【C++】【LeetCode】62. Unique Paths

题目

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?
m and n will be at most 100.

思路

其实就是一个排列组合的问题，mxn的矩形，其实就是向右走m-1步，向下走n-1步。即求$C_{m-1+n-1}^{min(n-1, m-1)}$。

代码

class Solution {
public:
    int uniquePaths(int m, int n) {
        if (m == 1 || n == 1) {
            return 1;
        }
        if (m * n == 0) {
            return 0;
        }

        int downNum = m - 1 + n - 1;
        int upNum = min(n - 1, m - 1);
        long result = 1;

        for (int i = downNum; i > downNum - upNum; i--) {
            result *= i;
        }
        for (int i = upNum; i > 1; i--) {
            result /= i;
        }
        return result;
    }
};