Solvers

classconstraint.Solver

Abstract base class for solvers.

getSolution(domains,constraints,vconstraints)

Return one solution for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to their domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutionIter(domains,constraints,vconstraints)

Return an iterator for the solutions of the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutions(domains,constraints,vconstraints)

Return all solutions for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.BacktrackingSolver(forwardcheck=True)

Problem solver with backtracking capabilities.

Examples

>>>result=[[('a',1),('b',2)],...[('a',1),('b',3)],...[('a',2),('b',3)]]

>>>problem=Problem(BacktrackingSolver())>>>problem.addVariables(["a","b"],[1,2,3])>>>problem.addConstraint(lambdaa,b:b>a,["a","b"])

>>>solution=problem.getSolution()>>>sorted(solution.items())inresultTrue

>>>forsolutioninproblem.getSolutionIter():...sorted(solution.items())inresultTrueTrueTrue

>>>forsolutioninproblem.getSolutions():...sorted(solution.items())inresultTrueTrueTrue

Initialization method.

Parameters:

forwardcheck (bool) – If false forward checking will not berequested to constraints while looking for solutions(default is true)

getSolution(domains,constraints,vconstraints)

Return one solution for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to their domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutionIter(domains,constraints,vconstraints)

Return an iterator for the solutions of the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutions(domains,constraints,vconstraints)

Return all solutions for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.OptimizedBacktrackingSolver(forwardcheck=True)

Problem solver with backtracking capabilities, implementing several optimizations for increased performance.

Optimizations are especially in obtaining all solutions.Viewhttps://github.com/python-constraint/python-constraint/pull/76 for more details.

Examples

>>>result=[[('a',1),('b',2)],...[('a',1),('b',3)],...[('a',2),('b',3)]]

>>>problem=Problem(OptimizedBacktrackingSolver())>>>problem.addVariables(["a","b"],[1,2,3])>>>problem.addConstraint(lambdaa,b:b>a,["a","b"])

>>>solution=problem.getSolution()>>>sorted(solution.items())inresultTrue

>>>forsolutioninproblem.getSolutionIter():...sorted(solution.items())inresultTrueTrueTrue

>>>forsolutioninproblem.getSolutions():...sorted(solution.items())inresultTrueTrueTrue

Initialization method.

Parameters:

forwardcheck (bool) – If false forward checking will not berequested to constraints while looking for solutions(default is true)

getSolution(domains,constraints,vconstraints)

Return one solution for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to their domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutionIter(domains,constraints,vconstraints)

Return an iterator for the solutions of the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutions(domains,constraints,vconstraints)

Return all solutions for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutionsList(domains,vconstraints)

Optimized all-solutions finder that skips forwardchecking and returns the solutions in a list.

Return type:

list[dict[Hashable,any]]

Parameters:

• domains – Dictionary mapping variables to domains

• vconstraints – Dictionary mapping variables to a list of constraints affecting the given variables.

Returns:

the list of solutions as a dictionary.

getSortedVariables(domains,vconstraints)

Sorts the list of variables on number of vconstraints to find unassigned variables quicker.

Return type:

list

Parameters:

• domains – Dictionary mapping variables to their domains

• vconstraints – Dictionary mapping variables to a listof constraints affecting the given variables.

Returns:

the list of variables, sorted from highest number of vconstraints to lowest.

classconstraint.RecursiveBacktrackingSolver(forwardcheck=True)

Recursive problem solver with backtracking capabilities.

Examples

>>>result=[[('a',1),('b',2)],...[('a',1),('b',3)],...[('a',2),('b',3)]]

>>>problem=Problem(RecursiveBacktrackingSolver())>>>problem.addVariables(["a","b"],[1,2,3])>>>problem.addConstraint(lambdaa,b:b>a,["a","b"])

>>>solution=problem.getSolution()>>>sorted(solution.items())inresultTrue

>>>forsolutioninproblem.getSolutions():...sorted(solution.items())inresultTrueTrueTrue

>>>problem.getSolutionIter()Traceback (most recent call last):...NotImplementedError:RecursiveBacktrackingSolver doesn't provide iteration

Initialization method.

Parameters:

forwardcheck (bool) – If false forward checking will not berequested to constraints while looking for solutions(default is true)

getSolution(domains,constraints,vconstraints)

Return one solution for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to their domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutions(domains,constraints,vconstraints)

Return all solutions for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

recursiveBacktracking(solutions,domains,vconstraints,assignments,single)

Mix the Degree and Minimum Remaing Values (MRV) heuristics.

Parameters:

• solutions – _description_

• domains – _description_

• vconstraints – _description_

• assignments – _description_

• single – _description_

Returns:

_description_

classconstraint.MinConflictsSolver(steps=1000,rand=None)

Problem solver based on the minimum conflicts theory.

Examples

>>>result=[[('a',1),('b',2)],...[('a',1),('b',3)],...[('a',2),('b',3)]]

>>>problem=Problem(MinConflictsSolver())>>>problem.addVariables(["a","b"],[1,2,3])>>>problem.addConstraint(lambdaa,b:b>a,["a","b"])

>>>solution=problem.getSolution()>>>sorted(solution.items())inresultTrue

>>>problem.getSolutions()Traceback (most recent call last):...NotImplementedError:MinConflictsSolver provides only a single solution

>>>problem.getSolutionIter()Traceback (most recent call last):...NotImplementedError:MinConflictsSolver doesn't provide iteration

Initialization method.

Parameters:

• steps (int) – Maximum number of steps to perform beforegiving up when looking for a solution (default is 1000)

• rand (Random) – Optional random.Random instance to use forrepeatability.

getSolution(domains,constraints,vconstraints)

Return one solution for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to their domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.ParallelSolver(process_mode=False)

Problem solver that executes all-solution solve in parallel (ProcessPool or ThreadPool mode).

Sorts the domains on size, creating jobs for each value in the domain with the most variables.Each leaf job is solved locally with either optimized backtracking or recursion.Whether this is actually faster than non-parallel solving depends on your problem, and hardware and software environment.

Uses ThreadPool by default. Instantiate with process_mode=True to use ProcessPool.In ProcessPool mode, the jobs do not share memory.In ProcessPool mode, precompiled FunctionConstraints are not allowed due to pickling, use string constraints instead.

Examples

>>>result=[[('a',1),('b',2)],...[('a',1),('b',3)],...[('a',2),('b',3)]]

>>>problem=Problem(ParallelSolver())>>>problem.addVariables(["a","b"],[1,2,3])>>>problem.addConstraint("b > a",["a","b"])

>>>forsolutioninproblem.getSolutions():...sorted(solution.items())inresultTrueTrueTrue

>>>problem.getSolution()Traceback (most recent call last):...NotImplementedError:ParallelSolver only provides all solutions

>>>problem.getSolutionIter()Traceback (most recent call last):...NotImplementedError:ParallelSolver doesn't provide iteration

Initialization method. Setprocess_mode to True for using ProcessPool, otherwise uses ThreadPool.

getSolution(domains,constraints,vconstraints)

Return one solution for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to their domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutions(domains,constraints,vconstraints)

Return all solutions for the given problem.

Parameters:

• domains (dict) – Dictionary mapping variables to domains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

getSolutionsList(domains,vconstraints)

Parallelized all-solutions finder using ProcessPoolExecutor for work-stealing.

Return type:

list[dict[Hashable,any]]

Constraints

classconstraint.Constraint

Abstract base class for constraints.

forwardCheck(variables,domains,assignments,_unassigned=Unassigned)

Helper method for generic forward checking.

Currently, this method acts only when there’s a singleunassigned variable.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• assignments (dict) – Dictionary mapping assigned variables totheir current assumed value

Returns:

Boolean value stating if this constraint is currentlybroken or not

Return type:

bool

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.FunctionConstraint(func,assigned=True)

Constraint which wraps a function defining the constraint logic.

Examples

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>deffunc(a,b):...returnb>a>>>problem.addConstraint(func,["a","b"])>>>problem.getSolution(){'a': 1, 'b': 2}

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>deffunc(a,b):...returnb>a>>>problem.addConstraint(FunctionConstraint(func),["a","b"])>>>problem.getSolution(){'a': 1, 'b': 2}

Initialization method.

Parameters:

• func (callable object) – Function wrapped and queried forconstraint logic

• assigned (bool) – Whether the function may receive unassignedvariables or not

classconstraint.AllDifferentConstraint

Constraint enforcing that values of all given variables are different.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(AllDifferentConstraint())>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 2)], [('a', 2), ('b', 1)]]

classconstraint.AllEqualConstraint

Constraint enforcing that values of all given variables are equal.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(AllEqualConstraint())>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1)], [('a', 2), ('b', 2)]]

classconstraint.ExactSumConstraint(exactsum,multipliers=None)

Constraint enforcing that values of given variables sum exactly to a given amount.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(ExactSumConstraint(3))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 2)], [('a', 2), ('b', 1)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-1,0,1])>>>problem.addConstraint(ExactSumConstraint(0))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -1), ('b', 1)], [('a', 0), ('b', 0)], [('a', 1), ('b', -1)]]

Initialization method.

Parameters:

• exactsum (number) – Value to be considered as the exact sum

• multipliers (sequence ofnumbers) – If given, variable valueswill be multiplied by the given factors before beingsummed to be checked

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.MinSumConstraint(minsum,multipliers=None)

Constraint enforcing that values of given variables sum at least to a given amount.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(MinSumConstraint(3))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 2)], [('a', 2), ('b', 1)], [('a', 2), ('b', 2)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-3,1])>>>problem.addConstraint(MinSumConstraint(-2))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -3), ('b', 1)], [('a', 1), ('b', -3)], [('a', 1), ('b', 1)]]

Initialization method.

Parameters:

• minsum (number) – Value to be considered as the minimum sum

• multipliers (sequence ofnumbers) – If given, variable valueswill be multiplied by the given factors before beingsummed to be checked

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.MaxSumConstraint(maxsum,multipliers=None)

Constraint enforcing that values of given variables sum up to a given amount.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(MaxSumConstraint(3))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1)], [('a', 1), ('b', 2)], [('a', 2), ('b', 1)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-3,1])>>>problem.addConstraint(MaxSumConstraint(-2))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -3), ('b', -3)], [('a', -3), ('b', 1)], [('a', 1), ('b', -3)]]

Initialization method.

Parameters:

• maxsum (number) – Value to be considered as the maximum sum

• multipliers (sequence ofnumbers) – If given, variable valueswill be multiplied by the given factors before beingsummed to be checked

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.ExactProdConstraint(exactprod)

Constraint enforcing that values of given variables create a product of exactly a given amount.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(ExactProdConstraint(2))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 2)], [('a', 2), ('b', 1)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-2,-1,1,2])>>>problem.addConstraint(ExactProdConstraint(-2))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -2), ('b', 1)], [('a', -1), ('b', 2)], [('a', 1), ('b', -2)], [('a', 2), ('b', -1)]]

Instantiate an ExactProdConstraint.

Parameters:

exactprod – Value to be considered as the product

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.MinProdConstraint(minprod)

Constraint enforcing that values of given variables create a product up to at least a given amount.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(MinProdConstraint(2))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 2)], [('a', 2), ('b', 1)], [('a', 2), ('b', 2)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-2,-1,1])>>>problem.addConstraint(MinProdConstraint(1))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -2), ('b', -2)], [('a', -2), ('b', -1)], [('a', -1), ('b', -2)], [('a', -1), ('b', -1)], [('a', 1), ('b', 1)]]

Instantiate a MinProdConstraint.

Parameters:

minprod – Value to be considered as the maximum product

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.MaxProdConstraint(maxprod)

Constraint enforcing that values of given variables create a product up to at most a given amount.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(MaxProdConstraint(2))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1)], [('a', 1), ('b', 2)], [('a', 2), ('b', 1)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-2,-1,1])>>>problem.addConstraint(MaxProdConstraint(-1))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -2), ('b', 1)], [('a', -1), ('b', 1)], [('a', 1), ('b', -2)], [('a', 1), ('b', -1)]]

Instantiate a MaxProdConstraint.

Parameters:

maxprod – Value to be considered as the maximum product

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.VariableExactSumConstraint(target_var,sum_vars,multipliers=None)

Constraint enforcing that the sum of variables equals the value of another variable.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b","c"],[1,2,3])>>>problem.addConstraint(VariableExactSumConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1), ('c', 2)], [('a', 1), ('b', 2), ('c', 3)], [('a', 2), ('b', 1), ('c', 3)]]>>>problem=Problem()>>>problem.addVariable('a',[-1,0,1])>>>problem.addVariable('b',[-1,0,1])>>>problem.addVariable('c',[0,2])>>>problem.addConstraint(VariableExactSumConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -1), ('b', 1), ('c', 0)], [('a', 0), ('b', 0), ('c', 0)], [('a', 1), ('b', -1), ('c', 0)], [('a', 1), ('b', 1), ('c', 2)]]

Initialization method.

Parameters:

• target_var (Variable) – The target variable to sum to.

• sum_vars (sequence ofVariables) – The variables to sum up.

• multipliers (sequence ofnumbers) – If given, variable values(except the last) will be multiplied by the given factors before beingsummed to match the last variable.

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.VariableMinSumConstraint(target_var,sum_vars,multipliers=None)

Constraint enforcing that the sum of variables sum at least to the value of another variable.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b","c"],[1,4])>>>problem.addConstraint(VariableMinSumConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1), ('c', 1)], [('a', 1), ('b', 4), ('c', 1)], [('a', 1), ('b', 4), ('c', 4)], [('a', 4), ('b', 1), ('c', 1)], [('a', 4), ('b', 1), ('c', 4)], [('a', 4), ('b', 4), ('c', 1)], [('a', 4), ('b', 4), ('c', 4)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-3,1])>>>problem.addVariable('c',[-2,2])>>>problem.addConstraint(VariableMinSumConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -3), ('b', 1), ('c', -2)], [('a', 1), ('b', -3), ('c', -2)], [('a', 1), ('b', 1), ('c', -2)], [('a', 1), ('b', 1), ('c', 2)]]

Initialization method.

Parameters:

• target_var (Variable) – The target variable to sum to.

• sum_vars (sequence ofVariables) – The variables to sum up.

• multipliers (sequence ofnumbers) – If given, variable values(except the last) will be multiplied by the given factors before beingsummed to match the last variable.

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.VariableMaxSumConstraint(target_var,sum_vars,multipliers=None)

Constraint enforcing that the sum of variables sum at most to the value of another variable.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b","c"],[1,3,4])>>>problem.addConstraint(VariableMaxSumConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1), ('c', 3)], [('a', 1), ('b', 1), ('c', 4)], [('a', 1), ('b', 3), ('c', 4)], [('a', 3), ('b', 1), ('c', 4)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-2,1])>>>problem.addVariable('c',[-3,-1])>>>problem.addConstraint(VariableMaxSumConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -2), ('b', -2), ('c', -3)], [('a', -2), ('b', -2), ('c', -1)], [('a', -2), ('b', 1), ('c', -1)], [('a', 1), ('b', -2), ('c', -1)]]

Initialization method.

Parameters:

• target_var (Variable) – The target variable to sum to.

• sum_vars (sequence ofVariables) – The variables to sum up.

• multipliers (sequence ofnumbers) – If given, variable values(except the last) will be multiplied by the given factors before beingsummed to match the last variable.

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.VariableExactProdConstraint(target_var,product_vars)

Constraint enforcing that the product of variables equals the value of another variable.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b","c"],[1,2])>>>problem.addConstraint(VariableExactProdConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1), ('c', 1)], [('a', 1), ('b', 2), ('c', 2)], [('a', 2), ('b', 1), ('c', 2)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-2,-1,2])>>>problem.addVariable('c',[-2,1])>>>problem.addConstraint(VariableExactProdConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -1), ('b', -1), ('c', 1)], [('a', -1), ('b', 2), ('c', -2)], [('a', 2), ('b', -1), ('c', -2)]]

Instantiate a VariableExactProdConstraint.

Parameters:

• target_var (Variable) – The target variable to match.

• product_vars (sequence ofVariables) – The variables to calculate the product of.

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.VariableMinProdConstraint(target_var,product_vars)

Constraint enforcing that the product of variables is at least the value of another variable.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b","c"],[-1,2])>>>problem.addConstraint(VariableMinProdConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -1), ('b', -1), ('c', -1)], [('a', 2), ('b', 2), ('c', -1)], [('a', 2), ('b', 2), ('c', 2)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-2,-1,1])>>>problem.addVariable('c',[2,5])>>>problem.addConstraint(VariableMinProdConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -2), ('b', -2), ('c', 2)], [('a', -2), ('b', -1), ('c', 2)], [('a', -1), ('b', -2), ('c', 2)]]

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.VariableMaxProdConstraint(target_var,product_vars)

Constraint enforcing that the product of variables is at most the value of another variable.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b","c"],[-1,2])>>>problem.addConstraint(VariableMaxProdConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -1), ('b', -1), ('c', 2)], [('a', -1), ('b', 2), ('c', -1)], [('a', -1), ('b', 2), ('c', 2)], [('a', 2), ('b', -1), ('c', -1)], [('a', 2), ('b', -1), ('c', 2)]]>>>problem=Problem()>>>problem.addVariables(["a","b"],[-2,-1,1])>>>problem.addVariable('c',[-2,-3])>>>problem.addConstraint(VariableMaxProdConstraint('c',['a','b']))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', -2), ('b', 1), ('c', -2)], [('a', 1), ('b', -2), ('c', -2)]]

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.InSetConstraint(set)

Constraint enforcing that values of given variables are present in the given set.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(InSetConstraint([1]))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1)]]

Initialization method.

Parameters:

set (set) – Set of allowed values

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.NotInSetConstraint(set)

Constraint enforcing that values of given variables are not present in the given set.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(NotInSetConstraint([1]))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 2), ('b', 2)]]

Initialization method.

Parameters:

set (set) – Set of disallowed values

preProcess(variables,domains,constraints,vconstraints)

Preprocess variable domains.

This method is called before starting to look for solutions,and is used to prune domains with specific constraint logicwhen possible. For instance, any constraints with a singlevariable may be applied on all possible values and removed,since they may act on individual values even without furtherknowledge about other assignments.

Parameters:

• variables (sequence) – Variables affected by that constraint,in the same order provided by the user

• domains (dict) – Dictionary mapping variables to theirdomains

• constraints (list) – List of pairs of (constraint, variables)

• vconstraints (dict) – Dictionary mapping variables to a listof constraints affecting the given variables.

classconstraint.SomeInSetConstraint(set,n=1,exact=False)

Constraint enforcing that at least some of the values of given variables must be present in a given set.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(SomeInSetConstraint([1]))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 1)], [('a', 1), ('b', 2)], [('a', 2), ('b', 1)]]

Initialization method.

Parameters:

• set (set) – Set of values to be checked

• n (int) – Minimum number of assigned values that should bepresent in set (default is 1)

• exact (bool) – Whether the number of assigned values whichare present in set must be exactlyn

classconstraint.SomeNotInSetConstraint(set,n=1,exact=False)

Constraint enforcing that at least some of the values of given variables must not be present in a given set.

Example

>>>problem=Problem()>>>problem.addVariables(["a","b"],[1,2])>>>problem.addConstraint(SomeNotInSetConstraint([1]))>>>sorted(sorted(x.items())forxinproblem.getSolutions())[[('a', 1), ('b', 2)], [('a', 2), ('b', 1)], [('a', 2), ('b', 2)]]

Initialization method.

Parameters:

• set (set) – Set of values to be checked

• n (int) – Minimum number of assigned values that should notbe present in set (default is 1)

• exact (bool) – Whether the number of assigned values whichare not present in set must be exactlyn