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

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2023-03-24 00:52:21 +00:00
## 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**
<p align="left">
<img src="../../assets/robot_maze.png" alt="Robot Maze">
</p>
```text
Input: m = 3, n = 7
Output: 28
```
**Example 2**
```text
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**
```text
Input: m = 7, n = 3
Output: 28
```
**Example 4**
```text
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`.