Ranking: **
A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
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?
![](http://4.bp.blogspot.com/_UElib2WLeDE/TNJf8VtC2VI/AAAAAAAACXU/UyUa-9LKp4E/s400/robot_maze.png)
Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
» Solve this problem[解题思路]
一维DP。 Step[i][j] = Step[i-1][j] + Step[i][j-1];
[Code]
1: int uniquePaths(int m, int n) {
2: vector<int> maxV(n,0);
3: maxV[0]=1;
4: for(int i =0; i< m; i++)
5: {
6: for(int j =1; j<n; j++)
7: {
8: maxV[j] = maxV[j-1] + maxV[j];
9: }
10: }
11: return maxV[n-1];
12: }