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GraphAware Framework Module exposing custom graph algorithms as Java and REST APIs
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/*
 * Copyright (c) 2013-2016 GraphAware
 *
 * This file is part of the GraphAware Framework.
 *
 * GraphAware Framework is free software: you can redistribute it and/or modify it under the terms of
 * the GNU General Public License as published by the Free Software Foundation, either
 * version 3 of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
 * without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 * See the GNU General Public License for more details. You should have received a copy of
 * the GNU General Public License along with this program.  If not, see
 * .
 */

package com.graphaware.module.algo.generator.distribution;

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

import static java.lang.Math.min;

/**
 * Simple {@link com.graphaware.module.algo.generator.distribution.DegreeDistribution} where the node degrees can be
 * directly passed into the constructor.
 */
public class SimpleDegreeDistribution implements DegreeDistribution {

    protected final List degrees = new ArrayList<>();

    /**
     * Create a new distribution.
     *
     * @param degrees degrees of nodes.
     */
    public SimpleDegreeDistribution(List degrees) {
        this.degrees.addAll(degrees);
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public List getDegrees() {
        return Collections.unmodifiableList(degrees);
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public boolean isZeroList() {
        for (int degree : degrees) {
            if (degree > 0) {
                return false;
            }
        }
        return true;
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public int get(int index) {
        return degrees.get(index);
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public int size() {
        return degrees.size();
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public boolean isValid() {
        return passesErdosGallaiTest();
    }

    /**
     * All valid distributions must be graphical. This is tested using Erdos-Gallai condition on degree distribution
     * graphicality. (see Blitzstein-Diaconis paper)
     *
     * @return true iff passes.
     */
    private boolean passesErdosGallaiTest() {
        MutableDegreeDistribution copy = new MutableSimpleDegreeDistribution(getDegrees());

        int L = copy.size();
        int degreeSum = 0;           // Has to be even by the handshaking lemma

        for (int degree : copy.getDegrees()) {
            if (degree < 0) {
                return false;
            }
            degreeSum += degree;
        }

        if (degreeSum % 2 != 0) {
            return false;
        }

        copy.sort(Collections.reverseOrder());

        // Erdos-Gallai test
        for (int k = 1; k < L; ++k) {
            int sum = 0;
            for (int i = 0; i < k; ++i) {
                sum += copy.get(i);
            }

            int comp = 0;
            for (int j = k; j < L; ++j) {
                comp += min(k, copy.get(j));
            }

            if (sum > k * (k - 1) + comp) {
                return false;
            }
        }

        return true;
    }

    /**
     * Havel-Hakimi is a recursive alternative to the Erdos-Gallai condition. This is a looped implementation, the
     * algorithm is recursive in nature, but recursion is slower.
     * 
     * Kept as a backup, might be useful as a replacement for E-G eventually.
     *
     * @return true iff passes.
     */
    protected final boolean passesHavelHakimiTest() {
        MutableDegreeDistribution copy = new MutableSimpleDegreeDistribution(getDegrees());

        int i = 0;
        int first;
        int L = this.size();

        while (L > 0) {
            first = copy.get(i);
            L--;

            int j = 1;
            for (int k = 0; k < first; ++k) {
                while (copy.get(j) == 0) {

                    j++;
                    if (j > L) {
                        return false;
                    }
                }

                copy.set(j, copy.get(j) - 1);
            }

            copy.set(i, 0);
            copy.sort(Collections.reverseOrder());
        }

        return true;
    }
}