* Python file for finding number of pairs

* updating DIRECTORY.md

* fixed iterative_pair.py

* further fixed with type casting

* fixed naming conventions

* further fixed with naming convention

* documented done

* build issue fixed

* updating DIRECTORY.md

* Revert "documented done"

This reverts commit 3be15ca.

* Update canny.py

* Update test_digital_image_processing.py

* Update sobel_filter.py

* requirements.txt fixed

* keras<2.7.0

* Update sock_merchant.py

* doctest with black fixed

* Update sock_merchant.py

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

* Improve solution

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

+ As per usage examples, clause literals are a list of strings.
  + Note: symbols extracted from literals are expected to be exactly two characters.
+ self.literal boolean values are initialized to None, so must be optional
+ model values should be Booleans, but aren't guaranteed to be non-None
  in the code.
+ uses newer '... | None' annotation for Optional values
+ clauses are passed to the Formula initializer as both lists and sets, they
  are stored as lists.  Returned clauses will always be lists.
+ use explicit tuple annotation from __future__  rather than using (..., ...)
  in return signatures
+ mapping returned by dpll_algorithm is optional per the documentation.

…mmon_ancestor.py` (TheAlgorithms#5757)

* Fix type annotations in lowest_common_ancestor.py

* Refactor line 53 in lowest_common_ancestor.py

* Added 5 README files

* corrected arithmetic_analysis README

* Update audio_filters/README.md

Co-authored-by: John Law <johnlaw.po@gmail.com>

* Update backtracking/README.md

Co-authored-by: John Law <johnlaw.po@gmail.com>

* Update bit_manipulation/README.md

Co-authored-by: John Law <johnlaw.po@gmail.com>

Co-authored-by: John Law <johnlaw.po@gmail.com>

)

* Add all_construct dynamic programming implementation

* all_construct: remove the main function

* all_construct: Add type hints

* all_construct: changed map to list comprehension,fix mutable default arguments

* all_construct: fixed type hints

* all_construct: cleaner code for initializing word_bank argument

* all_construct: added an import for annotations

* all_construct: added None in the argument with word_bank

* all_construct: fixed a type hint

* all_construct: Fixed some more type hints

* Rewritten reddit.py

* Removed logging module import

* Fixed minor bug which was causing extreme rate limiting

* Update reddit.py

* Update reddit.py

* Update reddit.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Improve solution

* Uncomment code that has been commented due to slow execution affecting Travis

* Fix

…_tree.py` (TheAlgorithms#5739)

* [mypy] Fix type annotations in red_black_tree.py

* Remove blank lines

* Update red_black_tree.py

* Improve solution

* Uncomment code that has been commented due to slow execution affecting Travis

* Fix

* scikit-fuzzy is causing broken builds

* fuzz = None

* Update fuzzy_operations.py

Co-authored-by: Christian Clauss <cclauss@me.com>

)

* Fix finding_bridges algorithms + tests

* update type hints

* Better, more obvious condition fix

* fix prev commit + more tests

* Short explanation + url

* Update finding_bridges.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Improve Project Euler Problem 10 Sol-1

* Name correction

* psf/black formatting

* More formatting

* updating DIRECTORY.md

* Fix typo

* Improve solution

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…lement.py` (TheAlgorithms#5763)

* Fix type annotations in next_greater_element.py

* Refactor next_greater_element.py

* DRAFT: Run a mypy reality check

Let's see what is required to finish  TheAlgorithms#4052

* mypy --ignore-missing-imports --install-types --non-interactive

* Check our progress...

* Update build.yml

* Update build.yml

* Update build.yml

* Update build.yml

* mypy --exclude 20 files

* --exclude with no `=`

* Update build.yml

* 558 character regex!!!

* With quotes

* mypy.ini: mega exclude

* Update mypy.ini

* Update build.yml

* Update mypy.ini

* Update build.yml

* Update mypy.ini

* .py --> .p*

* Escape the dots!: `.` --> `\.`

* Remove the comment

* Leading slash

* Update mypy.ini

Co-authored-by: Dylan Buchi <devybuchi@gmail.com>

Co-authored-by: Dylan Buchi <devybuchi@gmail.com>