UniquePaths.py

# -*- coding: utf-8 -*-
"""
Created on Sun May 26 16:59:40 2024

@author: USER
"""

""" 
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 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 """


class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        # Initialize a 2D dp array with dimensions m x n
        dp = [[0] * n for _ in range(m)]

        # Set the values for the first row and first column to 1
        for i in range(m):
            dp[i][0] = 1
        for j in range(n):
            dp[0][j] = 1

        # Fill in the rest of the dp array
        for i in range(1, m):
            for j in range(1, n):
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1]

        # The bottom-right cell contains the number of unique paths
        return dp[m - 1][n - 1]