83 lines
2.5 KiB
Python
83 lines
2.5 KiB
Python
'''
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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, never produce a palindrome. A number that never forms a palindrome 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, 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 (i) become a palindrome in less than fifty iterations, or, (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 to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
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Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
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How many Lychrel numbers are there below ten-thousand?
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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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'''
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import time
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import math
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def reverseInt(n):
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res = 0
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while n > 0:
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res *= 10
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res += n % 10
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n = n // 10
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return res
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def palint(n):
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if n == 0:
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return True
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if int(math.log10(n)) + 1 <= 1:
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return True
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s = str(n)
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if s[0] != s[-1]:
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return False
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if len(s) == 2:
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return True
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return palint(int(s[1:-1]))
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def lychrel(n, iterations):
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res = n
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visited = set()
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for _ in range(iterations):
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visited.add(res)
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res += reverseInt(res)
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if palint(res):
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return res, visited
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return False, visited
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def main():
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print("Hello, this is Patrick")
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t0 = time.time()
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counter = 0
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lychrels = set()
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nonLychrels = set()
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for i in range(1, 10000):
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if i in lychrels:
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counter += 1
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elif i in nonLychrels:
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continue
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else:
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ans, visited = lychrel(i, 50)
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if ans:
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nonLychrels = nonLychrels.union(visited)
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else:
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lychrels = lychrels.union(visited)
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counter += 1
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print(counter, time.time() - t0)
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if __name__ == "__main__":
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main() |