62. 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 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
典型的数据结构套路题，状态转移方程：f[i][j]=f[i][j-1]+f[i-1][j];
ac代码：

#include<iostream>
#include<vector>
using namespace std;
int uniquepaths(int m,int n)
{
vector<vector<int> > f(m, vector<int>(n)); //vector开辟二维数组
for(int i=0;i<m;i++)
f[i][0]=1;
for(int j=0;j<n;j++)
f[0][j]=1;
for(int i=1;i<m;i++)
for(int j=1;j<n;j++)
{
f[i][j]=f[i-1][j]+f[i][j-1];
}
return f[m-1][n-1];
}
int main()
{
int m,n;
while(cin>>m>>n)
{
cout<<uniquepaths(m,n)<<endl;
}
}