Python/project_euler/problem_047/sol1.py
Dhruv 44254cf112
Rename Project Euler directories and other dependent changes (#3300)
* 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
2020-10-15 12:43:28 +05:30

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"""
Combinatoric selections
Problem 47
The first two consecutive numbers to have two distinct prime factors are:
14 = 2 × 7
15 = 3 × 5
The first three consecutive numbers to have three distinct prime factors are:
644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.
Find the first four consecutive integers to have four distinct prime factors each.
What is the first of these numbers?
"""
from functools import lru_cache
def unique_prime_factors(n: int) -> set:
"""
Find unique prime factors of an integer.
Tests include sorting because only the set really matters,
not the order in which it is produced.
>>> sorted(set(unique_prime_factors(14)))
[2, 7]
>>> sorted(set(unique_prime_factors(644)))
[2, 7, 23]
>>> sorted(set(unique_prime_factors(646)))
[2, 17, 19]
"""
i = 2
factors = set()
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.add(i)
if n > 1:
factors.add(n)
return factors
@lru_cache
def upf_len(num: int) -> int:
"""
Memoize upf() length results for a given value.
>>> upf_len(14)
2
"""
return len(unique_prime_factors(num))
def equality(iterable: list) -> bool:
"""
Check equality of ALL elements in an interable.
>>> equality([1, 2, 3, 4])
False
>>> equality([2, 2, 2, 2])
True
>>> equality([1, 2, 3, 2, 1])
False
"""
return len(set(iterable)) in (0, 1)
def run(n: int) -> list:
"""
Runs core process to find problem solution.
>>> run(3)
[644, 645, 646]
"""
# Incrementor variable for our group list comprehension.
# This serves as the first number in each list of values
# to test.
base = 2
while True:
# Increment each value of a generated range
group = [base + i for i in range(n)]
# Run elements through out unique_prime_factors function
# Append our target number to the end.
checker = [upf_len(x) for x in group]
checker.append(n)
# If all numbers in the list are equal, return the group variable.
if equality(checker):
return group
# Increment our base variable by 1
base += 1
def solution(n: int = 4) -> int:
"""Return the first value of the first four consecutive integers to have four
distinct prime factors each.
>>> solution()
134043
"""
results = run(n)
return results[0] if len(results) else None
if __name__ == "__main__":
print(solution())