leetcode 64. Minimum Path Sum

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.

采用动态规划的方法，dp[i][j] = min(dp[i-1][j],dp[i],[j-1])+a[i][j];

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