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2104fa7aeb
* fixes #5434 * fixes broken solution * removes assert * removes assert * Apply suggestions from code review Co-authored-by: John Law <johnlaw.po@gmail.com> * Update project_euler/problem_003/sol1.py Co-authored-by: John Law <johnlaw.po@gmail.com>
77 lines
2.0 KiB
Python
77 lines
2.0 KiB
Python
"""
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Pandigital prime
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Problem 41: https://projecteuler.net/problem=41
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We shall say that an n-digit number is pandigital if it makes use of all the digits
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1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
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What is the largest n-digit pandigital prime that exists?
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All pandigital numbers except for 1, 4 ,7 pandigital numbers are divisible by 3.
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So we will check only 7 digit pandigital numbers to obtain the largest possible
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pandigital prime.
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"""
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from __future__ import annotations
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import math
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from itertools import permutations
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def is_prime(number: int) -> bool:
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"""Checks to see if a number is a prime in O(sqrt(n)).
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A number is prime if it has exactly two factors: 1 and itself.
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>>> is_prime(0)
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False
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>>> is_prime(1)
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False
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>>> is_prime(2)
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True
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>>> is_prime(3)
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True
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>>> is_prime(27)
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False
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>>> is_prime(87)
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False
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>>> is_prime(563)
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True
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>>> is_prime(2999)
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True
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>>> is_prime(67483)
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False
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"""
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if 1 < number < 4:
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# 2 and 3 are primes
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return True
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elif number < 2 or number % 2 == 0 or number % 3 == 0:
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# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
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return False
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# All primes number are in format of 6k +/- 1
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for i in range(5, int(math.sqrt(number) + 1), 6):
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if number % i == 0 or number % (i + 2) == 0:
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return False
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return True
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def solution(n: int = 7) -> int:
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"""
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Returns the maximum pandigital prime number of length n.
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If there are none, then it will return 0.
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>>> solution(2)
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0
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>>> solution(4)
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4231
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>>> solution(7)
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7652413
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"""
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pandigital_str = "".join(str(i) for i in range(1, n + 1))
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perm_list = [int("".join(i)) for i in permutations(pandigital_str, n)]
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pandigitals = [num for num in perm_list if is_prime(num)]
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return max(pandigitals) if pandigitals else 0
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if __name__ == "__main__":
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print(f"{solution() = }")
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