leetcode No64. Minimum Path Sum

Question：

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.

Algorithm：

比较从左边来的路径和和从上面来的路径谁小，再加上当前元素，还是用动态规划

Accepted Code：

class Solution {
public:
int minPathSum(vector<vector<int>>& grid) {
int M=grid.size();
int N=grid[0].size();
if(M==0) return 0;
vector<vector<int>> res(grid);
for(int j=1;j<N;j++)    //先要把边界的算出来
res[0][j]+=res[0][j-1];
for(int i=1;i<M;i++)
res[i][0]+=res[i-1][0];
for(int i=1;i<M;i++)
for(int j=1;j<N;j++)
{
res[i][j]=min(res[i-1][j],res[i][j-1])+res[i][j];
}
return res[M-1][N-1];
}
};