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]; }