Java tutorial
/* * 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 java.util.Iterator; import java.util.Comparator; import java.util.Arrays; import java.util.NoSuchElementException; import java.io.Serializable; import org.apache.commons.math3.exception.MathInternalError; import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.OutOfRangeException; /** * 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 static 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]} * </p> * 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]} * </p> * 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> * <li>{@code OutOfRangeException} if an element of the array is not * within the interval [0, {@code n}).</li> * </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> * <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. * </p> * */ 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. * </p> */ 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. * </p> * * @param n size of the set from which subsets are enumerated * @param k size of the subsets to enumerate */ public 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 */ public 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. */ public 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; } } }