code-challenges/src/leetcode/medium/unique-paths/unique_paths.py at master · nwthomas/code-challenges · GitHub

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"""
https://leetcode.com/problems/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.

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
"""

def unique_paths(m: int, n: int) -> int:
    dp = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
    dp[0][1] = 1

    for y in range(1, len(dp)):
        for x in range(1, len(dp[y])):
            dp[y][x] = dp[y - 1][x] + dp[y][x - 1]

    return dp[m][n]