Leetcode 931. Minimum falling path sum 最小下降路径和(动态规划)

Input: [[1,2,3],[4,5,6],[7,8,9]]
Output: 12

Explanation: 
可能的下降路径是:
[1,4,7], [1,4,8], [1,5,7], [1,5,8], [1,5,9]
[2,4,7], [2,4,8], [2,5,7], [2,5,8], [2,5,9], [2,6,8], [2,6,9]
[3,5,7], [3,5,8], [3,5,9], [3,6,8], [3,6,9]
最小下降路径是 [1,4,7], 所以答案是12.

class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& A) {
        int dp[200][200]={0};
        for(int i=0;i<A.size();i++){
            dp[0][i]=A[0][i];
        }
        
        for(int i=1;i<A.size();i++){
            for(int k=0;k<A[0].size();k++){
                if(k==0){
                    dp[i][k] = A[i][k]+ min(dp[i-1][k],dp[i-1][k+1]); 
                }else if(k==A.size()-1){
                    dp[i][k] = A[i][k]+ min(dp[i-1][k],dp[i-1][k-1]);
                }else{
                    dp[i][k] = A[i][k]+ min(dp[i-1][k],min(dp[i-1][k-1],dp[i-1][k+1]));
                }
            }
        }
        
        return *min_element(&dp[A.size()-1][0],&dp[A.size()-1][A.size()]);
    }
};