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.

#include<iostream>
#include<vector>
using namespace std;

int uniquePaths(int m, int n) {
	vector<int>a(n, 0);
	vector<vector<int> >Paths(m,a);
	for (int i = 0; i != m; ++i)
		Paths[i][0] = 1;
	for (int j = 0; j != n; ++j)
		Paths[0][j] = 1;

	for (int i = 1; i != m;++i)
	{
		for (int j = 1; j != n;++j)
		{
			Paths[i][j] = Paths[i - 1][j] + Paths[i][j - 1];
		}
	}
	return Paths[m - 1][n - 1];
}