LeetCode 221 Maximal Square DP

Given an m x n binary matrix filled with 0's and 1's, find the largest square containing only 1's and return its area.

Solution

设 \(dp[i][j]\) 表示能到达位置 \((i,j)\) 的最大正方形边长。对于初始化，即 \(i=0 \text{ or } j=0\)，最大的边长就是该位置的数字；否则的话考虑转移：

\[dp[i][j] = 1+\min(dp[i-1][j-1],dp[i-1][j],dp[i][j-1]) \]

即由周围的来进行限制，只能选最小的边长

点击查看代码

class Solution {
private:
    int dp[303][303];
    int ans = 0;
public:
    int maximalSquare(vector<vector<char>>& matrix) {
        if(matrix.empty())return 0;
        
        int n = matrix.size(), m = matrix[0].size();
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if((i==0)||(j==0)||(matrix[i][j]=='0')){
                    dp[i][j] = matrix[i][j]-'0';
                }
                else{
                   dp[i][j] = min(dp[i-1][j-1],min(dp[i-1][j],dp[i][j-1]))+1;
                }
                ans = max(ans, dp[i][j] * dp[i][j]);
            }
            
        }
        return ans;
    }
    
};