Problem 15：Lattice paths

题目描述：

Starting in the top left corner of a 22 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 2020 grid?

代码：

（一）递归法，用时很长

def fun(num1,num2):if num1==0 or num2==0:return 1else:return fun(num1-1,num2)+fun(num1,num2-1)print fun(20,20)

（二）非递归法

array=[[0 for col in range(21)]for row in range(21)]for i in range(21):for j in range(21):if i==0 or j==0:array[i][j]=1for i in range(1,21):for j in range(1,21):array[i][j]=array[i-1][j]+array[i][j-1]print array[20][20]