* Fix binary search with duplicates issue #13886
* Add docstrings to binary search functions
Added docstrings for lower_bound and upper_bound functions.
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* Update searches/binary_search.py
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* Refactor docstrings for lower_bound and upper_bound
Updated docstring parameter and return type annotations for lower_bound and upper_bound functions.
* Update searches/binary_search.py
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* feat: optimizing the prune function at the apriori_algorithm.py archive
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* fix: fixing the unsorted importing statment
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* fix: fixing the key structure to a tuple that can be an hashable structure
* Update apriori_algorithm.py
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* Update apriori_algorithm.py
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* Add doctest for circular queue overflow condition
Added a doctest to test the QUEUE IS FULL exception when attempting to enqueue an element into a full circular queue. This improves test coverage for line 67 in data_structures/queues/circular_queue.py.
Fixes#9943
* Update circular_queue.py
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- Add -> None return type annotation to pi_estimator function
- Improves code clarity and follows Python type hinting best practices
- Function already had proper type hints for parameters
Co-authored-by: Gunish Mukherji <gunishmukherji@Gunishs-MacBook-Air.local>
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* Fix typo in spheres intersection print statement
* Fix typo in CONTRIBUTING.md
* Improve comments in comb_sort.py
* pyproject.toml: tool.ruff.target-version = "py314"
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* Fix comment formatting in lint.ignore section
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* Added t-SNE with Iris dataset example
* Added t-SNE with Iris dataset example
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* Updated with descriptive variables
* Add descriptive variable names
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* Add Descriptive Variable names
* Adding Descriptive variable names
* Update machine_learning/t_stochastic_neighbour_embedding.py
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* Update machine_learning/t_stochastic_neighbour_embedding.py
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* Improved line formatting
* Adding URL for t-SNE Wikipedia
* Apply suggestion from @cclauss
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* added rotate_array.py
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* fixed issues
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* fixed reverse issue
* added doctests
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* changed k to steps for a descriptive name
* fixed non-pep
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* fix covid_stats_via_xpath.py
Improve error handling.
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* fix covid_stats_via_xpath.py typo
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* fix ruff
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* upgrade covid_stats_via_xpath.py
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* Update and fix covid_stats_via_xpath.py
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* pre-commit autoupdate 2025-09-11
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* Adding the function isProthNumber(n : int) which returns true if n is a Proth number
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* Fixing the issues of the isprothnumber function
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* New fixes on isprothnumber()
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* Fixes on isprothnumber()
* Fixes on isprothnumber
* Fixes on isprothnumber()
* Fixes on isprothnumber
* Update proth_number.py
* Update proth_number.py
* Update proth_number.py
* Update proth_number.py
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* Update proth_number.py
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* Added space complexity
Space complexity of merge sort is a key factor, when compared to quick sort
* Update merge_sort.py
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* Add weierstrass_method for approximating complex roots
- Implements Durand-Kerner (Weierstrass) method for polynomial root finding
- Accepts user-defined polynomial function and degree
- Uses random perturbation of complex roots of unity for initial guesses
- Handles validation, overflow clipping, and includes doctest
* Update weierstrass_method.py
* add more tests
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