67 lines
1.9 KiB
Python
67 lines
1.9 KiB
Python
#!/usr/bin/env python3
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"""
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Created on 02 Oct 2021
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@author: David Doblas Jiménez
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@email: daviddoji@pm.me
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Solution for problem 55 of Project Euler
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https://projecteuler.net/problem=55
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"""
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from utils import timeit, is_palindrome
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@timeit("Problem 55")
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def compute():
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"""
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If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
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Not all numbers produce palindromes so quickly. For example,
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349 + 943 = 1292,
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1292 + 2921 = 4213
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4213 + 3124 = 7337
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That is, 349 took three iterations to arrive at a palindrome.
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Although no one has proved it yet, it is thought that some numbers, like 196,
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never produce a palindrome. A number that never forms a palindrome through the
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reverse and add process is called a Lychrel number. Due to the theoretical nature
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of these numbers, and for the purpose of this problem, we shall assume that a
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number is Lychrel until proven otherwise. In addition you are given that for
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every number below ten-thousand, it will either:
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(i) become a palindrome in less than fifty iterations, or,
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(ii) no one, with all the computing power that exists, has managed so far to map
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it to a palindrome.
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In fact, 10677 is the first number to be shown to require over fifty iterations
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before producing a palindrome:
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4668731596684224866951378664 (53 iterations, 28-digits).
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Surprisingly, there are palindromic numbers that are themselves Lychrel numbers;
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the first example is 4994.
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How many Lychrel numbers are there below ten-thousand?
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"""
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ans = 0
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for n in range(11, 10_000):
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num = n
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is_lychrel = True
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for it in range(50):
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num += int(str(num)[::-1])
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if is_palindrome(num):
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is_lychrel = False
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break
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if is_lychrel:
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ans += 1
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return ans
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if __name__ == "__main__":
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print(f"Result for Problem 55: {compute()}")
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