unique paths to end of maze, solve back to front

unique-paths-py

# https://leetcode.com/problems/unique-paths/description/

"""
62. Unique Paths
Medium
Topics
Companies
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:


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
"""

class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        dp = [[1]*n for _ in range(m)]
        for i in range(1, m):
            for j in range(1, n):
                dp[i][j] = dp[i-1][j] + dp[i][j-1]
        return dp[-1][-1]

assert Solution().uniquePaths(3, 7) == 28
assert Solution().uniquePaths(3, 2) == 3