[LeetCode]Minimum Path Sum

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.

 

DP,递推公式f[i][j]=min(f[i-1][j],f[i][j-1])+grid[i][j]。

 1 class Solution {
 2 public:
 3     int minPathSum(vector<vector<int>>& grid) {
 4         if(grid.size()==0 || grid[0].size()==0) return 0;
 5         int m=grid.size(),n=grid[0].size();
 6         vector<vector<int>> f(m,vector<int>(n,0));
 7         f[0][0]=grid[0][0];
 8         for(int i=1;i<n;i++) f[0][i]=f[0][i-1]+grid[0][i];
 9         for(int i=1;i<m;i++) f[i][0]=f[i-1][0]+grid[i][0];
10         for(int i=1;i<m;i++)
11         {
12             for(int j=1;j<n;j++)
13             {
14                 f[i][j]=min(f[i-1][j],f[i][j-1])+grid[i][j];
15             }
16         }
17         return f[m-1][n-1];
18     }
19 };

 

posted @ 2015-09-09 19:47  Sean_le  阅读(130)  评论(0编辑  收藏  举报