Leetcode(64)Minimum Path Sum

题目：从左上到右下，只能向右和向下走，求经过的数字和的最小值。

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.
分析：动态规划。设dp[i][j]为从（0,0）点到（i,j）点的数字和最小值。则dp[i][j]=grip[i][j]+min(dp[i-1][j],dp[i][j-1])。边界值：dp[0][0]=grip[0][0]。复杂度：O（n²）。
代码：

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