sol1.py

"""
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?
"""


defsolution(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)

 >>> solution(1000000)
 837799
 >>> solution(200)
 171
 >>> solution(5000)
 3711
 >>> solution(15000)
 13255
 """
largest_number=1
pre_counter=1
counters= {1: 1}

forinput1inrange(2, n):
counter=0
number=input1

whileTrue:
ifnumberincounters:
counter+=counters[number]
break
ifnumber%2==0:
number//=2
counter+=1
else:
number= (3*number) +1
counter+=1

ifinput1notincounters:
counters[input1] =counter

ifcounter>pre_counter:
largest_number=input1
pre_counter=counter
returnlargest_number


if__name__=="__main__":
print(solution(int(input().strip())))