predict the number in a sequence of 3 billion

codeeval-125.py

'''
Sequence 011212201220200112 ... constructed as follows: first is 0, then repeated the following action: already written part is attributed to the right with replacement 0 to 1, 1 to 2, 2 to 0. E.g.

0 -> 01 -> 0112 -> 01121220 -> ...
Create an algorithm which determines what number is on the N-th position in the sequence.

INPUT SAMPLE:

Your program should accept as its first argument a path to a filename. Each line in this file contains an integer N such as 
0 <= N <= 3000000000. E.g.

0
5
101
25684
OUTPUT SAMPLE:

Print out the number which is on the N-th position in the sequence. E.g.

0
2
1
0
'''

s=[0]

def mapper(b):
  num_dict = {0:1 , 1:2 , 2:0}
  return num_dict[b]

class concat():
	def __init__(self, s1):
		self.s1 = s1
		self.s2 = tmap(map,self.s1)
		self.cachedlen = len(s1) * 2

	def __getitem__(self, i):
		if i < len(self.s1):
			return self.s1[i]
		else:
			return self.s2[i - len(self.s1)]

	def __len__(self):
		return self.cachedlen

class tmap():
	def __init__(self, fun, s):
		self.fun = fun
		self.list = s
		self.cachedlen = len(self.list)

	def __getitem__(self, i):
		return self.fun(self.list[i])

	def __len__(self):
		return self.cachedlen


for i in xrange(30):
	s = concat(s)

''' USE s[n] to obtain the n th number in the sequence '''
print  len(s)