path: root/src/main/java/org/apache/commons/math3/util/Combinations.java

/*
 * 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.util;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.OutOfRangeException;

import java.io.Serializable;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Iterator;
import java.util.NoSuchElementException;

/**
 * Utility to create <a href="http://en.wikipedia.org/wiki/Combination">combinations</a> {@code (n,
 * k)} of {@code k} elements in a set of {@code n} elements.
 *
 * @since 3.3
 */
public class Combinations implements Iterable<int[]> {
    /** Size of the set from which combinations are drawn. */
    private final int n;

    /** Number of elements in each combination. */
    private final int k;

    /** Iteration order. */
    private final IterationOrder iterationOrder;

    /** Describes the type of iteration performed by the {@link #iterator() iterator}. */
    private enum IterationOrder {
        /** Lexicographic order. */
        LEXICOGRAPHIC
    }

    /**
     * Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as
     * {@code int[]} arrays.
     *
     * <p>The iteration order is lexicographic: the arrays returned by the {@link #iterator()
     * iterator} are sorted in descending order and they are visited in lexicographic order with
     * significance from right to left. For example, {@code new Combinations(4, 2).iterator()}
     * returns an iterator that will generate the following sequence of arrays on successive calls
     * to {@code next()}:<br>
     * {@code [0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]} If {@code k == 0} an iterator
     * containing an empty array is returned; if {@code k == n} an iterator containing [0, ..., n -
     * 1] is returned.
     *
     * @param n Size of the set from which subsets are selected.
     * @param k Size of the subsets to be enumerated.
     * @throws org.apache.commons.math3.exception.NotPositiveException if {@code n < 0}.
     * @throws org.apache.commons.math3.exception.NumberIsTooLargeException if {@code k > n}.
     */
    public Combinations(int n, int k) {
        this(n, k, IterationOrder.LEXICOGRAPHIC);
    }

    /**
     * Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as
     * {@code int[]} arrays.
     *
     * <p>If the {@code iterationOrder} argument is set to {@link IterationOrder#LEXICOGRAPHIC}, the
     * arrays returned by the {@link #iterator() iterator} are sorted in descending order and they
     * are visited in lexicographic order with significance from right to left. For example, {@code
     * new Combinations(4, 2).iterator()} returns an iterator that will generate the following
     * sequence of arrays on successive calls to {@code next()}:<br>
     * {@code [0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]} If {@code k == 0} an iterator
     * containing an empty array is returned; if {@code k == n} an iterator containing [0, ..., n -
     * 1] is returned.
     *
     * @param n Size of the set from which subsets are selected.
     * @param k Size of the subsets to be enumerated.
     * @param iterationOrder Specifies the {@link #iterator() iteration order}.
     * @throws org.apache.commons.math3.exception.NotPositiveException if {@code n < 0}.
     * @throws org.apache.commons.math3.exception.NumberIsTooLargeException if {@code k > n}.
     */
    private Combinations(int n, int k, IterationOrder iterationOrder) {
        CombinatoricsUtils.checkBinomial(n, k);
        this.n = n;
        this.k = k;
        this.iterationOrder = iterationOrder;
    }

    /**
     * Gets the size of the set from which combinations are drawn.
     *
     * @return the size of the universe.
     */
    public int getN() {
        return n;
    }

    /**
     * Gets the number of elements in each combination.
     *
     * @return the size of the subsets to be enumerated.
     */
    public int getK() {
        return k;
    }

    /** {@inheritDoc} */
    public Iterator<int[]> iterator() {
        if (k == 0 || k == n) {
            return new SingletonIterator(MathArrays.natural(k));
        }

        switch (iterationOrder) {
            case LEXICOGRAPHIC:
                return new LexicographicIterator(n, k);
            default:
                throw new MathInternalError(); // Should never happen.
        }
    }

    /**
     * Defines a lexicographic ordering of combinations. The returned comparator allows to compare
     * any two combinations that can be produced by this instance's {@link #iterator() iterator}.
     * Its {@code compare(int[],int[])} method will throw exceptions if passed combinations that are
     * inconsistent with this instance:
     *
     * <ul>
     *   <li>{@code DimensionMismatchException} if the array lengths are not equal to {@code k},
     *   <li>{@code OutOfRangeException} if an element of the array is not within the interval [0,
     *       {@code n}).
     * </ul>
     *
     * @return a lexicographic comparator.
     */
    public Comparator<int[]> comparator() {
        return new LexicographicComparator(n, k);
    }

    /**
     * Lexicographic combinations iterator.
     *
     * <p>Implementation follows Algorithm T in <i>The Art of Computer Programming</i> Internet
     * Draft (PRE-FASCICLE 3A), "A Draft of Section 7.2.1.3 Generating All Combinations</a>, D.
     * Knuth, 2004.
     *
     * <p>The degenerate cases {@code k == 0} and {@code k == n} are NOT handled by this
     * implementation. If constructor arguments satisfy {@code k == 0} or {@code k >= n}, no
     * exception is generated, but the iterator is empty.
     */
    private static class LexicographicIterator implements Iterator<int[]> {
        /** Size of subsets returned by the iterator */
        private final int k;

        /**
         * c[1], ..., c[k] stores the next combination; c[k + 1], c[k + 2] are sentinels.
         *
         * <p>Note that c[0] is "wasted" but this makes it a little easier to follow the code.
         */
        private final int[] c;

        /** Return value for {@link #hasNext()} */
        private boolean more = true;

        /** Marker: smallest index such that c[j + 1] > j */
        private int j;

        /**
         * Construct a CombinationIterator to enumerate k-sets from n.
         *
         * <p>NOTE: If {@code k === 0} or {@code k >= n}, the Iterator will be empty (that is,
         * {@link #hasNext()} will return {@code false} immediately.
         *
         * @param n size of the set from which subsets are enumerated
         * @param k size of the subsets to enumerate
         */
        LexicographicIterator(int n, int k) {
            this.k = k;
            c = new int[k + 3];
            if (k == 0 || k >= n) {
                more = false;
                return;
            }
            // Initialize c to start with lexicographically first k-set
            for (int i = 1; i <= k; i++) {
                c[i] = i - 1;
            }
            // Initialize sentinels
            c[k + 1] = n;
            c[k + 2] = 0;
            j = k; // Set up invariant: j is smallest index such that c[j + 1] > j
        }

        /** {@inheritDoc} */
        public boolean hasNext() {
            return more;
        }

        /** {@inheritDoc} */
        public int[] next() {
            if (!more) {
                throw new NoSuchElementException();
            }
            // Copy return value (prepared by last activation)
            final int[] ret = new int[k];
            System.arraycopy(c, 1, ret, 0, k);

            // Prepare next iteration
            // T2 and T6 loop
            int x = 0;
            if (j > 0) {
                x = j;
                c[j] = x;
                j--;
                return ret;
            }
            // T3
            if (c[1] + 1 < c[2]) {
                c[1]++;
                return ret;
            } else {
                j = 2;
            }
            // T4
            boolean stepDone = false;
            while (!stepDone) {
                c[j - 1] = j - 2;
                x = c[j] + 1;
                if (x == c[j + 1]) {
                    j++;
                } else {
                    stepDone = true;
                }
            }
            // T5
            if (j > k) {
                more = false;
                return ret;
            }
            // T6
            c[j] = x;
            j--;
            return ret;
        }

        /** Not supported. */
        public void remove() {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Iterator with just one element to handle degenerate cases (full array, empty array) for
     * combination iterator.
     */
    private static class SingletonIterator implements Iterator<int[]> {
        /** Singleton array */
        private final int[] singleton;

        /** True on initialization, false after first call to next */
        private boolean more = true;

        /**
         * Create a singleton iterator providing the given array.
         *
         * @param singleton array returned by the iterator
         */
        SingletonIterator(final int[] singleton) {
            this.singleton = singleton;
        }

        /**
         * @return True until next is called the first time, then false
         */
        public boolean hasNext() {
            return more;
        }

        /**
         * @return the singleton in first activation; throws NSEE thereafter
         */
        public int[] next() {
            if (more) {
                more = false;
                return singleton;
            } else {
                throw new NoSuchElementException();
            }
        }

        /** Not supported */
        public void remove() {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Defines the lexicographic ordering of combinations, using the {@link #lexNorm(int[])} method.
     */
    private static class LexicographicComparator implements Comparator<int[]>, Serializable {
        /** Serializable version identifier. */
        private static final long serialVersionUID = 20130906L;

        /** Size of the set from which combinations are drawn. */
        private final int n;

        /** Number of elements in each combination. */
        private final int k;

        /**
         * @param n Size of the set from which subsets are selected.
         * @param k Size of the subsets to be enumerated.
         */
        LexicographicComparator(int n, int k) {
            this.n = n;
            this.k = k;
        }

        /**
         * {@inheritDoc}
         *
         * @throws DimensionMismatchException if the array lengths are not equal to {@code k}.
         * @throws OutOfRangeException if an element of the array is not within the interval [0,
         *     {@code n}).
         */
        public int compare(int[] c1, int[] c2) {
            if (c1.length != k) {
                throw new DimensionMismatchException(c1.length, k);
            }
            if (c2.length != k) {
                throw new DimensionMismatchException(c2.length, k);
            }

            // Method "lexNorm" works with ordered arrays.
            final int[] c1s = MathArrays.copyOf(c1);
            Arrays.sort(c1s);
            final int[] c2s = MathArrays.copyOf(c2);
            Arrays.sort(c2s);

            final long v1 = lexNorm(c1s);
            final long v2 = lexNorm(c2s);

            if (v1 < v2) {
                return -1;
            } else if (v1 > v2) {
                return 1;
            } else {
                return 0;
            }
        }

        /**
         * Computes the value (in base 10) represented by the digit (interpreted in base {@code n})
         * in the input array in reverse order. For example if {@code c} is {@code {3, 2, 1}}, and
         * {@code n} is 3, the method will return 18.
         *
         * @param c Input array.
         * @return the lexicographic norm.
         * @throws OutOfRangeException if an element of the array is not within the interval [0,
         *     {@code n}).
         */
        private long lexNorm(int[] c) {
            long ret = 0;
            for (int i = 0; i < c.length; i++) {
                final int digit = c[i];
                if (digit < 0 || digit >= n) {
                    throw new OutOfRangeException(digit, 0, n - 1);
                }

                ret += c[i] * ArithmeticUtils.pow(n, i);
            }
            return ret;
        }
    }
}