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.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

题目链接：https://leetcode.com/problems/minimum-path-sum/

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