Python/project_euler/problem_014/sol1.py

61 lines
1.5 KiB
Python
Raw Normal View History

"""
Problem 14: https://projecteuler.net/problem=14
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?
"""
2019-10-05 05:14:13 +00:00
def solution(n: int = 1000000) -> int:
"""Returns the number under n that generates the longest sequence using the
formula:
n n/2 (n is even)
n 3n + 1 (n is odd)
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)
# 837799
>>> solution(200)
171
>>> solution(5000)
3711
>>> solution(15000)
13255
"""
largest_number = 0
pre_counter = 0
for input1 in range(n):
counter = 1
number = input1
while number > 1:
if number % 2 == 0:
number //= 2
counter += 1
else:
number = (3 * number) + 1
counter += 1
if counter > pre_counter:
largest_number = input1
pre_counter = counter
return largest_number
if __name__ == "__main__":
print(solution(int(input().strip())))