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Add Dancing Links (DLX) algorithm for Exact Cover problem - #13183

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cclauss merged 4 commits into
TheAlgorithms:masterfrom
fab-c14:master
Sep 16, 2026
Merged

cclauss merged 4 commits into
TheAlgorithms:masterfrom
fab-c14:master

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@fab-c14

@fab-c14 fab-c14 commented Oct 4, 2025

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Describe your change:

  • Add an algorithm
  • Fix a bug or typo in an existing algorithm
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change

This pull request adds the Dancing Links (DLX) algorithm for solving the Exact Cover problem, following Donald Knuth's Algorithm X. The implementation is placed in other/dancing_links.py, includes type hints, docstrings, and a usage example. No such algorithm currently exists in this repository.

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. 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".

@algorithms-keeper algorithms-keeper Bot added awaiting reviews This PR is ready to be reviewed tests are failing Do not merge until tests pass labels Oct 4, 2025
@algorithms-keeper algorithms-keeper Bot removed the tests are failing Do not merge until tests pass label Oct 6, 2025
@fab-c14

fab-c14 commented Oct 6, 2025

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Please, Merge this request i was doing the fixes from last 2 days, it would be appreciated

Added references to Wikipedia for Algorithm X and Dancing Links.
@algorithms-keeper algorithms-keeper Bot added the require type hints https://docs.python.org/3/library/typing.html label Sep 16, 2026

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Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

Python:

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Comment thread other/dancing_links.py Outdated
class DLXNode:
"""Represents a node in the Dancing Links structure."""

def __init__(self):

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Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:

Comment thread other/dancing_links.py Outdated
class ColumnNode(DLXNode):
"""Represents a column header node, keeping track of its column size."""

def __init__(self, name):

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Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide type hint for the parameter: name

Comment thread other/dancing_links.py Outdated
class DancingLinks:
"""Dancing Links structure for solving the Exact Cover problem."""

def __init__(self, universe, subsets):

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Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide type hint for the parameter: universe

Please provide type hint for the parameter: subsets

Comment thread other/dancing_links.py Outdated
first_node.left.right = node
first_node.left = node

def _cover(self, col):

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Please provide return type hint for the function: _cover. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide type hint for the parameter: col

Comment thread other/dancing_links.py Outdated
node = node.right
row = row.down

def _uncover(self, col):

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Please provide return type hint for the function: _uncover. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide type hint for the parameter: col

Comment thread other/dancing_links.py Outdated
col.right.left = col
col.left.right = col

def _choose_column(self):

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Please provide return type hint for the function: _choose_column. If the function does not return a value, please provide the type hint as: def function() -> None:

Comment thread other/dancing_links.py Outdated
col = col.right
return chosen

def _search(self):

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Please provide return type hint for the function: _search. If the function does not return a value, please provide the type hint as: def function() -> None:

Comment thread other/dancing_links.py Outdated

self._uncover(col)

def solve(self):

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Please provide return type hint for the function: solve. If the function does not return a value, please provide the type hint as: def function() -> None:

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Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

Python:

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

algorithms-keeper commands and options

algorithms-keeper actions can be triggered by commenting on this PR:

  • @algorithms-keeper review to trigger the checks for only added pull request files
  • @algorithms-keeper review-all to trigger the checks for all the pull request files, including the modified files. As we cannot post review comments on lines not part of the diff, this command will post all the messages in one comment.

NOTE: Commands are in beta and so this feature is restricted only to a member or owner of the organization.

Comment thread other/dancing_links.py
node = node.right
row = row.down

def _uncover(self, col: ColumnNode):

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Please provide return type hint for the function: _uncover. If the function does not return a value, please provide the type hint as: def function() -> None:

@algorithms-keeper algorithms-keeper Bot removed the awaiting reviews This PR is ready to be reviewed label Sep 16, 2026
@cclauss
cclauss merged commit 78d3358 into TheAlgorithms:master Sep 16, 2026
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