LeetCode#62. Unique Paths

题意：

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.

题目分析：

这道题分析出其算法即可，一道高中组合计算的问题，若有m行和n列，并且只能向下或者向右，则共有m+n-2步，其中向右m-1步，向下n-1步。

即决定好m+n-1中哪m-1步向右即可，就是计算组合数C（m+n-1,m-1）

一种c++实现方式如下：

class Solution {public:    int uniquePaths(int m, int n) {        int total = m+n-2;        double u_num;        u_num = fact(total)/(fact(n-1)*fact(total-n+1));        if((u_num -(int)u_num) >= 0.5)        return u_num+1;        else return u_num;    }    double fact(int n) {        double res = 1;        for(int i = 1; i <= n; i++) {            res *= i;        }        return res;    }};

注意这里因为范围过大，故采用double计算，将计算得到的结果四舍五入即可