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project_euler/problem_014/sol1.py
66 строк
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Maxim Smolskiy
Improve Project Euler problem 014 solution 1 (#5747)
04 ноя 2021, 18:37
Не верифицирован
04 ноя 2021, 18:37
e835e96
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""" 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? """ 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) >>> solution(1000000) 837799 >>> solution(200) 171 >>> solution(5000) 3711 >>> solution(15000) 13255 """ largest_number = 1 pre_counter = 1 counters = {1: 1} for input1 in range(2, n): counter = 0 number = input1 while True: if number in counters: counter += counters[number] break if number % 2 == 0: number //= 2 counter += 1 else: number = (3 * number) + 1 counter += 1 if input1 not in counters: counters[input1] = counter if counter > pre_counter: largest_number = input1 pre_counter = counter return largest_number if __name__ == "__main__": print(solution(int(input().strip())))