# Algorithm Puzzles: Unique Paths

Algorithm Puzzles ~~everyday~~ ~~every week~~ sometimes: Unique Paths

## Puzzle

Puzzle from leetcode:

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 * 10^9.

## Solution

it’s easy to resolve via dfs, but without `lru_cache`

it might exceed time limit during check…

1 | from functools import lru_cache |

T.C. should be `O(n^n)`