Python/project_euler/problem_14/sol2.py

71 lines
2.1 KiB
Python
Raw Normal View History

# -*- coding: utf-8 -*-
"""
Collatz conjecture: start with any positive integer n. Next term obtained from
the previous term as follows:
If the previous term is even, the next term is one half the previous term.
If the previous term is odd, the next term is 3 times the previous term plus 1.
The conjecture states the sequence will always reach 1 regardless of starting
n.
Problem Statement:
The following iterative sequence is defined for the set of positive integers:
n n/2 (n is even)
n 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 40 20 10 5 16 8 4 2 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains
10 terms. Although it has not been proved yet (Collatz Problem), it is thought
that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
"""
from __future__ import print_function
try:
raw_input # Python 2
except NameError:
raw_input = input # Python 3
def collatz_sequence(n):
"""Returns the Collatz sequence for n."""
sequence = [n]
while n != 1:
if n % 2 == 0:
n //= 2
else:
n = 3 * n + 1
sequence.append(n)
return sequence
def solution(n):
"""Returns the number under n that generates the longest Collatz sequence.
Commented doctests that were causing slowness at Travis. (#1039) * Added doctest and more explanation about Dijkstra execution. * tests were not passing with python2 due to missing __init__.py file at number_theory folder * Removed the dot at the beginning of the imported modules names because 'python3 -m doctest -v data_structures/hashing/*.py' and 'python3 -m doctest -v data_structures/stacks/*.py' were failing not finding hash_table.py and stack.py modules. * Moved global code to main scope and added doctest for project euler problems 1 to 14. * Added test case for negative input. * Changed N variable to do not use end of line scape because in case there is a space after it the script will break making it much more error prone. * Added problems description and doctests to the ones that were missing. Limited line length to 79 and executed python black over all scripts. * Changed the way files are loaded to support pytest call. * Added __init__.py to problems to make them modules and allow pytest execution. * Added project_euler folder to test units execution * Changed 'os.path.split(os.path.realpath(__file__))' to 'os.path.dirname()' * Added Burrows-Wheeler transform algorithm. * Added changes suggested by cclauss * Fixes for issue 'Fix the LGTM issues #1024'. * Added doctest for different parameter types and negative values. * Fixed doctest issue added at last commit. * Commented doctest that were causing slowness at Travis. * Added comment with the reason for some doctest commented. * pytest --ignore
2019-07-18 22:34:29 +00:00
# The code below has been commented due to slow execution affecting Travis.
# >>> solution(1000000)
# {'counter': 525, 'largest_number': 837799}
>>> solution(200)
{'counter': 125, 'largest_number': 171}
>>> solution(5000)
{'counter': 238, 'largest_number': 3711}
>>> solution(15000)
{'counter': 276, 'largest_number': 13255}
"""
result = max([(len(collatz_sequence(i)), i) for i in range(1, n)])
return {"counter": result[0], "largest_number": result[1]}
if __name__ == "__main__":
result = solution(int(raw_input().strip()))
print(
"Longest Collatz sequence under one million is %d with length %d"
% (result["largest_number"], result["counter"])
)