Add splay tree (self-adjusting BST)

[priya-sundaram-dev]

Describe your change

Adds data_structures/binary_tree/splay_tree.py, implementing a splay tree — a self-adjusting binary search tree that moves every accessed node to the root via rotations ("splaying"), giving amortized O(log n) operations and excellent performance under locality of reference.

Requested by @cclauss in #13760.

The implementation covers:

• insert, search, delete — each splays the accessed node to the root
• Zig / zig-zig / zig-zag rotation cases in a single recursive _splay
• In-order iteration (__iter__) yielding keys in ascending order
• Full type hints and doctests for every public method

Verified locally: doctests pass, ruff check/ruff format clean, ty check clean, and a 200-trial randomized stress test confirms the tree stays consistent with a reference set across interleaved insert/search/delete.

Checklist

• Add an algorithm?
• 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 include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: Closes #13760.

Closes #13760

[algorithms-keeper]

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

• Contributing guidelines
• Project Euler solution guidelines

Python:

• Formatted string literals (f-strings)
• Type hints
• doctest
• unittest
• pytest

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[algorithms-keeper]

As there is no test file in this pull request nor any test function or class in the file data_structures/binary_tree/splay_tree.py, please provide doctest for the function __repr__

[cclauss]

Please simplify by making Node a dataclass.

[priya-sundaram-dev]

Done — pushed 4d86ab2b:

• Node is now a dataclass (key, left, right), which drops the hand-written __init__ and __repr__. The left/right children use field(repr=False) so a node still prints compactly as Node(key=10) rather than recursively dumping the whole subtree.
• Added a class docstring doctest for the repr (>>> Node(10) → Node(key=10)), which also addresses algorithms-keeper's note about __repr__.

All 30 doctests pass locally and ruff is clean. Thanks for the review!