mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
44254cf112
* 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
"""
|
|
Pandigital prime
|
|
Problem 41: https://projecteuler.net/problem=41
|
|
|
|
We shall say that an n-digit number is pandigital if it makes use of all the digits
|
|
1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
|
|
What is the largest n-digit pandigital prime that exists?
|
|
|
|
All pandigital numbers except for 1, 4 ,7 pandigital numbers are divisible by 3.
|
|
So we will check only 7 digit pandigital numbers to obtain the largest possible
|
|
pandigital prime.
|
|
"""
|
|
from __future__ import annotations
|
|
|
|
from itertools import permutations
|
|
from math import sqrt
|
|
|
|
|
|
def is_prime(n: int) -> bool:
|
|
"""
|
|
Returns True if n is prime,
|
|
False otherwise.
|
|
>>> is_prime(67483)
|
|
False
|
|
>>> is_prime(563)
|
|
True
|
|
>>> is_prime(87)
|
|
False
|
|
"""
|
|
if n % 2 == 0:
|
|
return False
|
|
for i in range(3, int(sqrt(n) + 1), 2):
|
|
if n % i == 0:
|
|
return False
|
|
return True
|
|
|
|
|
|
def solution(n: int = 7) -> int:
|
|
"""
|
|
Returns the maximum pandigital prime number of length n.
|
|
If there are none, then it will return 0.
|
|
>>> solution(2)
|
|
0
|
|
>>> solution(4)
|
|
4231
|
|
>>> solution(7)
|
|
7652413
|
|
"""
|
|
pandigital_str = "".join(str(i) for i in range(1, n + 1))
|
|
perm_list = [int("".join(i)) for i in permutations(pandigital_str, n)]
|
|
pandigitals = [num for num in perm_list if is_prime(num)]
|
|
return max(pandigitals) if pandigitals else 0
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|