mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 21:41:08 +00:00
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>
120 lines
3.2 KiB
Python
120 lines
3.2 KiB
Python
"""
|
|
Truncatable primes
|
|
Problem 37: https://projecteuler.net/problem=37
|
|
|
|
The number 3797 has an interesting property. Being prime itself, it is possible
|
|
to continuously remove digits from left to right, and remain prime at each stage:
|
|
3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
|
|
|
|
Find the sum of the only eleven primes that are both truncatable from left to right
|
|
and right to left.
|
|
|
|
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
|
|
"""
|
|
|
|
from __future__ import annotations
|
|
|
|
import math
|
|
|
|
|
|
def is_prime(number: int) -> bool:
|
|
"""Checks to see if a number is a prime in O(sqrt(n)).
|
|
|
|
A number is prime if it has exactly two factors: 1 and itself.
|
|
|
|
>>> is_prime(0)
|
|
False
|
|
>>> is_prime(1)
|
|
False
|
|
>>> is_prime(2)
|
|
True
|
|
>>> is_prime(3)
|
|
True
|
|
>>> is_prime(27)
|
|
False
|
|
>>> is_prime(87)
|
|
False
|
|
>>> is_prime(563)
|
|
True
|
|
>>> is_prime(2999)
|
|
True
|
|
>>> is_prime(67483)
|
|
False
|
|
"""
|
|
|
|
if 1 < number < 4:
|
|
# 2 and 3 are primes
|
|
return True
|
|
elif number < 2 or number % 2 == 0 or number % 3 == 0:
|
|
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
|
|
return False
|
|
|
|
# All primes number are in format of 6k +/- 1
|
|
for i in range(5, int(math.sqrt(number) + 1), 6):
|
|
if number % i == 0 or number % (i + 2) == 0:
|
|
return False
|
|
return True
|
|
|
|
|
|
def list_truncated_nums(n: int) -> list[int]:
|
|
"""
|
|
Returns a list of all left and right truncated numbers of n
|
|
>>> list_truncated_nums(927628)
|
|
[927628, 27628, 92762, 7628, 9276, 628, 927, 28, 92, 8, 9]
|
|
>>> list_truncated_nums(467)
|
|
[467, 67, 46, 7, 4]
|
|
>>> list_truncated_nums(58)
|
|
[58, 8, 5]
|
|
"""
|
|
str_num = str(n)
|
|
list_nums = [n]
|
|
for i in range(1, len(str_num)):
|
|
list_nums.append(int(str_num[i:]))
|
|
list_nums.append(int(str_num[:-i]))
|
|
return list_nums
|
|
|
|
|
|
def validate(n: int) -> bool:
|
|
"""
|
|
To optimize the approach, we will rule out the numbers above 1000,
|
|
whose first or last three digits are not prime
|
|
>>> validate(74679)
|
|
False
|
|
>>> validate(235693)
|
|
False
|
|
>>> validate(3797)
|
|
True
|
|
"""
|
|
if len(str(n)) > 3:
|
|
if not is_prime(int(str(n)[-3:])) or not is_prime(int(str(n)[:3])):
|
|
return False
|
|
return True
|
|
|
|
|
|
def compute_truncated_primes(count: int = 11) -> list[int]:
|
|
"""
|
|
Returns the list of truncated primes
|
|
>>> compute_truncated_primes(11)
|
|
[23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397]
|
|
"""
|
|
list_truncated_primes: list[int] = []
|
|
num = 13
|
|
while len(list_truncated_primes) != count:
|
|
if validate(num):
|
|
list_nums = list_truncated_nums(num)
|
|
if all(is_prime(i) for i in list_nums):
|
|
list_truncated_primes.append(num)
|
|
num += 2
|
|
return list_truncated_primes
|
|
|
|
|
|
def solution() -> int:
|
|
"""
|
|
Returns the sum of truncated primes
|
|
"""
|
|
return sum(compute_truncated_primes(11))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{sum(compute_truncated_primes(11)) = }")
|