leetcode/apps/docs/content/(05-decision-space)/multi-d-grid-dp/62-unique-paths.mdx

---
title: '62. Unique Paths'
description: There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time
icon: dot
topics:
  - { name: "Math", slug: "math" }
  - { name: "Dynamic Programming", slug: "dynamic-programming" }
  - { name: "Combinatorics", slug: "combinatorics" }
sidebar:
  label: 'Unique Paths'
  badge: 'Medium'
---

### Example 1:
- 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

### Constraints:

- `1 <= m, n <= 100`

## Solution

```py
class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        dp = [[0 for _ in range(n)] for _ in range(m)]

        for c in range(n):
            dp[0][c] = 1

        for r in range(m):
            dp[r][0] = 1

        for r in range(1, m):
            for c in range(1, n):
                dp[r][c] = dp[r - 1][c] + dp[r][c - 1]

        return dp[-1][-1]
```