LeetCode 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?

class Solution {
public:
    int uniquePaths(int m, int n) {
        if(m<0||n<0)
            return 0;
        int sum=m+n-2;
        long long mul=1;
        for(int i=sum;i>=m;i--){
            mul*=i;
        }
       for(int i=1;i<=n-1;i++){
            mul/=i;
        }
        return mul;
    }
};

上面这个解法是最简单的 ，但是却会造成越界怎么办呢

还是得用老方法

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<int> v(n,1);
        for(int i=1;i<m;i++){
            for(int j=1;j<n;j++){
                v[j]=v[j]+v[j-1];
            }
        }
        return v[n-1];
    }
};

这个方法是下面的方法的变种 

当然由于以下的方法是每次只需要“1”的空间，而且按层进行遍历。故而可以简化

 v[i][j]=v[i-1][j]+v[i][j-1];