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""" |
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Project Euler Problem 37: Truncatable Primes |
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============================================ |
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.. module:: solutions.problem37 |
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:synopsis: My solution to problem #37. |
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The source code for this problem can be |
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`found here <https://bitbucket.org/nekedome/project-euler/src/master/solutions/problem37.py>`_. |
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Problem Statement |
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################# |
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The number :math:`3797` has an interesting property. Being prime itself, it is possible to continuously remove digits |
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from left to right, and remain prime at each stage: :math:`3797, 797, 97`, and :math:`7`. Similarly we can work from |
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right to left: :math:`3797, 379, 37`, and :math:`3`. |
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Find the sum of the only eleven primes that are both truncatable from left to right and right to left. |
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.. note:: :math:`2, 3, 5`, and :math:`7` are not considered to be truncatable primes. |
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Solution Discussion |
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################### |
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Enumerate the prime numbers in ascending order, testing each in term for the truncatable property. For each truncatable |
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prime, accumulate their sum until eleven have been accounted for. |
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.. note:: due to the implementation of :func:`lib.sequence.Primes`, an upper-bound must be provided. This meant trial |
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and error was required to identify an appropriate bound before the code below was correct. |
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Solution Implementation |
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####################### |
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.. literalinclude:: ../../solutions/problem37.py |
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:language: python |
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:lines: 39- |
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""" |
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from typing import Set |
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from lib.digital import num_digits |
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from lib.sequence import Primes |
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def is_truncatable_prime(value: int, primes: Set[int]) -> bool: |
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""" Test whether `value` is both left to right and right to left truncatable or not |
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:param value: the integer to test |
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:param primes: a set of primes containing at least those in the range :math:`[2, value]` |
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:return: whether `value` is truncatable or not |
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""" |
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# Check for right to left truncatable |
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temp = value |
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while temp >= 10: |
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temp //= 10 |
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if temp not in primes: |
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return False |
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# Check for left to right truncatable |
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while num_digits(value) > 1: |
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value %= 10 ** (num_digits(value) - 1) |
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if value not in primes: |
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return False |
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return True |
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def solve(): |
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""" Compute the answer to Project Euler's problem #37 """ |
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upper_bound = 740000 # found by trial and error |
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primes = set(Primes(upper_bound=upper_bound)) |
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multidigit_primes = filter(lambda p: p >= 10, primes) |
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truncatable_primes = filter(lambda p: is_truncatable_prime(p, primes), multidigit_primes) |
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answer = sum(truncatable_primes) |
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return answer |
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expected_answer = 748317 |
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