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* 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
61 lines
1.5 KiB
Python
61 lines
1.5 KiB
Python
"""
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Problem 14: https://projecteuler.net/problem=14
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Problem Statement:
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The following iterative sequence is defined for the set of positive integers:
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n → n/2 (n is even)
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n → 3n + 1 (n is odd)
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Using the rule above and starting with 13, we generate the following sequence:
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13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
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It can be seen that this sequence (starting at 13 and finishing at 1) contains
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10 terms. Although it has not been proved yet (Collatz Problem), it is thought
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that all starting numbers finish at 1.
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Which starting number, under one million, produces the longest chain?
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"""
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def solution(n: int = 1000000) -> int:
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"""Returns the number under n that generates the longest sequence using the
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formula:
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n → n/2 (n is even)
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n → 3n + 1 (n is odd)
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# The code below has been commented due to slow execution affecting Travis.
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# >>> solution(1000000)
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# 837799
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>>> solution(200)
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171
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>>> solution(5000)
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3711
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>>> solution(15000)
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13255
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"""
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largest_number = 0
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pre_counter = 0
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for input1 in range(n):
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counter = 1
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number = input1
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while number > 1:
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if number % 2 == 0:
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number /= 2
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counter += 1
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else:
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number = (3 * number) + 1
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counter += 1
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if counter > pre_counter:
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largest_number = input1
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pre_counter = counter
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return largest_number
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if __name__ == "__main__":
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print(solution(int(input().strip())))
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