int[] allRequired, int requiredFrom, int requiredTo, double[] array, int from, int to) {
    // Choose the first selection to do...
    int requiredChosen = chooseNextSelection(allRequired, requiredFrom, requiredTo, from, to);
    int required = allRequired[requiredChosen];

    // ...do the first selection...
    selectInPlace(required, array, from, to);

    // ...then recursively perform the selections in the range below...

   * given object is also a multiset and contains equal elements with equal counts, regardless of
   * order.
   */
  @Override
  // TODO(kevinb): caveats about equivalence-relation?
  boolean equals(@CheckForNull Object object);

  /**
   * Returns the hash code for this multiset. This is defined as the sum of
   *
   * <pre>{@code

 * a traditional {@code HashMap} implementation which stores keys and count values as map entries,
 * {@code ObjectCountHashMap} minimizes object allocation and reduces memory footprint.
 *
 * <p>In the absence of element deletions, this will iterate over elements in insertion order.
 */
@GwtCompatible(serializable = true, emulated = true)
@ElementTypesAreNonnullByDefault
class ObjectCountHashMap<K extends @Nullable Object> {

      if (count == 0 && !isLinkedHash) {
        contents = new ObjectCountLinkedHashMap<E>(contents);
        isLinkedHash = true;
        // to preserve insertion order through deletions, we have to switch to an actual linked
        // implementation at least for now, but this should be a super rare case
      } else if (buildInvoked) {
        contents = new ObjectCountHashMap<E>(contents);

  /** Constructor for use by subclasses. */
  protected Equivalence() {}

  /**
   * Returns {@code true} if the given objects are considered equivalent.
   *
   * <p>This method describes an <i>equivalence relation</i> on object references, meaning that for
   * all references {@code x}, {@code y}, and {@code z} (any of which may be null):
   *
   * <ul>
   *   <li>{@code equivalent(x, x)} is true (<i>reflexive</i> property)

{
  /** Constructor for use by subclasses. */
  protected Equivalence() {}

  /**
   * Returns {@code true} if the given objects are considered equivalent.
   *
   * <p>This method describes an <i>equivalence relation</i> on object references, meaning that for
   * all references {@code x}, {@code y}, and {@code z} (any of which may be null):
   *
   * <ul>
   *   <li>{@code equivalent(x, x)} is true (<i>reflexive</i> property)

   *
   * <p>Being reflexive, antisymmetric and transitive, the {@code encloses} relation defines a
   * <i>partial order</i> over ranges. There exists a unique {@linkplain Range#all maximal} range
   * according to this relation, and also numerous {@linkplain #isEmpty minimal} ranges. Enclosure
   * also implies {@linkplain #isConnected connectedness}.
   */

   *       Double.NEGATIVE_INFINITY} are fuzzily equal only to themselves.
   * </ul>
   *
   * <p>This is reflexive and symmetric, but not transitive, so it is not an
   * equivalence relation and not suitable for use in {@link Object#equals}
   * implementations.
   *
   * @throws IllegalArgumentException if {@code tolerance} is {@code < 0} or NaN
   * @since 13.0
   */