/*
 * Java Genetic Algorithm Library (jenetics-7.1.0).
 * Copyright (c) 2007-2022 Franz Wilhelmstötter
 *
 * 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.
 *
 * Author:
 *    Franz Wilhelmstötter (franz.wilhelmstoetter@gmail.com)
 */
package io.jenetics;

import static java.lang.Math.abs;
import static java.lang.String.format;
import static java.util.Objects.requireNonNull;
import static io.jenetics.internal.math.Basics.pow;
import static io.jenetics.internal.math.Basics.ulpDistance;

import java.util.Comparator;
import java.util.function.Function;

import io.jenetics.internal.math.DoubleAdder;
import io.jenetics.internal.util.Arrays;
import io.jenetics.util.ISeq;
import io.jenetics.util.MSeq;
import io.jenetics.util.ProxySorter;
import io.jenetics.util.RandomRegistry;
import io.jenetics.util.Seq;

/**
 * Probability selectors are a variation of fitness proportional selectors and
 * selects individuals from a given population based on it's selection
 * probability <i>P(i)</i>.
 * <p>
 * <img src="doc-files/FitnessProportionalSelection.svg" width="400" alt="Selection">
 * <p>
 * Fitness proportional selection works as shown in the figure above. The
 * runtime complexity of the implemented probability selectors is
 * <i>O(n+</i>log<i>(n))</i> instead of <i>O(n<sup>2</sup>)</i> as for the naive
 * approach: <i>A binary (index) search is performed on the summed probability
 * array.</i>
 *
 * @author <a href="mailto:franz.wilhelmstoetter@gmail.com">Franz Wilhelmstötter</a>
 * @since 1.0
 * @version 4.0
 */
public abstract class ProbabilitySelector<
        G extends Gene<?, G>,
        C extends Comparable<? super C>
>
        implements Selector<G, C>
{
        private static final int SERIAL_INDEX_THRESHOLD = 35;

        private static final long MAX_ULP_DISTANCE = pow(10, 10);

        protected final Comparator<Phenotype<G, C>> POPULATION_COMPARATOR = (a, b) ->
                Optimize.MAXIMUM.<C>descending().compare(a.fitness(), b.fitness());

        protected final boolean _sorted;
        protected final Function<double[], double[]> _reverter;


        /**
         * Create a new {@code ProbabilitySelector} with the given {@code sorting}
         * flag. <em>This flag must set to {@code true} if the selector
         * implementation is sorting the population in the
         * {@link #probabilities(Seq, int)} method.</em>
         *
         * @param sorted {@code true} if the implementation is sorting the
         *        population when calculating the selection probabilities,
         *        {@code false} otherwise.
         */
        protected ProbabilitySelector(final boolean sorted) {
                _sorted = sorted;
                _reverter = sorted ? Arrays::revert : ProbabilitySelector::sortAndRevert;
        }

        /**
         * Create a new selector with {@code sorted = false}.
         */
        protected ProbabilitySelector() {
                this(false);
        }

        @Override
        public ISeq<Phenotype<G, C>> select(
                final Seq<Phenotype<G, C>> population,
                final int count,
                final Optimize opt
        ) {
                requireNonNull(population, "Population");
                requireNonNull(opt, "Optimization");
                if (count < 0) {
                        throw new IllegalArgumentException(format(
                                "Selection count must be greater or equal then zero, but was %s.",
                                count
                        ));
                }

                final MSeq<Phenotype<G, C>> selection = MSeq
                        .ofLength(population.isEmpty() ? 0 : count);

                if (count > 0 && !population.isEmpty()) {
                        final Seq<Phenotype<G, C>> pop = _sorted
                                ? population.asISeq().copy().sort(POPULATION_COMPARATOR)
                                : population;


                        final double[] prob = probabilities(pop, count, opt);
                        assert pop.size() == prob.length
                                : "Population size and probability length are not equal.";

                        checkAndCorrect(prob);
                        assert sum2one(prob) : "Probabilities doesn't sum to one.";

                        incremental(prob);

                        final var random = RandomRegistry.random();
                        selection.fill(() -> pop.get(indexOf(prob, random.nextDouble())));
                }

                return selection.toISeq();
        }

        /**
         * This method takes the probabilities from the
         * {@link #probabilities(Seq, int)} method and inverts it if needed.
         *
         * @param population The population.
         * @param count The number of phenotypes to select.
         * @param opt Determines whether the individuals with higher fitness values
         *        or lower fitness values must be selected. This parameter
         *        determines whether the GA maximizes or minimizes the fitness
         *        function.
         * @return Probability array.
         */
        protected final double[] probabilities(
                final Seq<Phenotype<G, C>> population,
                final int count,
                final Optimize opt
        ) {
                return requireNonNull(opt) == Optimize.MINIMUM
                        ? _reverter.apply(probabilities(population, count))
                        : probabilities(population, count);
        }

        // Package private for testing.
        static double[] sortAndRevert(final double[] array) {
                final int[] indexes = ProxySorter.sort(array);

                // Copy the elements in reversed order.
                final double[] result = new double[array.length];
                for (int i = 0; i < result.length; ++i) {
                        result[indexes[i]] = array[indexes[result.length - 1 - i]];
                }

                return result;
        }

        /**
         * <p>
         * Return an Probability array, which corresponds to the given Population.
         * The probability array and the population must have the same size. The
         * population is not sorted. If a subclass needs a sorted population, the
         * subclass is responsible to sort the population.
         * </p>
         * The implementer always assumes that higher fitness values are better. The
         * base class inverts the probabilities, by reverting the returned
         * probability array, if the GA is supposed to minimize the fitness function.
         *
         * @param population The <em>unsorted</em> population.
         * @param count The number of phenotypes to select. <i>This parameter is not
         *        needed for most implementations.</i>
         * @return Probability array. The returned probability array must have the
         *         length {@code population.size()} and <strong>must</strong> sum to
         *         one. The returned value is checked with
         *         {@code assert(Math.abs(math.sum(probabilities) - 1.0) < 0.0001)}
         *         in the base class.
         */
        protected abstract double[] probabilities(
                final Seq<Phenotype<G, C>> population,
                final int count
        );

        /**
         * Checks if the given probability values are finite. If not, all values are
         * set to the same probability.
         *
         * @param probabilities the probabilities to check.
         */
        private static void checkAndCorrect(final double[] probabilities) {
                boolean ok = true;
                for (int i = probabilities.length; --i >= 0 && ok;) {
                        ok = Double.isFinite(probabilities[i]);
                }

                if (!ok) {
                        final double value = 1.0/probabilities.length;
                        for (int i = probabilities.length; --i >= 0;) {
                                probabilities[i] = value;
                        }
                }
        }

        /**
         * Check if the given probabilities sum to one.
         *
         * @param probabilities the probabilities to check.
         * @return {@code true} if the sum of the probabilities are within the error
         *         range, {@code false} otherwise.
         */
        static boolean sum2one(final double[] probabilities) {
                final double sum = probabilities.length > 0
                        ? DoubleAdder.sum(probabilities)
                        : 1.0;
                return abs(ulpDistance(sum, 1.0)) < MAX_ULP_DISTANCE;
        }

        static boolean eq(final double a, final double b) {
                return abs(ulpDistance(a, b)) < MAX_ULP_DISTANCE;
        }

        static int indexOf(final double[] incr, final double v) {
                return incr.length <= SERIAL_INDEX_THRESHOLD
                        ? indexOfSerial(incr, v)
                        : indexOfBinary(incr, v);
        }

        /**
         * Perform a binary-search on the summed probability array.
         */
        static int indexOfBinary(final double[] incr, final double v) {
                int imin = 0;
                int imax = incr.length;
                int index = -1;

                while (imax > imin && index == -1) {
                        final int imid = (imin + imax) >>> 1;

                        if (imid == 0 || (incr[imid] >= v && incr[imid - 1] < v)) {
                                index = imid;
                        } else if (incr[imid] <= v) {
                                imin = imid + 1;
                        } else if (incr[imid] > v) {
                                imax = imid;
                        }
                }

                return index;
        }

        /**
         * Perform a serial-search on the summed probability array.
         */
        static int indexOfSerial(final double[] incr, final double v) {
                int index = -1;
                for (int i = 0; i < incr.length && index == -1; ++i) {
                        if (incr[i] >= v) {
                                index = i;
                        }
                }

                return index;
        }

        /**
         * In-place summation of the probability array.
         */
        static double[] incremental(final double[] values) {
                final DoubleAdder adder = new DoubleAdder(values[0]);
                for (int i = 1; i < values.length; ++i) {
                        values[i] = adder.add(values[i]).doubleValue();
                }
                return values;
        }

}