[LeetCode] 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，f[i][j] = min(f[i-1][j], f[i][j-1]) + a[i][j]

 1 class Solution {
 2 private:
 3     int f[1000][1000];
 4 public:
 5     int minPathSum(vector<vector<int> > &grid) {
 6         // Start typing your C/C++ solution below
 7         // DO NOT write int main() function
 8         if (grid.size() == 0 || grid[0].size() == 0)
 9             return 0;
10             
11         f[0][0] = grid[0][0];
12         
13         for(int i = 1; i < grid.size(); i++)
14             f[i][0] = f[i-1][0] + grid[i][0];
15             
16         for(int i = 1; i < grid[0].size(); i++)
17             f[0][i] = f[0][i-1] + grid[0][i];
18             
19         for(int i = 1; i < grid.size(); i++)
20             for(int j = 1; j < grid[0].size(); j++)
21                 f[i][j] = min(f[i-1][j], f[i][j-1]) + grid[i][j];
22                 
23         return f[grid.size()-1][grid[0].size()-1];
24     }
25 };