[parijat1222q]

Describe your change

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

Comparable in sorts/iterative_merge_sort.py requires only __lt__, but merge uses <=. Values that implement the declared protocol can therefore be sorted by Python's sorted and the sibling merge_sort, yet fail here with TypeError.

Select from the right when right[0] < left[0]; otherwise select from the left. This uses only the declared operation and keeps the left-first ordering for equal keys. It does not change the existing pop(0) implementation or other algorithms.

Related contract: #15234 and #15413. This is a runtime fix, not another type-annotation change. No closing keyword is used for the umbrella issue.

Reproduction

On master at 574d100b7181956e9c8384552fd078165e4cc326, with Python 3.15t:

from sorts.iterative_merge_sort import iter_merge_sort

class Item:
    def __init__(self, key):
        self.key = key

    def __lt__(self, other):
        return self.key < other.key

items = [Item(2), Item(1)]
print([item.key for item in iter_merge_sort(items)])

Before: TypeError: '<=' not supported between instances of 'Item' and 'Item'.
After: [1, 2].

Validation

The current contribution guide asks not to change code and doctests in the same PR, so this changes one algorithm source file only. Existing doctests are unchanged.

• External local regression failed on the base and passed with this fix. It checks all 1,093 key sequences of lengths 0 through 6 over keys {0, 1, 2}, using objects that define only __lt__; compares object identity/order with sorted (including stable ties), checks input preservation, exercises merge directly, and retains TypeError for [1, "a"].
• uv run --python 3.15t --no-project --with pytest python -m pytest -q -o addopts= tests/test_sorts.py sorts/iterative_merge_sort.py --doctest-modules: 456 passed.
• ruff check sorts/iterative_merge_sort.py and ruff format --check sorts/iterative_merge_sort.py: passed.
• Tested on Linux. The full repository suite and native Windows have not been run for this target 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.
• All new Python files are placed inside an existing directory. (No new files.)
• 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. (Unchanged.)
• All functions have doctests that pass the automated testing. (Existing selected doctests pass locally; CI pending.)
• All new algorithms include at least one reference URL. (No new algorithm.)
• If this pull request resolves open issues, the description includes closing keywords. (No open issue is claimed resolved.)