欧拉计划(python) problem 15

Lattice paths

Problem 15

Starting in the top left corner of a 2×2 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 20×20 grid?

python code :

dict={}

def func(i,j):

rest=dict.get(str(i)+‘_‘+str(j))

if rest!=None:

return rest

else:

if i==0 and j==0:

return 0

if i==0 or j==0:

return 1

temp=func(i-1,j)+func(i,j-1)

dict[str(i)+‘_‘+str(j)]=temp

return temp

result=func(20,20)

print(result)

time : <1s