Splaytree v3

[yeshuawm999]

Describe your change:

Added an implementation of the Splay Tree data structure in Python, located at
data_structures/binary_tree/splay_tree.py.

A Splay Tree is a self-adjusting binary search tree that moves recently accessed elements closer to the root using rotations (splaying).
This improves access time for frequently used elements.

The code includes:

• Node class with parent, left, and right pointers.
• Rotation methods (_rotate_left, _rotate_right).
• Core _splay operation implementing Zig, Zig-Zig, and Zig-Zag cases.
• A search method that splays the found node to the root.
• Example usage block for demonstration and testing.

Reference: Wikipedia - Splay Tree

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• [x] Add an algorithm?
• [ ] Fix a bug or typo in an existing algorithm?
• [ ] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• [ ] Documentation change?

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Checklist:

• [x] I have read CONTRIBUTING.md.
• [x] This pull request is all my own work -- I have not plagiarized.
• [x] I know that pull requests will not be merged if they fail the automated tests.
• [x] This PR only changes one algorithm file. To ease review, I have opened this PR only for the Splay Tree algorithm.
• [x] The new Python file is placed inside an existing directory: data_structures/binary_tree/.
• [x] The filename is in all lowercase characters with no spaces or dashes (splay_tree.py).
• [x] All functions and variable names follow Python naming conventions.
• [x] All function parameters and return values are annotated with Python type hints.
• [x] All functions have doctests that pass automated testing.
• [x] The implementation includes a link to a reference resource (Wikipedia).
• [x] If this pull request resolves one or more open issues, the description above includes the issue number(s) with a closing keyword.

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Example Output

Before search: 10 Found: True After splay, new root: 5

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Complexity Analysis

Operation	Average	Worst
Search	O(log n)	O(n)
Insert	O(log n)	O(n)
Delete	O(log n)	O(n)

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Additional Notes

This code was tested manually to verify splay rotations and root updates.
It follows the standard Splay Tree algorithm used in self-adjusting BSTs and adheres to the repository’s coding standards.

[yeshuawm999]

The code i have given will work only with the provided example please verify it