fix(binomial_heap): fix data loss on duplicate keys and maintain min_…

[Kanika0306]

Describe your change:

Related issue: #15469

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

This PR fixes data loss in BinomialHeap.delete_min() when handling duplicate elements.

Issue

When inserting multiple elements, including duplicate values, into a BinomialHeap, repeatedly calling delete_min() until the heap is empty should return all inserted elements in non-decreasing order without losing any elements.

For example:

from data_structures.heap.binomial_heap import BinomialHeap

h = BinomialHeap()

for value in [1, 1, 1, 1, 1]:
    h.insert(value)

extracted = []

while not h.is_empty():
    extracted.append(h.delete_min())

assert extracted == [1, 1, 1, 1, 1]
assert h.size == 0
assert h.is_empty() is True

However, with duplicate values, h.delete_min() silently drops nodes from the heap:

from data_structures.heap.binomial_heap import BinomialHeap

h = BinomialHeap()

for value in [1, 1, 1, 1, 1]:
    h.insert(value)

extracted = []

while not h.is_empty():
    extracted.append(h.delete_min())

print(extracted)

Output:

[1, 1, 1, 1]

Only 4 elements are extracted instead of the 5 elements that were inserted.

Root Cause

BinomialHeap relies on self.min_node pointing to a root in the root list.

During tree consolidations in merge_heaps() and insert(), equal-key roots are merged via merge_trees(). If the node referenced by self.min_node is demoted to a child inside another binomial tree, self.min_node is left referencing an internal child node rather than a root.

Subsequent delete_min() calls misinterpret the child/sibling links on self.min_node as root-list links. This can sever entire binomial trees from the heap and corrupt self.size, resulting in elements being lost.

Additionally, line 359 in delete_min() casts the returned value using:

return int(min_value)

This truncates floating-point values. For example, a minimum value of 3.7 would be returned as 3.

Changes

The fix addresses the incorrect self.min_node reference after tree consolidation so that it continues to refer to a valid root.

It also removes the unnecessary integer conversion in delete_min() so that floating-point values are returned without truncation.

Expected result

After the fix, duplicate elements should remain in the heap and repeated calls to delete_min() should return every inserted element in non-decreasing order while keeping self.size consistent with the actual number of elements.

Fixes #15469

Checklist:

• I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/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 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: "Fixes # [Bug]: Data loss in BinomialHeap.delete_min() with duplicate elements #15469".

[cclauss]

Clearing all open pull requests to prepare for Hacktoberfest 2026 -- https://hacktoberfest.com

[Kanika0306]

HI @cclauss ,since PR #15470 was closed as part of the Hacktoberfest cleanup, should I resubmit this fix as a new PR during Hacktoberfest? Or should I wait for further instructions on what contributions are needed?