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?
Note: m and n will be at most 100.
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
class Solution:
     def paths(self,m,n,a,b,memo):
         if m>a or n>b:
             return 0
         if m==a and n==b:
             return 1
         if str(m)+" "+str(n) not in memo:
             memo[str(m)+" "+str(n)] = self.paths(m+1,n,a,b,memo) + self.paths(m,n+1,a,b,memo)
 
         return memo[str(m)+" "+str(n)]
         
         
     def uniquePaths(self, m, n):
         memo =  dict()
         return(self.paths(0,0,m-1,n-1,memo))
class Solution:
     def paths(self,m,n,a,b,memo):
         if m>a or n>b:
             return 0
         if m==a and n==b:
             return 1
         if str(m)+" "+str(n) not in memo:
             memo[str(m)+" "+str(n)] = self.paths(m+1,n,a,b,memo) + self.paths(m,n+1,a,b,memo)
 
         return memo[str(m)+" "+str(n)]
         
         
     def uniquePaths(self, m, n):
         memo =  dict()
         return(self.paths(0,0,m-1,n-1,memo))