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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You 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.
+ */
+package org.apache.commons.math3.genetics;
+
+import org.apache.commons.math3.exception.DimensionMismatchException;
+import org.apache.commons.math3.exception.MathIllegalArgumentException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+
+import java.util.ArrayList;
+import java.util.HashSet;
+import java.util.List;
+import java.util.Set;
+
+/**
+ * Cycle Crossover [CX] builds offspring from <b>ordered</b> chromosomes by identifying cycles
+ * between two parent chromosomes. To form the children, the cycles are copied from the respective
+ * parents.
+ *
+ * <p>To form a cycle the following procedure is applied:
+ *
+ * <ol>
+ *   <li>start with the first gene of parent 1
+ *   <li>look at the gene at the same position of parent 2
+ *   <li>go to the position with the same gene in parent 1
+ *   <li>add this gene index to the cycle
+ *   <li>repeat the steps 2-5 until we arrive at the starting gene of this cycle
+ * </ol>
+ *
+ * The indices that form a cycle are then used to form the children in alternating order, i.e. in
+ * cycle 1, the genes of parent 1 are copied to child 1, while in cycle 2 the genes of parent 1 are
+ * copied to child 2, and so forth ... Example (zero-start cycle):
+ *
+ * <pre>
+ * p1 = (8 4 7 3 6 2 5 1 9 0)    X   c1 = (8 1 2 3 4 5 6 7 9 0)
+ * p2 = (0 1 2 3 4 5 6 7 8 9)    X   c2 = (0 4 7 3 6 2 5 1 8 9)
+ *
+ * cycle 1: 8 0 9
+ * cycle 2: 4 1 7 2 5 6
+ * cycle 3: 3
+ * </pre>
+ *
+ * This policy works only on {@link AbstractListChromosome}, and therefore it is parameterized by T.
+ * Moreover, the chromosomes must have same lengths.
+ *
+ * @see <a
+ *     href="http://www.rubicite.com/Tutorials/GeneticAlgorithms/CrossoverOperators/CycleCrossoverOperator.aspx">
+ *     Cycle Crossover Operator</a>
+ * @param <T> generic type of the {@link AbstractListChromosome}s for crossover
+ * @since 3.1
+ */
+public class CycleCrossover<T> implements CrossoverPolicy {
+
+    /** If the start index shall be chosen randomly. */
+    private final boolean randomStart;
+
+    /** Creates a new {@link CycleCrossover} policy. */
+    public CycleCrossover() {
+        this(false);
+    }
+
+    /**
+     * Creates a new {@link CycleCrossover} policy using the given {@code randomStart} behavior.
+     *
+     * @param randomStart whether the start index shall be chosen randomly or be set to 0
+     */
+    public CycleCrossover(final boolean randomStart) {
+        this.randomStart = randomStart;
+    }
+
+    /**
+     * Returns whether the starting index is chosen randomly or set to zero.
+     *
+     * @return {@code true} if the starting index is chosen randomly, {@code false} otherwise
+     */
+    public boolean isRandomStart() {
+        return randomStart;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * @throws MathIllegalArgumentException if the chromosomes are not an instance of {@link
+     *     AbstractListChromosome}
+     * @throws DimensionMismatchException if the length of the two chromosomes is different
+     */
+    @SuppressWarnings("unchecked")
+    public ChromosomePair crossover(final Chromosome first, final Chromosome second)
+            throws DimensionMismatchException, MathIllegalArgumentException {
+
+        if (!(first instanceof AbstractListChromosome<?>
+                && second instanceof AbstractListChromosome<?>)) {
+            throw new MathIllegalArgumentException(
+                    LocalizedFormats.INVALID_FIXED_LENGTH_CHROMOSOME);
+        }
+        return mate((AbstractListChromosome<T>) first, (AbstractListChromosome<T>) second);
+    }
+
+    /**
+     * Helper for {@link #crossover(Chromosome, Chromosome)}. Performs the actual crossover.
+     *
+     * @param first the first chromosome
+     * @param second the second chromosome
+     * @return the pair of new chromosomes that resulted from the crossover
+     * @throws DimensionMismatchException if the length of the two chromosomes is different
+     */
+    protected ChromosomePair mate(
+            final AbstractListChromosome<T> first, final AbstractListChromosome<T> second)
+            throws DimensionMismatchException {
+
+        final int length = first.getLength();
+        if (length != second.getLength()) {
+            throw new DimensionMismatchException(second.getLength(), length);
+        }
+
+        // array representations of the parents
+        final List<T> parent1Rep = first.getRepresentation();
+        final List<T> parent2Rep = second.getRepresentation();
+        // and of the children: do a crossover copy to simplify the later processing
+        final List<T> child1Rep = new ArrayList<T>(second.getRepresentation());
+        final List<T> child2Rep = new ArrayList<T>(first.getRepresentation());
+
+        // the set of all visited indices so far
+        final Set<Integer> visitedIndices = new HashSet<Integer>(length);
+        // the indices of the current cycle
+        final List<Integer> indices = new ArrayList<Integer>(length);
+
+        // determine the starting index
+        int idx = randomStart ? GeneticAlgorithm.getRandomGenerator().nextInt(length) : 0;
+        int cycle = 1;
+
+        while (visitedIndices.size() < length) {
+            indices.add(idx);
+
+            T item = parent2Rep.get(idx);
+            idx = parent1Rep.indexOf(item);
+
+            while (idx != indices.get(0)) {
+                // add that index to the cycle indices
+                indices.add(idx);
+                // get the item in the second parent at that index
+                item = parent2Rep.get(idx);
+                // get the index of that item in the first parent
+                idx = parent1Rep.indexOf(item);
+            }
+
+            // for even cycles: swap the child elements on the indices found in this cycle
+            if (cycle++ % 2 != 0) {
+                for (int i : indices) {
+                    T tmp = child1Rep.get(i);
+                    child1Rep.set(i, child2Rep.get(i));
+                    child2Rep.set(i, tmp);
+                }
+            }
+
+            visitedIndices.addAll(indices);
+            // find next starting index: last one + 1 until we find an unvisited index
+            idx = (indices.get(0) + 1) % length;
+            while (visitedIndices.contains(idx) && visitedIndices.size() < length) {
+                idx++;
+                if (idx >= length) {
+                    idx = 0;
+                }
+            }
+            indices.clear();
+        }
+
+        return new ChromosomePair(
+                first.newFixedLengthChromosome(child1Rep),
+                second.newFixedLengthChromosome(child2Rep));
+    }
+}