The Wayback Machine - https://web.archive.org/web/20201024220338/https://github.com/TheAlgorithms/Python/pull/3513
Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Added a solution for Project Euler Problem 203 "Squarefree Binomial Coefficients" #3513

Open
wants to merge 2 commits into
base: master
from

Conversation

@fernandobperezm
Copy link

@fernandobperezm fernandobperezm commented Oct 18, 2020

Describe your change:

Added a solution to Project Euler Problem 203 "Squarefree Binomial Coefficients" Link.

The solution is based on three main pilars.

  1. Calculate the unique coefficients of a Pascal's Triangle of depth d .
  2. Calculate the prime numbers between 2 and the maximum coefficient Cmax using a variant of the Sieve of Eratosthenes Link and considering that the square of each prime must be less or equal than that Cmax. The calculation returns the square of those primes.
  3. Calculate all squarefree numbers by decomposing each number n into n = p * p * r where p is a prime number calculated before and r is a positive integer. If no r can be found for all squared primes, then the number is squarefree, else, the number is non-squarefree.

After all unique squarefree numbers are calculated, they're summed-up to provide the final answer.

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms have a URL in its comments that points to Wikipedia or other similar explanation.
  • If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.
coefficients = set()
previous_coefficients = []
for step in range(1, depth + 1):
if step == 1:
coefficients.add(1)
previous_coefficients = [1]
else:
coefficients_begins_one = previous_coefficients + [0]
coefficients_ends_one = [0] + previous_coefficients
previous_coefficients = []
Comment on lines 52 to 61

This comment has been minimized.

@dhruvmanila

dhruvmanila Oct 19, 2020
Member
Suggested change
coefficients = set()
previous_coefficients = []
for step in range(1, depth + 1):
if step == 1:
coefficients.add(1)
previous_coefficients = [1]
else:
coefficients_begins_one = previous_coefficients + [0]
coefficients_ends_one = [0] + previous_coefficients
previous_coefficients = []
coefficients = {1}
previous_coefficients = [1]
for step in range(2, depth + 1):
coefficients_begins_one = previous_coefficients + [0]
coefficients_ends_one = [0] + previous_coefficients
previous_coefficients = []

Please test whether this works or not.

This comment has been minimized.

@fernandobperezm

fernandobperezm Oct 19, 2020
Author

Tested locally and works. Also black, flake8 and doctests pass. Commit is already on the branch :-D

…ngle. Changes based on review suggestion.
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Projects
None yet
Linked issues

Successfully merging this pull request may close these issues.

None yet

2 participants
You can’t perform that action at this time.