leetcode/work/1/Medium/Math/62.unique-paths.py

"""
62. Unique Paths
Difficulty: Medium
https://leetcode.com/problems/unique-paths/

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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.



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 = [[0 for _ in range(n)] for _ in range(m)]

        for c in range(n):
            dp[0][c] = 1

        for r in range(m):
            dp[r][0] = 1

        for r in range(1, m):
            for c in range(1, n):
                dp[r][c] = dp[r - 1][c] + dp[r][c - 1]

        return dp[-1][-1]