[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.

 

Hide Tags

  Array Dynamic Programming

 

---

     找矩阵左上到右下的最短路径，标准的动态规划。

1. 初始化统计矩阵的最上行，最右列。
2. 从上往下，从左到右填写每格。
3. 输出结果

 1 #include <iostream>

 2 #include <vector>

 3 using namespace std;

 4 

 5 

 6 class Solution {

 7 public:

 8     int minPathSum(vector<vector<int> > &grid) {

 9         int nrow = grid.size();

10         if(nrow==0) return 0;

11         int ncol = grid[0].size();

12         vector<vector<int> > cnt(nrow,vector<int>(ncol,0));

13         cnt[0][0] = grid[0][0];

14         for(int i =1;i<nrow;i++)

15             cnt[i][0]=cnt[i-1][0]+grid[i][0];

16         for(int j = 1;j<ncol;j++)

17             cnt[0][j]=cnt[0][j-1] + grid[0][j];

18         for(int i=1;i<nrow;i++){

19             for(int j=1;j<ncol;j++){

20                 cnt[i][j] = grid[i][j] + min(cnt[i-1][j],cnt[i][j-1]);

21             }

22         }

23         return cnt[nrow-1][ncol-1];

24     }

25 };

26 

27 int main()

28 {

29     vector<vector<int> > grid({{1,2,3},{4,5,6},{7,8,9}});

30     Solution sol;

31     cout<<sol.minPathSum(grid)<<endl;

32     for(int i=0;i<grid.size();i++){

33         for(int j=0;j<grid[i].size();j++)

34             cout<<grid[i][j]<<" ";

35         cout<<endl;

36     }

37     return 0;

38 }

View Code