Unique Paths

Unique Paths

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.

Examples

Example 1:

Input: m = 3, n = 7
Output: 28
Explanation: From the top-left corner, there are 28 unique paths to the bottom-right corner.

Example 2:

Input: m = 3, n = 2
Output: 3
Explanation: There are three paths:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Example 3:

Input: m = 1, n = 1
Output: 1
Explanation: The robot is already at the destination.

Constraints

• 1 <= m, n <= 100

Expected Complexity

• Time: O(m * n)
• Space: O(n) with space optimization, or O(m * n) with a full 2D table