問題：
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?
Note: m and n will be at most 100.
分析：
1、採用DFS，時間複雜度O(n^4)，大集合會超時；採用DFS+緩衝（即“備忘錄”法）時間O(n^2)。
2、用動規，時間O(n^2)，空間O(n^2)；可以優化，後續補上。
3、還可以用數學公式，後續補上。
代碼：
class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>> p(m,vector<int>(n,1));
//邊界
for(int i=0;i<m;i++) p[i][0]=1;
for(int j=0;j<n;j++) p[0][j]=1;
for(int i=1;i<m;i++)
for(int j=1;j<n;j++){
//動規：自底向上
p[i][j]=p[i-1][j]+p[i][j-1];
}
return p[m-1][n-1];
}
};