leetcode 62. 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.

class Solution {
public:
	int uniquePaths(int m, int n) {
		if (m == 1 || n == 1)
			return 1;
		//return uniquePaths(m - 1, n) + uniquePaths(m, n - 1);
		if (m > n)
		{
			int t = n;
			n = m;
			m = t;
		}
		long long int numer = 1;
		long long int denomi = 1;
		for (int i = m + n - 2; i >= n; i--)
			numer *= i;
		for (int i = 1; i <= m - 1; i++)
			denomi *= i;
		return numer / denomi;
	}
};

简单考虑一下，就是一个排列组合问题，直接写公式就行（递归显然效率不高）。

accepted