feat(algorithms, strings): shortest common supersequence

[BrianLusina]

Describe your change:

Shortest common supersequence algorithm challenge and refactor on sorting algorithms

• 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}.

Summary by CodeRabbit

• New Features

  • Added Shortest Common Supersequence algorithm for computing the shortest string containing two input strings as subsequences
  • Added alternative Heapsort implementation with optimized recursive approach

• Tests

  • Comprehensive test suites added for Heapsort covering multiple numeric lists
  • Test suite added for Mergesort with edge cases

• Documentation

  • Navigation structure updated with new algorithm entries
  • Detailed documentation provided for Shortest Common Supersequence algorithm

_{✏️ Tip: You can customize this high-level summary in your review settings.}

[coderabbitai]

Caution

Review failed

The pull request is closed.

📝 Walkthrough

Walkthrough

The pull request adds documentation entries for three new algorithm implementations: Shortest Common Supersequence with its module and tests, heapsort type annotations with an alternative heapsort_2 variant using heapify_2, and test coverage for mergesort. No behavioral changes to existing code.

Changes

Cohort / File(s)	Summary
Documentation & Navigation DIRECTORY.md	Added navigation entries for Shortest Common Supersequence, Heapsort, and Mergesort sections with corresponding test links.
Shortest Common Supersequence algorithms/dynamic_programming/shortest_common_supersequence/README.md, algorithms/dynamic_programming/shortest_common_supersequence/__init__.py, algorithms/dynamic_programming/shortest_common_supersequence/test_shortest_common_supersequence.py	Introduced new SCS algorithm module with problem documentation, DP-based implementation (builds 2D table, reconstructs sequence via backtracking), and parameterized unit tests covering multiple input pairs.
Heapsort algorithms/sorting/heapsort/__init__.py, algorithms/sorting/heapsort/test_heap_sort.py	Enhanced heapsort module with comprehensive type annotations (List[Any]) across all functions, introduced heapify_2 and heapsort_2 as alternative recursive heap-building and sorting variants, and added new test module with parameterized cases for both in-place and functional heapsort variants.
Mergesort Tests algorithms/sorting/mergesort/test_merge_sort.py	Added test module validating merge_sort_in_place and merge_sort_out_of_place implementations with parameterized test cases covering various inputs including negatives and duplicates.

Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~22 minutes

Suggested labels

Strings

Poem

🐰 A sequence string unfolds so true,
With heaps and sorts, the code's renewed!
Dynamic paths through letters dance,
Merging order in each glance—
Algorithms bloom from root to leaf! 🌿

✨ Finishing touches

• 📝 Generate docstrings

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📜 Recent review details

Configuration used: defaults

Review profile: CHILL

Plan: Pro

📥 Commits

Reviewing files that changed from the base of the PR and between 599b271 and f366e87.

⛔ Files ignored due to path filters (4)

• algorithms/dynamic_programming/shortest_common_supersequence/images/examples/shortest_common_supersequence_example_1.png is excluded by !**/*.png
• algorithms/dynamic_programming/shortest_common_supersequence/images/examples/shortest_common_supersequence_example_2.png is excluded by !**/*.png
• algorithms/dynamic_programming/shortest_common_supersequence/images/examples/shortest_common_supersequence_example_3.png is excluded by !**/*.png
• algorithms/dynamic_programming/shortest_common_supersequence/images/examples/shortest_common_supersequence_example_4.png is excluded by !**/*.png

📒 Files selected for processing (7)

• DIRECTORY.md
• algorithms/dynamic_programming/shortest_common_supersequence/README.md
• algorithms/dynamic_programming/shortest_common_supersequence/__init__.py
• algorithms/dynamic_programming/shortest_common_supersequence/test_shortest_common_supersequence.py
• algorithms/sorting/heapsort/__init__.py
• algorithms/sorting/heapsort/test_heap_sort.py
• algorithms/sorting/mergesort/test_merge_sort.py

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