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



Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book.

Contrary to popular belief, Lorem Ipsum is not simply random text.

  >>> a = [1, 2, 3]
  >>> a[-1]

Get premium for instant access to all content and solutions