[j]);
                }else{
                    dp[j] = 0;
                }
                prev = tmp;
            }
        }
        return ans*ans;

    }
};