private ISet <VAR> getConflictedVariables(Assignment <VAR, VAL> assignment, CSP <VAR, VAL> csp)
{
ISet <VAR> result = CollectionFactory.CreateSet <VAR>();
foreach (IConstraint <VAR, VAL> constraint in csp.getConstraints())
{
if (!constraint.isSatisfiedWith(assignment))
{
foreach (VAR var in constraint.getScope())
{
if (!result.Contains(var))
{
result.Add(var);
}
}
}
}
return(result);
}
/** Returns the values of Dom(var) in a special order. The least constraining value comes first. */
public ICollection <VAL> apply(CSP <VAR, VAL> csp, Assignment <VAR, VAL> assignment, VAR var)
{
ICollection <Pair <VAL, int> > pairs = CollectionFactory.CreateQueue <Pair <VAL, int> >();
foreach (VAL value in csp.getDomain(var))
{
int num = countLostValues(csp, assignment, var, value);
pairs.Add(new Pair <VAL, int>(value, num));
}
pairs.Sort(new PairComparer <VAL>());
ICollection <VAL> obj = CollectionFactory.CreateQueue <VAL>();
foreach (Pair <VAL, int> val in pairs)
{
obj.Add(val.GetFirst());
}
return(obj);
}
/** Returns variables from <code>vars</code> which are the best with respect to DEG. */
public ICollection <VAR> apply(CSP <VAR, VAL> csp, ICollection <VAR> vars)
{
ICollection <VAR> result = CollectionFactory.CreateQueue <VAR>();
int maxDegree = -1;
foreach (VAR var in vars)
{
int degree = csp.getConstraints(var).Size();
if (degree >= maxDegree)
{
if (degree > maxDegree)
{
result.Clear();
maxDegree = degree;
}
result.Add(var);
}
}
return(result);
}
/** Returns variables from <code>vars</code> which are the best with respect to MRV. */
public ICollection <VAR> apply(CSP <VAR, VAL> csp, ICollection <VAR> vars)
{
ICollection <VAR> result = CollectionFactory.CreateQueue <VAR>();
int mrv = int.MaxValue;
foreach (VAR var in vars)
{
int rv = csp.getDomain(var).size();
if (rv <= mrv)
{
if (rv < mrv)
{
result.Clear();
mrv = rv;
}
result.Add(var);
}
}
return(result);
}
/**
* Computes an explicit representation of the tree structure and a total order which is consistent with the
* parent-child relations. If the provided CSP has not the required properties (CSP contains only binary
* constraints, constraint graph is tree-structured and connected), an exception is thrown.
*
* @param csp A CSP
* @param root A root variable
* @param orderedVars The computed total order (initially empty)
* @param parentConstraints The tree structure, maps a variable to the constraint representing the arc to the parent
* variable (initially empty)
*/
private void topologicalSort(CSP <VAR, VAL> csp, VAR root, ICollection <VAR> orderedVars,
IMap <VAR, IConstraint <VAR, VAL> > parentConstraints)
{
orderedVars.Add(root);
parentConstraints.Put(root, null);
int currParentIdx = -1;
while (currParentIdx < orderedVars.Size() - 1)
{
currParentIdx++;
VAR currParent = orderedVars.Get(currParentIdx);
int arcsPointingUpwards = 0;
foreach (IConstraint <VAR, VAL> constraint in csp.getConstraints(currParent))
{
VAR neighbor = csp.getNeighbor(currParent, constraint);
if (neighbor == null)
{
throw new IllegalArgumentException("Constraint " + constraint + " is not binary.");
}
if (parentConstraints.ContainsKey(neighbor))
{ // faster than orderedVars.contains(neighbor)!
arcsPointingUpwards++;
if (arcsPointingUpwards > 1)
{
throw new IllegalArgumentException("CSP is not tree-structured.");
}
}
else
{
orderedVars.Add(neighbor);
parentConstraints.Put(neighbor, constraint);
}
}
}
if (orderedVars.Size() < csp.getVariables().Size())
{
throw new IllegalArgumentException("Constraint graph is not connected.");
}
}
public override Assignment <VAR, VAL> solve(CSP <VAR, VAL> csp)
{
Assignment <VAR, VAL> current = generateRandomAssignment(csp);
fireStateChanged(csp, current, null);
for (int i = 0; i < maxSteps && !currIsCancelled; ++i)
{
if (current.isSolution(csp))
{
return(current);
}
else
{
ISet <VAR> vars = getConflictedVariables(current, csp);
VAR var = Util.selectRandomlyFromSet(vars);
VAL value = getMinConflictValueFor(var, current, csp);
current.add(var, value);
fireStateChanged(csp, current, var);
}
}
return(null);
}
/// <summary>
/// Template method, which can be configured by overriding the three primitive operations below.
/// </summary>
/// <param name="csp"></param>
/// <param name="assignment"></param>
/// <returns>An assignment (possibly incomplete if task was cancelled) or null if no solution was found.</returns>
private Assignment <VAR, VAL> backtrack(CSP <VAR, VAL> csp, Assignment <VAR, VAL> assignment)
{
Assignment <VAR, VAL> result = null;
if (assignment.isComplete(csp.getVariables()) || currIsCancelled)
{
result = assignment;
}
else
{
VAR var = selectUnassignedVariable(csp, assignment);
foreach (VAL value in orderDomainValues(csp, assignment, var))
{
assignment.add(var, value);
fireStateChanged(csp, assignment, var);
if (assignment.isConsistent(csp.getConstraints(var)))
{
IInferenceLog <VAR, VAL> log = inference(csp, assignment, var);
if (!log.isEmpty())
{
fireStateChanged(csp, null, null);
}
if (!log.inconsistencyFound())
{
result = backtrack(csp, assignment);
if (result != null)
{
break;
}
}
log.undo(csp);
}
assignment.remove(var);
}
}
return(result);
}
/** * Computes a solution to the given CSP, which specifies values for all * variables of the CSP such that all constraints are satisfied. * * @param csp a CSP to be solved. * @return the computed solution or empty if no solution was found. */ public abstract Assignment <VAR, VAL> solve(CSP <VAR, VAL> csp);
/// <summary>
/// Applies a recursive backtracking search to solve the CSP.
/// </summary>
/// <param name="csp"></param>
/// <returns></returns>
public override Assignment <VAR, VAL> solve(CSP <VAR, VAL> csp)
{
Assignment <VAR, VAL> result = backtrack(csp, new Assignment <VAR, VAL>());
return(result);
}
/// <summary> /// Primitive operation, which tries to optimize the CSP representation with respect to a new assignment. /// </summary> /// <param name="csp"></param> /// <param name="assignment"></param> /// <param name="var">The variable which just got a new value in the assignment.</param> /// <returns> /// An object which provides information about /// (1) whether changes have been performed, /// (2) possibly inferred empty domains, and /// (3) how to restore the original CSP. /// </returns> protected abstract IInferenceLog <VAR, VAL> inference(CSP <VAR, VAL> csp, Assignment <VAR, VAL> assignment, VAR var);
/// <summary> /// Primitive operation, ordering the domain values of the specified variable. /// </summary> /// <param name="csp"></param> /// <param name="assignment"></param> /// <param name="var"></param> /// <returns></returns> protected abstract IEnumerable <VAL> orderDomainValues(CSP <VAR, VAL> csp, Assignment <VAR, VAL> assignment, VAR var);
/// <summary> /// Primitive operation, selecting a not yet assigned variable. /// </summary> /// <param name="csp"></param> /// <param name="assignment"></param> /// <returns></returns> protected abstract VAR selectUnassignedVariable(CSP <VAR, VAL> csp, Assignment <VAR, VAL> assignment);
public ICollection <VAR> apply(CSP <VAR, VAL> csp, ICollection <VAR> vars)
{
return(new DegHeuristic <VAR, VAL>().apply(csp, new MrvHeuristic <VAR, VAL>().apply(csp, vars)));
}
/**
* Establishes arc-consistency for (xi, xj).
* @return value true if the domain of xi was reduced.
*/
private bool makeArcConsistent(VAR xi, VAR xj, IConstraint <VAR, VAL> constraint, CSP <VAR, VAL> csp)
{
Domain <VAL> currDomain = csp.getDomain(xi);
ICollection <VAL> newValues = CollectionFactory.CreateQueue <VAL>();
Assignment <VAR, VAL> assignment = new Assignment <VAR, VAL>();
foreach (VAL vi in currDomain)
{
assignment.add(xi, vi);
foreach (VAL vj in csp.getDomain(xj))
{
assignment.add(xj, vj);
if (constraint.isSatisfiedWith(assignment))
{
newValues.Add(vi);
break;
}
}
}
if (newValues.Size() < currDomain.size())
{
csp.setDomain(xi, new Domain <VAL>(newValues));
return(true);
}
return(false);
}
/// <summary>
/// Returns true if this assignment is consistent as well as complete with
/// respect to the given CSP.
/// </summary>
/// <param name="csp"></param>
/// <returns></returns>
public bool isSolution(CSP <VAR, VAL> csp)
{
return(isConsistent(csp.getConstraints()) && isComplete(csp.getVariables()));
}
private VAL getMinConflictValueFor(VAR var, Assignment <VAR, VAL> assignment, CSP <VAR, VAL> csp)
{
ICollection <IConstraint <VAR, VAL> > constraints = csp.getConstraints(var);
Assignment <VAR, VAL> testAssignment = assignment.Clone();
int minConflict = int.MaxValue;
ICollection <VAL> resultCandidates = CollectionFactory.CreateQueue <VAL>();
foreach (VAL value in csp.getDomain(var))
{
testAssignment.add(var, value);
int currConflict = countConflicts(testAssignment, constraints);
if (currConflict <= minConflict)
{
if (currConflict < minConflict)
{
resultCandidates.Clear();
minConflict = currConflict;
}
resultCandidates.Add(value);
}
}
return((!resultCandidates.IsEmpty()) ? Util.selectRandomlyFromList <VAL>(resultCandidates) : default(VAL));
}