Number of Unique Paths to Go from Top Left to Bottom Right

A robot is located at the top-left corner of a m x n grid.

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?

Example 1:

Input: m = 3, n = 2

Output: 3


From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:

  1. Right -> Right -> Down

  2. Right -> Down -> Right

  3. Down -> Right -> Right

Example 2:

Input: m = 5, n = 3

Output: 15

Try it yourself