62-unique-paths.py

"""
Problem Link: https://leetcode.com/problems/unique-paths/

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right 
corner of the grid (marked 'Finish' in the diagram below).
How many possible unique paths are there?

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

Example 3:
Input: m = 7, n = 3
Output: 28

Example 4:
Input: m = 3, n = 3
Output: 6
 
Constraints:
1 <= m, n <= 100
It's guaranteed that the answer will be less than or equal to 2 * 109.
"""
class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        board = [[0] * n for _ in range(m)]
        
        for row in range(m):
            for col in range(n):
                if row == 0 or col == 0:
                    board[row][col] = 1
                else:
                    board[row][col] = board[row-1][col] + board[row][col-1]
        
        return board[-1][-1]