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* Rename all Project Euler directories: Reason: The change was done to maintain consistency throughout the directory and to keep all directories in sorted order. Due to the above change, some config files had to be modified: 'problem_22` -> `problem_022` * Update scripts to pad zeroes in PE directories
57 lines
1.5 KiB
Python
57 lines
1.5 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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from itertools import permutations
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from math import sqrt
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def is_prime(n: int) -> bool:
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"""
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Returns True if n is prime,
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False otherwise.
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>>> is_prime(67483)
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False
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>>> is_prime(563)
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True
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>>> is_prime(87)
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False
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"""
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if n % 2 == 0:
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return False
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for i in range(3, int(sqrt(n) + 1), 2):
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if n % i == 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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