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