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.

注意关系对应之处

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) 
    {
        int m,n;
        int sum = 0;
        m = grid.size();
        n = grid[0].size();
        if(m*n==0)return 0;
        int dp[m+1][n+1];
        dp[1][1] = grid[0][0];
        int i,j;
        for(i=2;i<m+1;i++)
        {
            dp[i][1] = dp[i-1][1] + grid[i-1][0];
        }
         for(i=2;i<n+1;i++)
        {
            dp[1][i] = dp[1][i-1] + grid[0][i-1];
        }
        for(i=2;i<=m;i++)
        for(j=2;j<=n;j++)
        {
            if(dp[i-1][j] < dp[i][j-1])
                dp[i][j] = dp[i-1][j]+grid[i-1][j-1];
            else
                dp[i][j] = dp[i][j-1]+grid[i-1][j-1];
                
        }
        return dp[m][n];
    }
    
};