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Fix kahns algo sparse vertex performance - #15072

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Kanika0306 wants to merge 3 commits into
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Kanika0306:fix-kahns-algo-sparse-vertex-performance
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Fix kahns algo sparse vertex performance#15072
Kanika0306 wants to merge 3 commits into
TheAlgorithms:masterfrom
Kanika0306:fix-kahns-algo-sparse-vertex-performance

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@Kanika0306

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Describe your change:

  • Fixes the O(N) queue operation caused by list.pop(0) by using collections.deque and queue.popleft(), ensuring constant-time dequeue operations and preserving the expected O(V + E) time complexity of Kahn's topological sort algorithm.

  • Fixes an IndexError for sparse/non-contiguous integer vertex IDs by changing indegree from a list to a dictionary keyed by the graph vertices.

  • Adds doctests covering topological sorting with sparse/non-contiguous integer vertex IDs.

  • Adds doctests covering cycle detection with non-contiguous vertex IDs.

  • Add an algorithm?

  • Fix a bug or typo in an existing algorithm?

  • Add or change doctests?

  • Documentation change?

Checklist:

  • I have read 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 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: "Fixes #<ISSUE_NUMBER>".

Fixes #15071

Copilot AI lite review requested due to automatic review settings August 22, 2026 21:21
@algorithms-keeper algorithms-keeper Bot added enhancement This PR modified some existing files awaiting reviews This PR is ready to be reviewed labels Aug 22, 2026

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awaiting reviews This PR is ready to be reviewed enhancement This PR modified some existing files

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[BUG] Inefficient pop(0) queue operations and IndexError on sparse vertex IDs in graphs/kahns_algorithm_topo.py

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