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?

意思很明确，只能往下往右，从左上角到右下角，有多少条路？

第一个思路：动态规划、

到达某一格的路径数目=到达它上一格的路径数目+达到它左侧一格的路径数目

由于只能往下或者往右，故第一行和第一列的所有格子都只有一条路径。

class Solution:

    # @return an integer

    def uniquePaths(self, m, n):

        if m == 1 and n == 1:

            return 1

        feat = [[1] * n for row in range(m)]

        feat[0][0] = 0

        for i in range(1,n):  #第一行第一列都是1

            for j in range(1,m):

                feat[j][i] = feat[j-1][i] + feat[j][i-1]

        return feat[m-1][n-1]

第二个思路：用0，1分别表示往下，往右，对于m*n的格子，结果就是有多少种m-1个0和n-1个1的排列方式。