fix: correct treap split() comparison to match docstring behavior

[maitriupadhyay03-cell]

Describe your change:

The split() function in data_structures/binary_tree/treap.py uses a strict < comparison, but the docstring states:

Left tree contains all values less than split value.
Right tree contains all values greater or equal, than split value

This means when splitting by a value that already exists in the treap, the existing node ends up in the LEFT subtree instead of the RIGHT subtree, which contradicts the documented behavior.

Fix: Changed elif value < root.value: to elif value <= root.value: so that equal values go to the right subtree as documented.

Fixes #7854

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
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• Documentation change?

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[priya-sundaram-dev]

Thanks for this @maitriupadhyay03-cell — the split change is correct and finally matches the docstring. 🙌

One thing to finish before it can close #7854: this one-liner breaks erase, which was written against the old split semantics (a known gotcha noted on the issue back in 2022). The current interact_treap doctest fails after your change:

-0  → Got 0,1,2,...   (0 not erased)
-4  → Got 0,1,2,4,4,4,4,5,...

Updating erase to the new semantics fixes it and makes all doctests pass:

def erase(root: Node | None, value: int) -> Node | None:
    left, right = split(root, value)
    _, right = split(right, value + 1)
    return merge(left, right)

With both split and erase updated, python -m doctest treap.py -v is green. 👍

[priya-sundaram-dev]

Nice — that's exactly it. ✅ Pulled your branch and ran python -m doctest treap.py -v: 11 tests in 12 items, 11 passed / 0 failed. Both split and erase now line up with the docstring, and the interact_treap doctest (the -0 / -4 erase cases) is green again. This should be good to close #7854. Thanks for following through! 🙌