TheAlgorithms-Python

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"""
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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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