Unique Paths

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

 

解答：动态规划

1. int uniquePaths(int m, int n) {
3. vector<int> res(n,0);
4. for(int i=0;i<n;i++) res[i]=1;
5. for(int i=1;i<m;i++) {
6. for(int j=0;j<n;j++) {
7. if(j==0) res[j]=1;
8. else {
9. res[j] = res[j] + res[j-1];
10. }
11. }
12. }
13. return res[n-1];
14. }