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/*
 * Copyright (c) 2013, SRI International
 * All rights reserved.
 * Licensed under the The BSD 3-Clause License;
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at:
 * 
 * http://opensource.org/licenses/BSD-3-Clause
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 
 * Redistributions of source code must retain the above copyright
 * notice, this list of conditions and the following disclaimer.
 * 
 * Redistributions in binary form must reproduce the above copyright
 * notice, this list of conditions and the following disclaimer in the
 * documentation and/or other materials provided with the distribution.
 * 
 * Neither the name of the aic-expresso nor the names of its
 * contributors may be used to endorse or promote products derived from
 * this software without specific prior written permission.
 * 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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package com.sri.ai.grinder.sgdpllt.theory.equality;

import static com.sri.ai.expresso.helper.Expressions.TRUE;
import static com.sri.ai.expresso.helper.Expressions.apply;
import static com.sri.ai.expresso.helper.Expressions.zipApply;
import static com.sri.ai.grinder.sgdpllt.library.FunctorConstants.DISEQUALITY;
import static com.sri.ai.util.Util.arrayList;
import static com.sri.ai.util.Util.arrayListFrom;
import static com.sri.ai.util.Util.in;
import static com.sri.ai.util.Util.list;
import static com.sri.ai.util.Util.thereExists;
import static com.sri.ai.util.Util.toLinkedHashSet;
import static com.sri.ai.util.base.PairOf.makePairOf;
import static com.sri.ai.util.collect.FunctionIterator.functionIterator;

import java.util.ArrayList;
import java.util.Iterator;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.Set;

import com.google.common.annotations.Beta;
import com.google.common.base.Function;
import com.sri.ai.expresso.api.Expression;
import com.sri.ai.expresso.api.Type;
import com.sri.ai.grinder.helper.GrinderUtil;
import com.sri.ai.grinder.sgdpllt.api.Context;
import com.sri.ai.grinder.sgdpllt.core.solver.AbstractBooleanWithPropagatedLiteralsRequiringPropagatedLiteralsAndCNFToBeSatisfiedStepSolver;
import com.sri.ai.grinder.sgdpllt.library.Equality;
import com.sri.ai.util.Util;
import com.sri.ai.util.base.PairOf;
import com.sri.ai.util.collect.CartesianProductIterator;
import com.sri.ai.util.collect.FunctionIterator;
import com.sri.ai.util.collect.NestedIterator;
import com.sri.ai.util.collect.PairOfElementsInListIterator;
import com.sri.ai.util.collect.PermutationIterator;
import com.sri.ai.util.collect.PredicateIterator;
import com.sri.ai.util.collect.SubsetsOfKIterator;

/**
 * A {@link AbstractBooleanWithPropagatedLiteralsRequiringPropagatedLiteralsAndCNFToBeSatisfiedStepSolver} for a {@link SingleVariableEqualityConstraint}.
 * 
 * This step solver works by providing propagated literals of the form Y op Z
 * for every pair of literals X = Y and X op Z,
 * where X is the constraint's variable and op is either = or !=.
 * 

 * It also provides a propagated CNF that encodes the requirement that the number of distinct values
 * from which X is constrained to be disequal from does not exceed the domain size.
 * For example, X != Y and X != Z and X != a, with X's type {a, b, c, d},
 * propagates the CNF (Y != b or Z = c) and (Y != b or Z != d) and (Y != c or Z != b) and (Y != c or Z != d) and (Y != d and Z != b) and (Y != d and Z != c).
 * 

 * In general, we must generate a CNF with a clause negating each possible assignment of variables disequal from X
 * to a permutation of k distinct uniquely named constants not constrained to be disequal from X,
 * where k is the type size minus the number of uniquely named constants not constrained to be disequal from X.
 * The reason for that is that, if any of these assignments were true, then X would be constrained
 * to be difference from the uniquely named constants it already is constrained against in the constraint itself,
 * plus constrained to be different from k other uniquely named constants,
 * meaning that has to be disequal from a number of uniquely named constants equal to its type's size,
 * leaving no possible assignment to it.
 * 

 * While the size of this propagated CNF depends on X's type size, which can be very large,
 * this check is only needed if the number of terms to which X is constrained to be
 * disequal from is equally large. This preserves
 * the fact that the algorithm's time complexity depends on the constraint size alone,
 * not the type size.
 *
 * @author braz
 *
 */
@Beta
public class SatisfiabilityOfSingleVariableEqualityConstraintStepSolver extends AbstractBooleanWithPropagatedLiteralsRequiringPropagatedLiteralsAndCNFToBeSatisfiedStepSolver {

	private boolean alreadyCheckedIfNumberOfDistinctExpressionsIsLessThanStepSolverShouldBeMade = false;
	private NumberOfDistinctExpressionsIsLessThanStepSolver numberOfDistinctExpressionsIsLessThanStepSolver;
	
	public SatisfiabilityOfSingleVariableEqualityConstraintStepSolver(SingleVariableEqualityConstraint constraint) {
		super(constraint);
	}
	
	@Override
	public SingleVariableEqualityConstraint getConstraint() {
		return (SingleVariableEqualityConstraint) super.getConstraint();
	}
	
	private NumberOfDistinctExpressionsIsLessThanStepSolver getNumberOfDistinctExpressionsIsLessThanStepSolver(Context context) {
		if ( ! alreadyCheckedIfNumberOfDistinctExpressionsIsLessThanStepSolverShouldBeMade) {
			long variableTypeSize = getConstraint().getVariableTypeSize(context);
			if (variableTypeSize >= 0) {
				numberOfDistinctExpressionsIsLessThanStepSolver = new NumberOfDistinctExpressionsIsLessThanStepSolver((int) variableTypeSize, getConstraint().getDisequals());
			}
			alreadyCheckedIfNumberOfDistinctExpressionsIsLessThanStepSolverShouldBeMade = true;
		}
		return numberOfDistinctExpressionsIsLessThanStepSolver;
	}

	private void setNumberOfDistinctExpressionsIsLessThanStepSolver(NumberOfDistinctExpressionsIsLessThanStepSolver numberOfDistinctExpressionsIsLessThanStepSolver) {
		this.numberOfDistinctExpressionsIsLessThanStepSolver = numberOfDistinctExpressionsIsLessThanStepSolver;
	}
	
	@Override
	protected boolean usingDefaultImplementationOfMakePropagatedCNF() {
		return true;
	}

	@Override
	protected Iterable getPropagatedLiterals(Context context) {
		
		Iterator propagatedLiteralsIterator;

		if (getConstraint().getPropagateAllLiteralsWhenVariableIsBound()) {
			propagatedLiteralsIterator = new NestedIterator<>(getConstraint().getExternalLiterals());
		}
		else {
			
			Iterator> pairsOfEqualsToVariableIterator = pairsOfEqualsToVariableIterator();
			Iterator propagatedEqualities = functionIterator(pairsOfEqualsToVariableIterator, p -> Equality.make(p.first, p.second));

			Iterator propagatedDisequalities =
					functionIterator(arrayListsOfEqualAndDisequalToVariableIterator(), p -> apply(DISEQUALITY, p));

			propagatedLiteralsIterator =
					new NestedIterator<>(getConstraint().getExternalLiterals(), propagatedEqualities, propagatedDisequalities);
		}
	
		Iterable result = in(propagatedLiteralsIterator);
		
		return result;
	}

	protected Iterator> pairsOfEqualsToVariableIterator() {
		PairOfElementsInListIterator pairsOfPositiveAtomsIterator = 
				new PairOfElementsInListIterator<>(getConstraint().getPositiveNormalizedAtoms());
		
//		Function, PairOf> makePairOfSecondArguments = p -> makePairOf(p.first.get(1), p.second.get(1));
// above lambda somehow not working at Ciaran's environment, replacing with seemingly identical anonymous class object below		
		Function, PairOf> makePairOfSecondArguments = new Function, PairOf>() {
			@Override
			public PairOf apply(PairOf p) {
				return makePairOf(p.first.get(1), p.second.get(1));
			}
		};
		Iterator> pairsOfEqualsToVariableIterator = functionIterator(pairsOfPositiveAtomsIterator, makePairOfSecondArguments);
		
		return pairsOfEqualsToVariableIterator;
	}

	@Override
	protected Iterable> getPropagatedCNFBesidesPropagatedLiterals(Context context) {
		if ( ! variableIsBoundToUniquelyNamedConstant(context)) {
			// the following logic only holds if the variable is not bound to a uniquely named constants,
			// since that eliminates all disequalities to other uniquely named constants as redundant
	
			long variableDomainSize = getConstraint().getVariableTypeSize(context);
			if (variableDomainSize >= 0 &&
					getConstraint().numberOfDisequals() >= variableDomainSize) {
				// the following procedure can be very expensive but the condition above will rarely be satisfied
	
				ArrayList variableDisequals = getVariableDisequals(context);
				Set uniquelyNamedConstantDisequals = getUniquelyNamedConstantDisequals(context);
		
				Expression typeExpression = GrinderUtil.getTypeExpressionOfExpression(getConstraint().getVariable(), context);
				Type type = context.getTypeFromTypeExpression(typeExpression);
				ArrayList remainingUniquelyNamedConstants =
						arrayListFrom(new PredicateIterator<>(type.iterator(), c -> ! uniquelyNamedConstantDisequals.contains(c)));
	
				CartesianProductIterator> subsetOfVariableDisequalsAndRemainingConstantsPermutationIterator
				= new CartesianProductIterator>(
						() -> new SubsetsOfKIterator(variableDisequals, remainingUniquelyNamedConstants.size()),
						() -> new PermutationIterator(remainingUniquelyNamedConstants));
	
				FunctionIterator>, Iterable> clausesIterator =
						FunctionIterator.make(
								subsetOfVariableDisequalsAndRemainingConstantsPermutationIterator,
								(ArrayList> subsetAndPermutation)
								->
								clauseNegatingAssignmentOfSubsetOfVariablesToParticularPermutationOfRemainingConstants(subsetAndPermutation)
								);
	
				Iterable> clauses = in(clausesIterator);
	
				return clauses;
			}
		}
	
		// otherwise, nothing is implied.
		return list();
	}

	/**
	 * @param subsetAndPermutation
	 * @return
	 */
	private List clauseNegatingAssignmentOfSubsetOfVariablesToParticularPermutationOfRemainingConstants(ArrayList> subsetAndPermutation) {
		return zipApply(
				DISEQUALITY,
				list(
						subsetAndPermutation.get(0).iterator(),
						subsetAndPermutation.get(1).iterator()));
	}

	private Iterator> arrayListsOfEqualAndDisequalToVariableIterator() {
		
		Function, ArrayList> extractSecondArguments =
				equalityAndDisequality -> arrayList(equalityAndDisequality.get(0).get(1), equalityAndDisequality.get(1).get(1));
				
		Iterator> result =
				FunctionIterator.make(
				new CartesianProductIterator(
						() -> getConstraint().getPositiveNormalizedAtoms().iterator(),
						() -> getConstraint().getNegativeNormalizedAtoms().iterator()),
						extractSecondArguments);
		
		return result;
	}

	private boolean variableIsBoundToUniquelyNamedConstant(Context context) {
		return thereExists(getConstraint().getPositiveNormalizedAtoms(), l -> context.isUniquelyNamedConstant(l.get(1)));
	}

	private ArrayList getVariableDisequals(Context context) {
		return getConstraint().getNegativeNormalizedAtoms().stream().
		map(e -> e.get(1)). // second arguments of Variable != Term
		filter(e -> ! context.isUniquelyNamedConstant(e)). // only Variables
		collect(Util.toArrayList(10));
	}

	private LinkedHashSet getUniquelyNamedConstantDisequals(Context context) {
		return getConstraint().getNegativeNormalizedAtoms().stream().
		map(e -> e.get(1)). // second arguments of Variable != Term
		filter(e -> context.isUniquelyNamedConstant(e)). // only constants
		collect(toLinkedHashSet());
	}

	@Override
	protected Step solutionIfPropagatedLiteralsAndSplittersCNFAreSatisfied(Context context) {
		Step result;
		if (getNumberOfDistinctExpressionsIsLessThanStepSolver(context) != null) {
			Step numberStep = getNumberOfDistinctExpressionsIsLessThanStepSolver(context).step(context);
			if (numberStep.itDepends()) {
				SatisfiabilityOfSingleVariableEqualityConstraintStepSolver stepSolverIfExpressionIsTrue = clone();
				stepSolverIfExpressionIsTrue.setNumberOfDistinctExpressionsIsLessThanStepSolver((NumberOfDistinctExpressionsIsLessThanStepSolver) numberStep.getStepSolverForWhenSplitterIsTrue());
				
				SatisfiabilityOfSingleVariableEqualityConstraintStepSolver stepSolverIfExpressionIsFalse = clone();
				stepSolverIfExpressionIsFalse.setNumberOfDistinctExpressionsIsLessThanStepSolver((NumberOfDistinctExpressionsIsLessThanStepSolver) numberStep.getStepSolverForWhenSplitterIsFalse());
				
				result = new ItDependsOn(numberStep.getSplitterLiteral(), numberStep.getContextSplittingWhenSplitterIsLiteral(), stepSolverIfExpressionIsTrue, stepSolverIfExpressionIsFalse);
			}
			else {
				result = new Solution(numberStep.getValue());
			}
		}
		else {
			result = new Solution(TRUE);
		}
		return result;
	}
	
	@Override
	public SatisfiabilityOfSingleVariableEqualityConstraintStepSolver clone() {
		return (SatisfiabilityOfSingleVariableEqualityConstraintStepSolver) super.clone();
	}
}