Day-29_Unique_Paths.py

'''
    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?


Above is a 7 x 3 grid. How many possible unique paths are there?

 

Example 1:

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 -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

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

Constraints:

1 <= m, n <= 100
It's guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.


'''
class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        if m==0 or n==0:
            return 0
        arr = [[0 for x in range(n)] for y in range(m)] 
        for i in range (m):
            arr[i][0]=1
        for j in range (n):
            arr[0][j]=1
        for i in range (1,m):
            for j in range(1,n):
                arr[i][j]=arr[i][j-1]+arr[i-1][j]
        return arr[m-1][n-1]