mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
44254cf112
* Rename all Project Euler directories: Reason: The change was done to maintain consistency throughout the directory and to keep all directories in sorted order. Due to the above change, some config files had to be modified: 'problem_22` -> `problem_022` * Update scripts to pad zeroes in PE directories
63 lines
1.7 KiB
Python
63 lines
1.7 KiB
Python
"""
|
|
Problem 14: https://projecteuler.net/problem=14
|
|
|
|
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 typing import List
|
|
|
|
|
|
def collatz_sequence(n: int) -> List[int]:
|
|
"""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: int = 1000000) -> int:
|
|
"""Returns the number under n that generates the longest Collatz sequence.
|
|
|
|
# The code below has been commented due to slow execution affecting Travis.
|
|
# >>> solution(1000000)
|
|
# 837799
|
|
>>> solution(200)
|
|
171
|
|
>>> solution(5000)
|
|
3711
|
|
>>> solution(15000)
|
|
13255
|
|
"""
|
|
|
|
result = max([(len(collatz_sequence(i)), i) for i in range(1, n)])
|
|
return result[1]
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(solution(int(input().strip())))
|