54 lines
955 B
Markdown
54 lines
955 B
Markdown
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## Unique Paths
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A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
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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).
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How many possible unique paths are there?
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### Examples
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**Example 1**
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<p align="left">
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<img src="../../assets/robot_maze.png" alt="Robot Maze">
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</p>
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```text
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Input: m = 3, n = 7
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Output: 28
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```
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**Example 2**
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```text
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Input: m = 3, n = 2
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Output: 3
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Explanation:
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From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
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1. Right -> Down -> Down
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2. Down -> Down -> Right
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3. Down -> Right -> Down
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```
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**Example 3**
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```text
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Input: m = 7, n = 3
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Output: 28
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```
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**Example 4**
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```text
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Input: m = 3, n = 3
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Output: 6
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```
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---
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### Constraints
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- `1 <= m, n <= 100`
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- It's guaranteed that the answer will be less than or equal to `2 * 109`.
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