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:
- Right -> Right -> Down
- Right -> Down -> Right
- Down -> Right -> Right
Example 2:
Input: m = 7, n = 3
Output: 28
class Solution:
def uniquePaths(self, m, n):
"""
:type m: int
:type n: int
:rtype: int
"""
dp = [[0 for i in range(n+2)] for j in range(m+2)]
dp[1][2] = dp[2][1] =1
for i in range(1,m+1):
for j in range(1,n+1):
if (i==1 and j==2) or (i==2 and j==1) or(i==1 and j==1):
dp[i][j]=1
continue
dp[i][j] = dp[i-1][j] + dp[i][j-1]
return dp[m][n]