LeetCode 64 Minimum Path Sum DP

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Solution

很显然的DP：

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

点击查看代码

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int dp[202][202];
        int n = grid.size(), m = grid[0].size();
        if(n==1 && m==1){return grid[0][0];}
        else{
            dp[0][0] = grid[0][0];
            for(int i=1;i<n;i++)dp[i][0]=dp[i-1][0]+grid[i][0];
            for(int i=1;i<m;i++)dp[0][i]=dp[0][i-1]+grid[0][i];
            for(int i=1;i<n;i++){
                for(int j=1;j<m;j++){
                    dp[i][j] = min(dp[i][j-1]+grid[i][j],dp[i-1][j]+grid[i][j]);
                }
            }
        }
        return dp[n-1][m-1];
    }
};