The Unique Path leetcode Python

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 is there?

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

There are two ways of solving this problem.

1. Direct mathematical expression Choose M-1 from M+n-2

Class solution:    # @return An integer    def FAC (self,n):        if N==1 or n==0:            return 1        return N*SELF.FAC ( n-1)    def uniquepaths (self, M, n):        if M==1 or n==1:            return 1        val1=self.fac (m+n-2)        VAL2=SELF.FAC ( m-1)        Val3=self.fac (n-1)        result=val1/(VAL2*VAL3)        return result     

2. Dynamic planning, each step is adjacent to the nearest lattice and.

The code is as follows

Class solution:    # @return An integer    def uniquepaths (self, M, n):        dp=[[0 for index in range (n)] for index in R Ange (m)] for        row in range (m):            dp[row][0]=1 for Col in        Range (n):            dp[0][col]=1 for row in        range (1,m): For            col in Range (1,n):                dp[row][col]=dp[row-1][col]+dp[row][col-1]        return dp[m-1][n-1]        

The Unique Path leetcode Python