Python/project_euler/problem_47/sol1.py

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project_euler/problem_47/sol1.py (#2150) * Create __init__.py * Initial commit Not sure if this should be formatted differently. I'm open to ideas! * Completing testing/updates Ran code through `black`, `flake8`, and `doctest`. Added some type hints. `doctest` is finicky on sets, so I had to sort and reformat as set to pass those tests. * Update project_euler/problem_47/sol1.py Nice. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Okay, this should work. Thank you for the reminder on map(), filter(), reduce(). Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py My IDE needs a spellchecker. Or, lighter comment font. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py This means that `results = run(N)` should be updated to `results = run(n)`, correct? Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good! Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Works for me! I spent way too much time getting this to pass doctest, so any improvement is welcome. Co-authored-by: Christian Clauss <cclauss@me.com> * Update sol1.py Added some suggested changes from the pull request: * Updated tests outputs in `unique_prime_factors` function. * Changed `@lru_cache(maxsize=5)` to `@lru_cache(maxsize=None)` * Removed duplicate `return` line in `equality` function * Changed `i` to `base` in run function. * Added some commentary to `run()` function. * Replaced `group = list(map(lambda x: base + x, [i for i in range(n)]))` with `group = [base + i for i in range(n)]` * Update sol1.py * Trailing whitespace * Update sol1.py * Update __init__.py * Update sol1.py * Update __init__.py Co-authored-by: Christian Clauss <cclauss@me.com>
2020-06-25 10:25:19 +00:00
"""
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)))
project_euler/problem_47/sol1.py (#2150) * Create __init__.py * Initial commit Not sure if this should be formatted differently. I'm open to ideas! * Completing testing/updates Ran code through `black`, `flake8`, and `doctest`. Added some type hints. `doctest` is finicky on sets, so I had to sort and reformat as set to pass those tests. * Update project_euler/problem_47/sol1.py Nice. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Okay, this should work. Thank you for the reminder on map(), filter(), reduce(). Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py My IDE needs a spellchecker. Or, lighter comment font. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py This means that `results = run(N)` should be updated to `results = run(n)`, correct? Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good! Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Works for me! I spent way too much time getting this to pass doctest, so any improvement is welcome. Co-authored-by: Christian Clauss <cclauss@me.com> * Update sol1.py Added some suggested changes from the pull request: * Updated tests outputs in `unique_prime_factors` function. * Changed `@lru_cache(maxsize=5)` to `@lru_cache(maxsize=None)` * Removed duplicate `return` line in `equality` function * Changed `i` to `base` in run function. * Added some commentary to `run()` function. * Replaced `group = list(map(lambda x: base + x, [i for i in range(n)]))` with `group = [base + i for i in range(n)]` * Update sol1.py * Trailing whitespace * Update sol1.py * Update __init__.py * Update sol1.py * Update __init__.py Co-authored-by: Christian Clauss <cclauss@me.com>
2020-06-25 10:25:19 +00:00
[2, 7, 23]
>>> sorted(set(unique_prime_factors(646)))
project_euler/problem_47/sol1.py (#2150) * Create __init__.py * Initial commit Not sure if this should be formatted differently. I'm open to ideas! * Completing testing/updates Ran code through `black`, `flake8`, and `doctest`. Added some type hints. `doctest` is finicky on sets, so I had to sort and reformat as set to pass those tests. * Update project_euler/problem_47/sol1.py Nice. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Okay, this should work. Thank you for the reminder on map(), filter(), reduce(). Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py My IDE needs a spellchecker. Or, lighter comment font. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py This means that `results = run(N)` should be updated to `results = run(n)`, correct? Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good! Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Works for me! I spent way too much time getting this to pass doctest, so any improvement is welcome. Co-authored-by: Christian Clauss <cclauss@me.com> * Update sol1.py Added some suggested changes from the pull request: * Updated tests outputs in `unique_prime_factors` function. * Changed `@lru_cache(maxsize=5)` to `@lru_cache(maxsize=None)` * Removed duplicate `return` line in `equality` function * Changed `i` to `base` in run function. * Added some commentary to `run()` function. * Replaced `group = list(map(lambda x: base + x, [i for i in range(n)]))` with `group = [base + i for i in range(n)]` * Update sol1.py * Trailing whitespace * Update sol1.py * Update __init__.py * Update sol1.py * Update __init__.py Co-authored-by: Christian Clauss <cclauss@me.com>
2020-06-25 10:25:19 +00:00
[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
project_euler/problem_47/sol1.py (#2150) * Create __init__.py * Initial commit Not sure if this should be formatted differently. I'm open to ideas! * Completing testing/updates Ran code through `black`, `flake8`, and `doctest`. Added some type hints. `doctest` is finicky on sets, so I had to sort and reformat as set to pass those tests. * Update project_euler/problem_47/sol1.py Nice. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Okay, this should work. Thank you for the reminder on map(), filter(), reduce(). Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py My IDE needs a spellchecker. Or, lighter comment font. Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py This means that `results = run(N)` should be updated to `results = run(n)`, correct? Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Looks good! Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update project_euler/problem_47/sol1.py Works for me! I spent way too much time getting this to pass doctest, so any improvement is welcome. Co-authored-by: Christian Clauss <cclauss@me.com> * Update sol1.py Added some suggested changes from the pull request: * Updated tests outputs in `unique_prime_factors` function. * Changed `@lru_cache(maxsize=5)` to `@lru_cache(maxsize=None)` * Removed duplicate `return` line in `equality` function * Changed `i` to `base` in run function. * Added some commentary to `run()` function. * Replaced `group = list(map(lambda x: base + x, [i for i in range(n)]))` with `group = [base + i for i in range(n)]` * Update sol1.py * Trailing whitespace * Update sol1.py * Update __init__.py * Update sol1.py * Update __init__.py Co-authored-by: Christian Clauss <cclauss@me.com>
2020-06-25 10:25:19 +00:00
"""
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())