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//                   __                _      _   ________               //
//                  / /   ____  ____ _(_)____/ | / / ____/               //
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//                           /____/                                      //
//                                                                       //
//               The Next Generation Logic Library                       //
//                                                                       //
///////////////////////////////////////////////////////////////////////////
//                                                                       //
//  Copyright 2015-20xx Christoph Zengler                                //
//                                                                       //
//  Licensed under the Apache License, Version 2.0 (the "License");      //
//  you may not use this file except in compliance with the License.     //
//  You may obtain a copy of the License at                              //
//                                                                       //
//  http://www.apache.org/licenses/LICENSE-2.0                           //
//                                                                       //
//  Unless required by applicable law or agreed to in writing, software  //
//  distributed under the License is distributed on an "AS IS" BASIS,    //
//  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or      //
//  implied.  See the License for the specific language governing        //
//  permissions and limitations under the License.                       //
//                                                                       //
///////////////////////////////////////////////////////////////////////////

/*
 * Open-WBO -- Copyright (c) 2013-2015, Ruben Martins, Vasco Manquinho, Ines Lynce
 * <p>
 * Permission is hereby granted, free of charge, to any person obtaining a copy of
 * this software and associated documentation files (the "Software"), to deal in
 * the Software without restriction, including without limitation the rights to
 * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 * the Software, and to permit persons to whom the Software is furnished to do so,
 * subject to the following conditions:
 * <p>
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 * <p>
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
 * COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
 * IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */

package org.logicng.cardinalityconstraints;

import org.logicng.collections.LNGVector;
import org.logicng.datastructures.EncodingResult;
import org.logicng.formulas.Variable;

/**
 * Totalizer due to Bailleux and Boufkhad.
 * @version 2.0.0
 * @since 1.0
 */
public final class CCTotalizer {

    private enum Bound {LOWER, UPPER, BOTH}

    private LNGVector<Variable> cardinalityInvars;
    private EncodingResult result;
    private CCIncrementalData incData;

    /**
     * Constructs a new totalizer.
     */
    CCTotalizer() {
        // intentionally left empty
    }

    /**
     * Builds an at-most-k constraint.
     * @param result the result
     * @param vars   the variables
     * @param rhs    the right-hand side
     * @throws IllegalArgumentException if the right-hand side of the constraint was negative
     */
    void buildAMK(final EncodingResult result, final Variable[] vars, final int rhs) {
        final LNGVector<Variable> cardinalityOutvars = this.initializeConstraint(result, vars);
        this.incData = new CCIncrementalData(result, CCConfig.AMK_ENCODER.TOTALIZER, rhs, cardinalityOutvars);
        this.toCNF(cardinalityOutvars, rhs, Bound.UPPER);
        assert this.cardinalityInvars.size() == 0;
        for (int i = rhs; i < cardinalityOutvars.size(); i++) {
            this.result.addClause(cardinalityOutvars.get(i).negate());
        }
    }

    /**
     * Builds an at-least-k constraint.
     * @param result the result
     * @param vars   the variables
     * @param rhs    the right-hand side
     * @throws IllegalArgumentException if the right-hand side of the constraint was negative
     */
    void buildALK(final EncodingResult result, final Variable[] vars, final int rhs) {
        final LNGVector<Variable> cardinalityOutvars = this.initializeConstraint(result, vars);
        this.incData = new CCIncrementalData(result, CCConfig.ALK_ENCODER.TOTALIZER, rhs, vars.length, cardinalityOutvars);
        this.toCNF(cardinalityOutvars, rhs, Bound.LOWER);
        assert this.cardinalityInvars.size() == 0;
        for (int i = 0; i < rhs; i++) {
            this.result.addClause(cardinalityOutvars.get(i));
        }
    }

    /**
     * Builds an exactly-k constraint.
     * @param vars the variables
     * @param rhs  the right-hand side
     * @throws IllegalArgumentException if the right-hand side of the constraint was negative
     */
    void buildEXK(final EncodingResult result, final Variable[] vars, final int rhs) {
        final LNGVector<Variable> cardinalityOutvars = this.initializeConstraint(result, vars);
        this.toCNF(cardinalityOutvars, rhs, Bound.BOTH);
        assert this.cardinalityInvars.size() == 0;
        for (int i = 0; i < rhs; i++) {
            this.result.addClause(cardinalityOutvars.get(i));
        }
        for (int i = rhs; i < cardinalityOutvars.size(); i++) {
            this.result.addClause(cardinalityOutvars.get(i).negate());
        }
    }

    /**
     * Initializes the constraint.
     * @param vars the variables
     * @return the auxiliary variables
     */
    private LNGVector<Variable> initializeConstraint(final EncodingResult result, final Variable[] vars) {
        result.reset();
        this.result = result;
        this.cardinalityInvars = new LNGVector<>(vars.length);
        final LNGVector<Variable> cardinalityOutvars = new LNGVector<>(vars.length);
        for (final Variable var : vars) {
            this.cardinalityInvars.push(var);
            cardinalityOutvars.push(this.result.newVariable());
        }
        return cardinalityOutvars;
    }

    /**
     * Returns the incremental data for the current encoded constraint.
     * @return the incremental data for the current encoded constraint
     */
    CCIncrementalData incrementalData() {
        return this.incData;
    }

    private void toCNF(final LNGVector<Variable> vars, final int rhs, final Bound bound) {
        final LNGVector<Variable> left = new LNGVector<>();
        final LNGVector<Variable> right = new LNGVector<>();
        assert vars.size() > 1;
        final int split = vars.size() / 2;
        for (int i = 0; i < vars.size(); i++) {
            if (i < split) {
                if (split == 1) {
                    assert this.cardinalityInvars.size() > 0;
                    left.push(this.cardinalityInvars.back());
                    this.cardinalityInvars.pop();
                } else {
                    left.push(this.result.newVariable());
                }
            } else {
                if (vars.size() - split == 1) {
                    assert this.cardinalityInvars.size() > 0;
                    right.push(this.cardinalityInvars.back());
                    this.cardinalityInvars.pop();
                } else {
                    right.push(this.result.newVariable());
                }
            }
        }
        if (bound == Bound.UPPER || bound == Bound.BOTH) {
            this.adderAMK(left, right, vars, rhs);
        }
        if (bound == Bound.LOWER || bound == Bound.BOTH) {
            this.adderALK(left, right, vars);
        }
        if (left.size() > 1) {
            this.toCNF(left, rhs, bound);
        }
        if (right.size() > 1) {
            this.toCNF(right, rhs, bound);
        }
    }

    private void adderAMK(final LNGVector<Variable> left, final LNGVector<Variable> right,
                          final LNGVector<Variable> output, final int rhs) {
        assert output.size() == left.size() + right.size();
        for (int i = 0; i <= left.size(); i++) {
            for (int j = 0; j <= right.size(); j++) {
                if (i == 0 && j == 0) {
                    continue;
                }
                if (i + j > rhs + 1) {
                    continue;
                }
                if (i == 0) {
                    this.result.addClause(right.get(j - 1).negate(), output.get(j - 1));
                } else if (j == 0) {
                    this.result.addClause(left.get(i - 1).negate(), output.get(i - 1));
                } else {
                    this.result.addClause(left.get(i - 1).negate(), right.get(j - 1).negate(), output.get(i + j - 1));
                }
            }
        }
    }

    private void adderALK(final LNGVector<Variable> left, final LNGVector<Variable> right,
                          final LNGVector<Variable> output) {
        assert output.size() == left.size() + right.size();
        for (int i = 0; i <= left.size(); i++) {
            for (int j = 0; j <= right.size(); j++) {
                if (i == 0 && j == 0) {
                    continue;
                }
                if (i == 0) {
                    this.result.addClause(right.get(j - 1), output.get(left.size() + j - 1).negate());
                } else if (j == 0) {
                    this.result.addClause(left.get(i - 1), output.get(right.size() + i - 1).negate());
                } else {
                    this.result.addClause(left.get(i - 1), right.get(j - 1), output.get(i + j - 2).negate());
                }
            }
        }
    }

    @Override
    public String toString() {
        return this.getClass().getSimpleName();
    }
}
