## Introduction

The Python constraint module offers solvers for Constraint Solving Problems (CSPs) over finite domains in simple and pure Python. 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, ...).

## Examples

### Basics

This interactive Python session demonstrates the module basic operation:

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

### Rooks problem

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() ```

### Magic squares

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() ```

## Features

The following solvers are available:

• Backtracking solver
• Recursive backtracking solver
• Minimum conflicts solver

Predefined constraint types currently available:

• FunctionConstraint
• AllDifferentConstraint
• AllEqualConstraint
• ExactSumConstraint
• MaxSumConstraint
• MinSumConstraint
• InSetConstraint
• NotInSetConstraint
• SomeInSetConstraint
• SomeNotInSetConstraint

## API documentation

Documentation for the module is available at:

http://labix.org/doc/constraint/