62. Unique Paths

源链接:https://leetcode.com/problems/unique-paths/

题目描述: 

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.

解题思路:    可以理解为一个排列问题:一个7 * 3的网格,必然要下降2次,向右6次,那么问题的解就是一个可以重复的插空问题    

代码:

class Solution {
public:
    int uniquePaths(int m, int n) {
        long a = (m > n ? m : n);
        long b = (m < n ? m : n) - 1;
        
        long c = b;
        long res = 1;
        while (c--) {
            res *= a++;
        }
        
        long div = 1;
        while (b != 0) {
            div *= b--;
        }
        
        return res / div;
    }
};

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