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100-days-of-rust/Week-03/Day-18_Unique-Paths/README.md
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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?

Examples

Example 1

Robot Maze 

Input: m = 3, n = 7
Output: 28

Example 2

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Example 3

Input: m = 7, n = 3
Output: 28

Example 4

Input: m = 3, n = 3
Output: 6

Constraints

  • 1 <= m, n <= 100
  • It's guaranteed that the answer will be less than or equal to 2 * 109.