Unique Paths

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?

Note: m and n will be at most 100.

解题技巧：

从（1,1）到（m, n）需要向下走m步，向右走n步，共有(m+n)! / （m! * n!）种方法，但是m, n<100，故在求阶乘时，存在数据过大问题。本题采用的

解法是动态规划，状态转移方程为A[i][j] = A[i-1][j] + A[i][j-1]

代码：

int uniquePaths(int m, int n){     int A[m][n];     for(int i = 0; i < m; i ++)     {         for(int j = 0; j < n; j ++)         {             if(i == 0 || j == 0) A[i][j] = 1;             else A[i][j] = A[i-1][j] + A[i][j-1];         }     }     return A[m-1][n-1];}