Unique Paths

Desicription

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?

fuck!

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Solution

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class Solution{
public:
int uniquePaths(int m, int n){
int a = m - 1;
int b = n + m - 2;
double res = 1;
for(int i = 1; i <= a; i++)
res = res * (b - a + i) / i;
return res;
}
};