# 62. Unique Paths

#### Medium

***

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.

Given the two integers `m` and `n`, return *the number of possible unique paths that the robot can take to reach the bottom-right corner*.

The test cases are generated so that the answer will be less than or equal to `2 * 109`.

 

**Example 1:**

![](https://assets.leetcode.com/uploads/2018/10/22/robot_maze.png)

```
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`

```python
class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        arr = [[0 for i in range(n)] for j in range(m)]
        for i in range(m):
            for j in range(n):
                arr[i][j] = 1 if i == 0 or j ==0 else arr[i-1][j] + arr[i][j-1]
        return arr[m-1][n-1]
```