62.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?

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 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]