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AIMA-Java Core Algorithms from the book Artificial Intelligence a Modern Approach 3rd Ed.
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package aima.core.search.csp;

import aima.core.util.CancelableThread;

/**
 * Artificial Intelligence A Modern Approach (3rd Ed.): Figure 6.5, Page 215.

 * 

 * 
 *  * 
 * function BACKTRACKING-SEARCH(csp) returns a solution, or failure
 *    return BACKTRACK({ }, csp)
 * 
 * function BACKTRACK(assignment, csp) returns a solution, or failure
 *    if assignment is complete then return assignment
 *    var = SELECT-UNASSIGNED-VARIABLE(csp)
 *    for each value in ORDER-DOMAIN-VALUES(var, assignment, csp) do
 *       if value is consistent with assignment then
 *          add {var = value} to assignment
 *          inferences = INFERENCE(csp, var, value)
 *          if inferences != failure then
 *             add inferences to assignment
 *             result = BACKTRACK(assignment, csp)
 *             if result != failure then
 *                return result
 *          remove {var = value} and inferences from assignment
 *    return failure
 * 
 * 
 * 
 * Figure 6.5 A simple backtracking algorithm for constraint satisfaction
 * problems. The algorithm is modeled on the recursive depth-first search of
 * Chapter 3. By varying the functions SELECT-UNASSIGNED-VARIABLE and
 * ORDER-DOMAIN-VALUES, we can implement the general-purpose heuristic discussed
 * in the text. The function INFERENCE can optionally be used to impose arc-,
 * path-, or k-consistency, as desired. If a value choice leads to failure
 * (noticed wither by INFERENCE or by BACKTRACK), then value assignments
 * (including those made by INFERENCE) are removed from the current assignment
 * and a new value is tried.
 * 
 * @author Ruediger Lunde
 */
public class BacktrackingStrategy extends SolutionStrategy {

	public Assignment solve(CSP csp) {
		return recursiveBackTrackingSearch(csp, new Assignment());
	}

	/**
	 * Template method, which can be configured by overriding the three
	 * primitive operations below.
	 */
	private Assignment recursiveBackTrackingSearch(CSP csp,
			Assignment assignment) {
		Assignment result = null;
		if (assignment.isComplete(csp.getVariables()) || CancelableThread.currIsCanceled()) {
			result = assignment;
		} else {
			Variable var = selectUnassignedVariable(assignment, csp);
			for (Object value : orderDomainValues(var, assignment, csp)) {
				assignment.setAssignment(var, value);
				fireStateChanged(assignment, csp);
				if (assignment.isConsistent(csp.getConstraints(var))) {
					DomainRestoreInfo info = inference(var, assignment, csp);
					if (!info.isEmpty())
						fireStateChanged(csp);
					if (!info.isEmptyDomainFound()) {
						result = recursiveBackTrackingSearch(csp, assignment);
						if (result != null)
							break;
					}
					info.restoreDomains(csp);
				}
				assignment.removeAssignment(var);
			}
		}
		return result;
	}

	/**
	 * Primitive operation, selecting a not yet assigned variable. This default
	 * implementation just selects the first in the ordered list of variables
	 * provided by the CSP.
	 */
	protected Variable selectUnassignedVariable(Assignment assignment, CSP csp) {
		for (Variable var : csp.getVariables()) {
			if (!(assignment.hasAssignmentFor(var)))
				return var;
		}
		return null;
	}

	/**
	 * Primitive operation, ordering the domain values of the specified
	 * variable. This default implementation just takes the default order
	 * provided by the CSP.
	 */
	protected Iterable orderDomainValues(Variable var,
			Assignment assignment, CSP csp) {
		return csp.getDomain(var);
	}

	/**
	 * Primitive operation, which tries to prune out values from the CSP which
	 * are not possible anymore when extending the given assignment to a
	 * solution. This default implementation just leaves the original CSP as it
	 * is.
	 * 
	 * @return An object which provides informations about (1) whether changes
	 *         have been performed, (2) possibly inferred empty domains , and
	 *         (3) how to restore the domains.
	 */
	protected DomainRestoreInfo inference(Variable var, Assignment assignment,
			CSP csp) {
		return new DomainRestoreInfo().compactify();
	}
}