70 lines
2.2 KiB
Python
70 lines
2.2 KiB
Python
#!/usr/bin/python
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# If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
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#
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# Not all numbers produce palindromes so quickly. For example,
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#
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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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#
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# That is, 349 took three iterations to arrive at a palindrome.
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#
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# Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome
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# through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem,
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# we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for 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 it to a palindrome. In fact, 10677 is the first number to be shown
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# to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
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#
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# Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
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#
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# How many Lychrel numbers are there below ten-thousand?
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#
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# NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
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from projecteuler import is_palindrome, timing
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def is_lychrel(n: int) -> bool:
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tmp = n
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# Run for 50 iterations
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for _ in range(50):
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reverse = 0
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# Find the reverse of the given number
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while tmp > 0:
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reverse = reverse * 10
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reverse = reverse + tmp % 10
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tmp = tmp // 10
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# Add the reverse to the original number
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tmp = n + reverse
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# If the sum is palindrome, the number is not a Lychrel number.
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if is_palindrome(tmp, 10):
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return False
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n = tmp
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return True
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@timing
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def p055() -> None:
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count = 0
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# For each number, use the is_lychrel function to check if the number
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# is a Lychrel number.
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for i in range(1, 10000):
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if is_lychrel(i):
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count = count + 1
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print('Project Euler, Problem 55')
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print(f'Answer: {count}')
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if __name__ == '__main__':
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p055()
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