The python-constraint module offers efficient solvers for Constraint Satisfaction Problems (CSPs) over finite domains in an accessible Python package. CSP is class of problems which may be represented in terms of variables (a, b, ...), domains (a in [1, 2, 3], ...), and constraints (a < b, ...).

This interactive Python session demonstrates basic operations:

>>> from constraint import *
>>> problem = Problem()
>>> problem.addVariable("a", [1,2,3])
>>> problem.addVariable("b", [4,5,6])
>>> problem.getSolutions()  # doctest: +NORMALIZE_WHITESPACE
[{'a': 3, 'b': 6}, {'a': 3, 'b': 5}, {'a': 3, 'b': 4},
 {'a': 2, 'b': 6}, {'a': 2, 'b': 5}, {'a': 2, 'b': 4},
 {'a': 1, 'b': 6}, {'a': 1, 'b': 5}, {'a': 1, 'b': 4}]

>>> problem.addConstraint("a*2 == b") # string constraints are preferable over the black-box problem.addConstraint(lambda a, b: a*2 == b, ("a", "b"))
>>> problem.getSolutions()
[{'a': 3, 'b': 6}, {'a': 2, 'b': 4}]

>>> problem = Problem()
>>> problem.addVariables(["a", "b"], [1, 2, 3])
>>> problem.addConstraint(AllDifferentConstraint())
>>> problem.getSolutions()  # doctest: +NORMALIZE_WHITESPACE
[{'a': 3, 'b': 2}, {'a': 3, 'b': 1}, {'a': 2, 'b': 3},
 {'a': 2, 'b': 1}, {'a': 1, 'b': 2}, {'a': 1, 'b': 3}]

The following example solves the classical Eight Rooks problem:

>>> problem = Problem()
>>> numpieces = 8
>>> cols = range(numpieces)
>>> rows = range(numpieces)
>>> problem.addVariables(cols, rows)
>>> for col1 in cols:
...     for col2 in cols:
...         if col1 < col2:
...             problem.addConstraint(lambda row1, row2: row1 != row2, (col1, col2))
>>> solutions = problem.getSolutions()
>>> solutions   # doctest: +NORMALIZE_WHITESPACE +ELLIPSIS
[{0: 7, 1: 6, 2: 5, 3: 4, 4: 3, 5: 2, 6: 1, 7: 0},
 {0: 7, 1: 6, 2: 5, 3: 4, 4: 3, 5: 2, 6: 0, 7: 1},
 {0: 7, 1: 6, 2: 5, 3: 4, 4: 3, 5: 1, 6: 2, 7: 0},
 {0: 7, 1: 6, 2: 5, 3: 4, 4: 3, 5: 1, 6: 0, 7: 2},
 ...
 {0: 7, 1: 5, 2: 3, 3: 6, 4: 2, 5: 1, 6: 4, 7: 0},
 {0: 7, 1: 5, 2: 3, 3: 6, 4: 1, 5: 2, 6: 0, 7: 4},
 {0: 7, 1: 5, 2: 3, 3: 6, 4: 1, 5: 2, 6: 4, 7: 0},
 {0: 7, 1: 5, 2: 3, 3: 6, 4: 1, 5: 4, 6: 2, 7: 0},
 {0: 7, 1: 5, 2: 3, 3: 6, 4: 1, 5: 4, 6: 0, 7: 2},
 ...]

This example solves a 4x4 magic square:

>>> problem = Problem()
>>> problem.addVariables(range(0, 16), range(1, 16 + 1))
>>> problem.addConstraint(AllDifferentConstraint(), range(0, 16))
>>> problem.addConstraint(ExactSumConstraint(34), [0, 5, 10, 15])
>>> problem.addConstraint(ExactSumConstraint(34), [3, 6, 9, 12])
>>> for row in range(4):
...     problem.addConstraint(ExactSumConstraint(34), [row * 4 + i for i in range(4)])
>>> for col in range(4):
...     problem.addConstraint(ExactSumConstraint(34), [col + 4 * i for i in range(4)])
>>> solutions = problem.getSolutions()  # doctest: +SKIP

The following solvers are available:

• OptimizedBacktrackingSolver (default)
• BacktrackingSolver
• RecursiveBacktrackingSolver
• MinConflictsSolver
• ParallelSolver

Predefined constraint types currently available (use the parsing for automatic conversion to these types):

• FunctionConstraint
• AllDifferentConstraint
• AllEqualConstraint
• ExactSumConstraint
• MinSumConstraint
• MaxSumConstraint
• MinProdConstraint
• ExactProdConstraint
• MaxProdConstraint
• VariableExactSumConstraint
• VariableMinSumConstraint
• VariableMaxSumConstraint
• VariableMinProdConstraint
• VariableExactProdConstraint
• VariableMaxProdConstraint
• InSetConstraint
• NotInSetConstraint
• SomeInSetConstraint
• SomeNotInSetConstraint

Documentation for the module is available at: http://python-constraint.github.io/python-constraint/. It can be built locally by running make clean html from the docs folder. For viewing RST files locally, restview is recommended.

$ pip install python-constraint2

Run nox (tests for all supported Python versions in own virtual environment).

To test against your local Python version: make sure you have the development dependencies installed. Run pytest (optionally add --no-cov if you have the C-extensions enabled).

Feel free to contribute by submitting pull requests or opening issues. Please refer to the contribution guidelines before doing so.

This GitHub organization and repository is a global effort to help to maintain python-constraint, which was written by Gustavo Niemeyer and originaly located at https://labix.org/python-constraint. For an overview of recent changes, visit the Changelog.

Planned development:

• Support constant modifiers on parsed (variable) constraints instead defaulting to FunctionConstraint, e.g. problem.addConstraint("a+2 == b") or problem.addConstraint("x / y == 100")
• Parse using Abstract Syntax Trees (AST) instead of the current parser to be more robust and support decomposing lambdas
• Rewrite hotspots in C / Pyx instead of pure python mode
• Improvements to make the ParallelSolver competitive (experiments reveal the freethreading mode to be promising)
• Versioned documentation

• Floris-Jan Willemsen <fjwillemsen97@gmail.com> (current maintainer)
• Sébastien Celles <s.celles@gmail.com> (former maintainer)
• Gustavo Niemeyer <gustavo@niemeyer.net> (initial developer)

But it's probably better to open an issue.