/*                        __    __  __  __    __  ___
    *                       \  \  /  /    \  \  /  /  __/
    *                        \  \/  /  /\  \  \/  /  /
    *                         \____/__/  \__\____/__/.ɪᴏ
    * ᶜᵒᵖʸʳᶦᵍʰᵗ ᵇʸ ᵛᵃᵛʳ ⁻ ˡᶦᶜᵉⁿˢᵉᵈ ᵘⁿᵈᵉʳ ᵗʰᵉ ᵃᵖᵃᶜʰᵉ ˡᶦᶜᵉⁿˢᵉ ᵛᵉʳˢᶦᵒⁿ ᵗʷᵒ ᵈᵒᵗ ᶻᵉʳᵒ
    */
   package io.vavr.collection;
   
   import io.vavr.*;
  import io.vavr.control.Option;
  
  import java.io.*;
  import java.util.ArrayList;
  import java.util.Comparator;
  import java.util.NoSuchElementException;
  import java.util.Objects;
  import java.util.function.*;
  import java.util.stream.Collector;
  
  /**
   * An immutable {@code HashSet} implementation.
   *
   * @param <T> Component type
   * @author Ruslan Sennov, Patryk Najda, Daniel Dietrich
   */
  public final class HashSet<T> implements Set<T>, Serializable {
  
      private static final long serialVersionUID = 1L;
  
      private static final HashSet<?> EMPTY = new HashSet<>(HashArrayMappedTrie.empty());
  
      private final HashArrayMappedTrie<T, T> tree;
  
      private HashSet(HashArrayMappedTrie<T, T> tree) {
          this.tree = tree;
      }
  
      @SuppressWarnings("unchecked")
      public static <T> HashSet<T> empty() {
          return (HashSet<T>) EMPTY;
      }
  
      /**
       * Returns a {@link java.util.stream.Collector} which may be used in conjunction with
       * {@link java.util.stream.Stream#collect(java.util.stream.Collector)} to obtain a {@link HashSet}.
       *
       * @param <T> Component type of the HashSet.
       * @return A io.vavr.collection.HashSet Collector.
       */
      public static <T> Collector<T, ArrayList<T>, HashSet<T>> collector() {
          final Supplier<ArrayList<T>> supplier = ArrayList::new;
          final BiConsumer<ArrayList<T>, T> accumulator = ArrayList::add;
          final BinaryOperator<ArrayList<T>> combiner = (left, right) -> {
              left.addAll(right);
              return left;
          };
          final Function<ArrayList<T>, HashSet<T>> finisher = HashSet::ofAll;
          return Collector.of(supplier, accumulator, combiner, finisher);
      }
  
      /**
       * Narrows a widened {@code HashSet<? extends T>} to {@code HashSet<T>}
       * by performing a type-safe cast. This is eligible because immutable/read-only
       * collections are covariant.
       *
       * @param hashSet A {@code HashSet}.
       * @param <T>     Component type of the {@code HashSet}.
       * @return the given {@code hashSet} instance as narrowed type {@code HashSet<T>}.
       */
      @SuppressWarnings("unchecked")
      public static <T> HashSet<T> narrow(HashSet<? extends T> hashSet) {
          return (HashSet<T>) hashSet;
      }
  
      /**
       * Returns a singleton {@code HashSet}, i.e. a {@code HashSet} of one element.
       *
       * @param element An element.
       * @param <T>     The component type
       * @return A new HashSet instance containing the given element
       */
      public static <T> HashSet<T> of(T element) {
          return HashSet.<T> empty().add(element);
      }
  
      /**
       * Creates a HashSet of the given elements.
       *
       * <pre><code>HashSet.of(1, 2, 3, 4)</code></pre>
       *
       * @param <T>      Component type of the HashSet.
       * @param elements Zero or more elements.
       * @return A set containing the given elements.
       * @throws NullPointerException if {@code elements} is null
       */
      @SafeVarargs
      public static <T> HashSet<T> of(T... elements) {
          Objects.requireNonNull(elements, "elements is null");
          HashArrayMappedTrie<T, T> tree = HashArrayMappedTrie.empty();
         for (T element : elements) {
             tree = tree.put(element, element);
         }
         return tree.isEmpty() ? empty() : new HashSet<>(tree);
     }
 
     /**
      * Returns an HashSet containing {@code n} values of a given Function {@code f}
      * over a range of integer values from 0 to {@code n - 1}.
      *
      * @param <T> Component type of the HashSet
      * @param n   The number of elements in the HashSet
      * @param f   The Function computing element values
      * @return An HashSet consisting of elements {@code f(0),f(1), ..., f(n - 1)}
      * @throws NullPointerException if {@code f} is null
      */
     public static <T> HashSet<T> tabulate(int n, Function<? super Integer, ? extends T> f) {
         Objects.requireNonNull(f, "f is null");
         return Collections.tabulate(n, f, HashSet.empty(), HashSet::of);
     }
 
     /**
      * Returns an HashSet containing {@code n} values supplied by a given Supplier {@code s}.
      *
      * @param <T> Component type of the HashSet
      * @param n   The number of elements in the HashSet
      * @param s   The Supplier computing element values
      * @return An HashSet of size {@code n}, where each element contains the result supplied by {@code s}.
      * @throws NullPointerException if {@code s} is null
      */
     public static <T> HashSet<T> fill(int n, Supplier<? extends T> s) {
         Objects.requireNonNull(s, "s is null");
         return Collections.fill(n, s, HashSet.empty(), HashSet::of);
     }
 
     /**
      * Creates a HashSet of the given elements.
      *
      * @param elements Set elements
      * @param <T>      The value type
      * @return A new HashSet containing the given entries
      */
     @SuppressWarnings("unchecked")
     public static <T> HashSet<T> ofAll(Iterable<? extends T> elements) {
         Objects.requireNonNull(elements, "elements is null");
         if (elements instanceof HashSet) {
             return (HashSet<T>) elements;
         } else {
             final HashArrayMappedTrie<T, T> tree = addAll(HashArrayMappedTrie.empty(), elements);
             return tree.isEmpty() ? empty() : new HashSet<>(tree);
         }
     }
 
     /**
      * Creates a HashSet that contains the elements of the given {@link java.util.stream.Stream}.
      *
      * @param javaStream A {@link java.util.stream.Stream}
      * @param <T>        Component type of the Stream.
      * @return A HashSet containing the given elements in the same order.
      */
     public static <T> HashSet<T> ofAll(java.util.stream.Stream<? extends T> javaStream) {
         Objects.requireNonNull(javaStream, "javaStream is null");
         return HashSet.ofAll(Iterator.ofAll(javaStream.iterator()));
     }
 
     /**
      * Creates a HashSet from boolean values.
      *
      * @param elements boolean values
      * @return A new HashSet of Boolean values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Boolean> ofAll(boolean... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet from byte values.
      *
      * @param elements byte values
      * @return A new HashSet of Byte values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Byte> ofAll(byte... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet from char values.
      *
      * @param elements char values
      * @return A new HashSet of Character values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Character> ofAll(char... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet from double values.
      *
      * @param elements double values
      * @return A new HashSet of Double values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Double> ofAll(double... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet from float values.
      *
      * @param elements float values
      * @return A new HashSet of Float values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Float> ofAll(float... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet from int values.
      *
      * @param elements int values
      * @return A new HashSet of Integer values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Integer> ofAll(int... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet from long values.
      *
      * @param elements long values
      * @return A new HashSet of Long values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Long> ofAll(long... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet from short values.
      *
      * @param elements short values
      * @return A new HashSet of Short values
      * @throws NullPointerException if elements is null
      */
     public static HashSet<Short> ofAll(short... elements) {
         Objects.requireNonNull(elements, "elements is null");
         return HashSet.ofAll(Iterator.ofAll(elements));
     }
 
     /**
      * Creates a HashSet of int numbers starting from {@code from}, extending to {@code toExclusive - 1}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.range(0, 0)  // = HashSet()
      * HashSet.range(2, 0)  // = HashSet()
      * HashSet.range(-2, 2) // = HashSet(-2, -1, 0, 1)
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toExclusive the last number + 1
      * @return a range of int values as specified or the empty range if {@code from >= toExclusive}
      */
     public static HashSet<Integer> range(int from, int toExclusive) {
         return HashSet.ofAll(Iterator.range(from, toExclusive));
     }
 
     public static HashSet<Character> range(char from, char toExclusive) {
         return HashSet.ofAll(Iterator.range(from, toExclusive));
     }
 
     /**
      * Creates a HashSet of int numbers starting from {@code from}, extending to {@code toExclusive - 1},
      * with {@code step}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.rangeBy(1, 3, 1)  // = HashSet(1, 2)
      * HashSet.rangeBy(1, 4, 2)  // = HashSet(1, 3)
      * HashSet.rangeBy(4, 1, -2) // = HashSet(4, 2)
      * HashSet.rangeBy(4, 1, 2)  // = HashSet()
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toExclusive the last number + 1
      * @param step        the step
      * @return a range of long values as specified or the empty range if<br>
      * {@code from >= toInclusive} and {@code step > 0} or<br>
      * {@code from <= toInclusive} and {@code step < 0}
      * @throws IllegalArgumentException if {@code step} is zero
      */
     public static HashSet<Integer> rangeBy(int from, int toExclusive, int step) {
         return HashSet.ofAll(Iterator.rangeBy(from, toExclusive, step));
     }
 
     public static HashSet<Character> rangeBy(char from, char toExclusive, int step) {
         return HashSet.ofAll(Iterator.rangeBy(from, toExclusive, step));
     }
 
     @GwtIncompatible
     public static HashSet<Double> rangeBy(double from, double toExclusive, double step) {
         return HashSet.ofAll(Iterator.rangeBy(from, toExclusive, step));
     }
 
     /**
      * Creates a HashSet of long numbers starting from {@code from}, extending to {@code toExclusive - 1}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.range(0L, 0L)  // = HashSet()
      * HashSet.range(2L, 0L)  // = HashSet()
      * HashSet.range(-2L, 2L) // = HashSet(-2L, -1L, 0L, 1L)
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toExclusive the last number + 1
      * @return a range of long values as specified or the empty range if {@code from >= toExclusive}
      */
     public static HashSet<Long> range(long from, long toExclusive) {
         return HashSet.ofAll(Iterator.range(from, toExclusive));
     }
 
     /**
      * Creates a HashSet of long numbers starting from {@code from}, extending to {@code toExclusive - 1},
      * with {@code step}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.rangeBy(1L, 3L, 1L)  // = HashSet(1L, 2L)
      * HashSet.rangeBy(1L, 4L, 2L)  // = HashSet(1L, 3L)
      * HashSet.rangeBy(4L, 1L, -2L) // = HashSet(4L, 2L)
      * HashSet.rangeBy(4L, 1L, 2L)  // = HashSet()
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toExclusive the last number + 1
      * @param step        the step
      * @return a range of long values as specified or the empty range if<br>
      * {@code from >= toInclusive} and {@code step > 0} or<br>
      * {@code from <= toInclusive} and {@code step < 0}
      * @throws IllegalArgumentException if {@code step} is zero
      */
     public static HashSet<Long> rangeBy(long from, long toExclusive, long step) {
         return HashSet.ofAll(Iterator.rangeBy(from, toExclusive, step));
     }
 
     /**
      * Creates a HashSet of int numbers starting from {@code from}, extending to {@code toInclusive}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.rangeClosed(0, 0)  // = HashSet(0)
      * HashSet.rangeClosed(2, 0)  // = HashSet()
      * HashSet.rangeClosed(-2, 2) // = HashSet(-2, -1, 0, 1, 2)
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toInclusive the last number
      * @return a range of int values as specified or the empty range if {@code from > toInclusive}
      */
     public static HashSet<Integer> rangeClosed(int from, int toInclusive) {
         return HashSet.ofAll(Iterator.rangeClosed(from, toInclusive));
     }
 
     public static HashSet<Character> rangeClosed(char from, char toInclusive) {
         return HashSet.ofAll(Iterator.rangeClosed(from, toInclusive));
     }
 
     /**
      * Creates a HashSet of int numbers starting from {@code from}, extending to {@code toInclusive},
      * with {@code step}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.rangeClosedBy(1, 3, 1)  // = HashSet(1, 2, 3)
      * HashSet.rangeClosedBy(1, 4, 2)  // = HashSet(1, 3)
      * HashSet.rangeClosedBy(4, 1, -2) // = HashSet(4, 2)
      * HashSet.rangeClosedBy(4, 1, 2)  // = HashSet()
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toInclusive the last number
      * @param step        the step
      * @return a range of int values as specified or the empty range if<br>
      * {@code from > toInclusive} and {@code step > 0} or<br>
      * {@code from < toInclusive} and {@code step < 0}
      * @throws IllegalArgumentException if {@code step} is zero
      */
     public static HashSet<Integer> rangeClosedBy(int from, int toInclusive, int step) {
         return HashSet.ofAll(Iterator.rangeClosedBy(from, toInclusive, step));
     }
 
     public static HashSet<Character> rangeClosedBy(char from, char toInclusive, int step) {
         return HashSet.ofAll(Iterator.rangeClosedBy(from, toInclusive, step));
     }
 
     @GwtIncompatible
     public static HashSet<Double> rangeClosedBy(double from, double toInclusive, double step) {
         return HashSet.ofAll(Iterator.rangeClosedBy(from, toInclusive, step));
     }
 
     /**
      * Creates a HashSet of long numbers starting from {@code from}, extending to {@code toInclusive}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.rangeClosed(0L, 0L)  // = HashSet(0L)
      * HashSet.rangeClosed(2L, 0L)  // = HashSet()
      * HashSet.rangeClosed(-2L, 2L) // = HashSet(-2L, -1L, 0L, 1L, 2L)
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toInclusive the last number
      * @return a range of long values as specified or the empty range if {@code from > toInclusive}
      */
     public static HashSet<Long> rangeClosed(long from, long toInclusive) {
         return HashSet.ofAll(Iterator.rangeClosed(from, toInclusive));
     }
 
     /**
      * Creates a HashSet of long numbers starting from {@code from}, extending to {@code toInclusive},
      * with {@code step}.
      * <p>
      * Examples:
      * <pre>
      * <code>
      * HashSet.rangeClosedBy(1L, 3L, 1L)  // = HashSet(1L, 2L, 3L)
      * HashSet.rangeClosedBy(1L, 4L, 2L)  // = HashSet(1L, 3L)
      * HashSet.rangeClosedBy(4L, 1L, -2L) // = HashSet(4L, 2L)
      * HashSet.rangeClosedBy(4L, 1L, 2L)  // = HashSet()
      * </code>
      * </pre>
      *
      * @param from        the first number
      * @param toInclusive the last number
      * @param step        the step
      * @return a range of int values as specified or the empty range if<br>
      * {@code from > toInclusive} and {@code step > 0} or<br>
      * {@code from < toInclusive} and {@code step < 0}
      * @throws IllegalArgumentException if {@code step} is zero
      */
     public static HashSet<Long> rangeClosedBy(long from, long toInclusive, long step) {
         return HashSet.ofAll(Iterator.rangeClosedBy(from, toInclusive, step));
     }
 
     @Override
     public HashSet<T> add(T element) {
         return contains(element) ? this : new HashSet<>(tree.put(element, element));
     }
 
     @Override
     public HashSet<T> addAll(Iterable<? extends T> elements) {
         Objects.requireNonNull(elements, "elements is null");
         if (isEmpty() && elements instanceof HashSet) {
             @SuppressWarnings("unchecked")
             final HashSet<T> set = (HashSet<T>) elements;
             return set;
         }
         final HashArrayMappedTrie<T, T> that = addAll(tree, elements);
         if (that.size() == tree.size()) {
             return this;
         } else {
             return new HashSet<>(that);
         }
     }
 
     @Override
     public <R> HashSet<R> collect(PartialFunction<? super T, ? extends R> partialFunction) {
         return ofAll(iterator().<R> collect(partialFunction));
     }
 
     @Override
     public boolean contains(T element) {
         return tree.get(element).isDefined();
     }
 
     @Override
     public HashSet<T> diff(Set<? extends T> elements) {
         Objects.requireNonNull(elements, "elements is null");
         if (isEmpty() || elements.isEmpty()) {
             return this;
         } else {
             return removeAll(elements);
         }
     }
 
     @Override
     public HashSet<T> distinct() {
         return this;
     }
 
     @Override
     public HashSet<T> distinctBy(Comparator<? super T> comparator) {
         Objects.requireNonNull(comparator, "comparator is null");
         return HashSet.ofAll(iterator().distinctBy(comparator));
     }
 
     @Override
     public <U> HashSet<T> distinctBy(Function<? super T, ? extends U> keyExtractor) {
         Objects.requireNonNull(keyExtractor, "keyExtractor is null");
         return HashSet.ofAll(iterator().distinctBy(keyExtractor));
     }
 
     @Override
     public HashSet<T> drop(int n) {
         if (n <= 0) {
             return this;
         } else {
             return HashSet.ofAll(iterator().drop(n));
         }
     }
 
     @Override
     public HashSet<T> dropRight(int n) {
         return drop(n);
     }
 
     @Override
     public HashSet<T> dropUntil(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         return dropWhile(predicate.negate());
     }
 
     @Override
     public HashSet<T> dropWhile(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         final HashSet<T> dropped = HashSet.ofAll(iterator().dropWhile(predicate));
         return dropped.length() == length() ? this : dropped;
     }
 
     @Override
     public HashSet<T> filter(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         final HashSet<T> filtered = HashSet.ofAll(iterator().filter(predicate));
 
         if (filtered.isEmpty()) {
             return empty();
         } else if (filtered.length() == length()) {
             return this;
         } else {
             return filtered;
         }
     }
 
     @Override
     public <U> HashSet<U> flatMap(Function<? super T, ? extends Iterable<? extends U>> mapper) {
         Objects.requireNonNull(mapper, "mapper is null");
         if (isEmpty()) {
             return empty();
         } else {
             final HashArrayMappedTrie<U, U> that = foldLeft(HashArrayMappedTrie.empty(),
                     (tree, t) -> addAll(tree, mapper.apply(t)));
             return new HashSet<>(that);
         }
     }
 
     @Override
     public <U> U foldRight(U zero, BiFunction<? super T, ? super U, ? extends U> f) {
         return foldLeft(zero, (u, t) -> f.apply(t, u));
     }
 
     @Override
     public <C> Map<C, HashSet<T>> groupBy(Function<? super T, ? extends C> classifier) {
         return Collections.groupBy(this, classifier, HashSet::ofAll);
     }
 
     @Override
     public Iterator<HashSet<T>> grouped(int size) {
         return sliding(size, size);
     }
 
     @Override
     public boolean hasDefiniteSize() {
         return true;
     }
 
     @Override
     public T head() {
         if (tree.isEmpty()) {
             throw new NoSuchElementException("head of empty set");
         }
         return iterator().next();
     }
 
     @Override
     public Option<T> headOption() {
         return iterator().headOption();
     }
 
     @Override
     public HashSet<T> init() {
         return tail();
     }
 
     @Override
     public Option<HashSet<T>> initOption() {
         return tailOption();
     }
 
     @Override
     public HashSet<T> intersect(Set<? extends T> elements) {
         Objects.requireNonNull(elements, "elements is null");
         if (isEmpty() || elements.isEmpty()) {
             return empty();
         } else {
             final int size = size();
             if (size <= elements.size()) {
                 return retainAll(elements);
             } else {
                 final HashSet<T> results = HashSet.<T> ofAll(elements).retainAll(this);
                 return (size == results.size()) ? this : results;
             }
         }
     }
 
     /**
      * A {@code HashSet} is computed synchronously.
      *
      * @return false
      */
     @Override
     public boolean isAsync() {
         return false;
     }
 
     @Override
     public boolean isEmpty() {
         return tree.isEmpty();
     }
     
     /**
      * A {@code HashSet} is computed eagerly.
      *
      * @return false
      */
     @Override
     public boolean isLazy() {
         return false;
     }
 
     @Override
     public boolean isTraversableAgain() {
         return true;
     }
 
     @Override
     public Iterator<T> iterator() {
         return tree.keysIterator();
     }
 
     @Override
     public int length() {
         return tree.size();
     }
 
     @Override
     public <U> HashSet<U> map(Function<? super T, ? extends U> mapper) {
         Objects.requireNonNull(mapper, "mapper is null");
         if (isEmpty()) {
             return empty();
         } else {
             final HashArrayMappedTrie<U, U> that = foldLeft(HashArrayMappedTrie.empty(), (tree, t) -> {
                 final U u = mapper.apply(t);
                 return tree.put(u, u);
             });
             return new HashSet<>(that);
         }
     }
 
     @Override
     public String mkString(CharSequence prefix, CharSequence delimiter, CharSequence suffix) {
         return iterator().mkString(prefix, delimiter, suffix);
     }
 
     @Override
     public HashSet<T> orElse(Iterable<? extends T> other) {
         return isEmpty() ? ofAll(other) : this;
     }
 
     @Override
     public HashSet<T> orElse(Supplier<? extends Iterable<? extends T>> supplier) {
         return isEmpty() ? ofAll(supplier.get()) : this;
     }
 
     @Override
     public Tuple2<HashSet<T>, HashSet<T>> partition(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         final Tuple2<Iterator<T>, Iterator<T>> p = iterator().partition(predicate);
         return Tuple.of(HashSet.ofAll(p._1), HashSet.ofAll(p._2));
     }
 
     @Override
     public HashSet<T> peek(Consumer<? super T> action) {
         Objects.requireNonNull(action, "action is null");
         if (!isEmpty()) {
             action.accept(iterator().head());
         }
         return this;
     }
 
     @Override
     public HashSet<T> remove(T element) {
         final HashArrayMappedTrie<T, T> newTree = tree.remove(element);
         return (newTree == tree) ? this : new HashSet<>(newTree);
     }
 
     @Override
     public HashSet<T> removeAll(Iterable<? extends T> elements) {
         return Collections.removeAll(this, elements);
     }
 
     @Override
     public HashSet<T> replace(T currentElement, T newElement) {
         if (tree.containsKey(currentElement)) {
             return remove(currentElement).add(newElement);
         } else {
             return this;
         }
     }
 
     @Override
     public HashSet<T> replaceAll(T currentElement, T newElement) {
         return replace(currentElement, newElement);
     }
 
     @Override
     public HashSet<T> retainAll(Iterable<? extends T> elements) {
         return Collections.retainAll(this, elements);
     }
 
     @Override
     public HashSet<T> scan(T zero, BiFunction<? super T, ? super T, ? extends T> operation) {
         return scanLeft(zero, operation);
     }
 
     @Override
     public <U> HashSet<U> scanLeft(U zero, BiFunction<? super U, ? super T, ? extends U> operation) {
         return Collections.scanLeft(this, zero, operation, HashSet::ofAll);
     }
 
     @Override
     public <U> HashSet<U> scanRight(U zero, BiFunction<? super T, ? super U, ? extends U> operation) {
         return Collections.scanRight(this, zero, operation, HashSet::ofAll);
     }
 
     @Override
     public Iterator<HashSet<T>> slideBy(Function<? super T, ?> classifier) {
         return iterator().slideBy(classifier).map(HashSet::ofAll);
     }
 
     @Override
     public Iterator<HashSet<T>> sliding(int size) {
         return sliding(size, 1);
     }
 
     @Override
     public Iterator<HashSet<T>> sliding(int size, int step) {
         return iterator().sliding(size, step).map(HashSet::ofAll);
     }
 
     @Override
     public Tuple2<HashSet<T>, HashSet<T>> span(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         final Tuple2<Iterator<T>, Iterator<T>> t = iterator().span(predicate);
         return Tuple.of(HashSet.ofAll(t._1), HashSet.ofAll(t._2));
     }
 
     @Override
     public HashSet<T> tail() {
         if (tree.isEmpty()) {
             throw new UnsupportedOperationException("tail of empty set");
         }
         return remove(head());
     }
 
     @Override
     public Option<HashSet<T>> tailOption() {
         if (tree.isEmpty()) {
             return Option.none();
         } else {
             return Option.some(tail());
         }
     }
 
     @Override
     public HashSet<T> take(int n) {
         if (n >= size() || isEmpty()) {
             return this;
         } else if (n <= 0) {
             return empty();
         } else {
             return ofAll(() -> iterator().take(n));
         }
     }
 
     @Override
     public HashSet<T> takeRight(int n) {
         return take(n);
     }
 
     @Override
     public HashSet<T> takeUntil(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         return takeWhile(predicate.negate());
     }
 
     @Override
     public HashSet<T> takeWhile(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         final HashSet<T> taken = HashSet.ofAll(iterator().takeWhile(predicate));
         return taken.length() == length() ? this : taken;
     }
 
     /**
      * Transforms this {@code HashSet}.
      *
      * @param f   A transformation
      * @param <U> Type of transformation result
      * @return An instance of type {@code U}
      * @throws NullPointerException if {@code f} is null
      */
     public <U> U transform(Function<? super HashSet<T>, ? extends U> f) {
         Objects.requireNonNull(f, "f is null");
         return f.apply(this);
     }
 
     @Override
     public java.util.HashSet<T> toJavaSet() {
         return toJavaSet(java.util.HashSet::new);
     }
 
     @SuppressWarnings("unchecked")
     @Override
     public HashSet<T> union(Set<? extends T> elements) {
         Objects.requireNonNull(elements, "elements is null");
         if (isEmpty()) {
             if (elements instanceof HashSet) {
                 return (HashSet<T>) elements;
             } else {
                 return HashSet.ofAll(elements);
             }
         } else if (elements.isEmpty()) {
             return this;
         } else {
             final HashArrayMappedTrie<T, T> that = addAll(tree, elements);
             if (that.size() == tree.size()) {
                 return this;
             } else {
                 return new HashSet<>(that);
             }
         }
     }
 
     @Override
     public <T1, T2> Tuple2<HashSet<T1>, HashSet<T2>> unzip(
             Function<? super T, Tuple2<? extends T1, ? extends T2>> unzipper) {
         Objects.requireNonNull(unzipper, "unzipper is null");
         final Tuple2<Iterator<T1>, Iterator<T2>> t = iterator().unzip(unzipper);
         return Tuple.of(HashSet.ofAll(t._1), HashSet.ofAll(t._2));
     }
 
     @Override
     public <T1, T2, T3> Tuple3<HashSet<T1>, HashSet<T2>, HashSet<T3>> unzip3(
             Function<? super T, Tuple3<? extends T1, ? extends T2, ? extends T3>> unzipper) {
         Objects.requireNonNull(unzipper, "unzipper is null");
         final Tuple3<Iterator<T1>, Iterator<T2>, Iterator<T3>> t = iterator().unzip3(unzipper);
         return Tuple.of(HashSet.ofAll(t._1), HashSet.ofAll(t._2), HashSet.ofAll(t._3));
     }
 
     @Override
     public <U> HashSet<Tuple2<T, U>> zip(Iterable<? extends U> that) {
         return zipWith(that, Tuple::of);
     }
 
     @Override
     public <U, R> HashSet<R> zipWith(Iterable<? extends U> that, BiFunction<? super T, ? super U, ? extends R> mapper) {
         Objects.requireNonNull(that, "that is null");
         Objects.requireNonNull(mapper, "mapper is null");
         return HashSet.ofAll(iterator().zipWith(that, mapper));
     }
 
     @Override
     public <U> HashSet<Tuple2<T, U>> zipAll(Iterable<? extends U> that, T thisElem, U thatElem) {
         Objects.requireNonNull(that, "that is null");
         return HashSet.ofAll(iterator().zipAll(that, thisElem, thatElem));
     }
 
     @Override
     public HashSet<Tuple2<T, Integer>> zipWithIndex() {
         return zipWithIndex(Tuple::of);
     }
 
     @Override
     public <U> HashSet<U> zipWithIndex(BiFunction<? super T, ? super Integer, ? extends U> mapper) {
         Objects.requireNonNull(mapper, "mapper is null");
         return HashSet.ofAll(iterator().zipWithIndex(mapper));
     }
 
     // -- Object
 
     @Override
     public boolean equals(Object o) {
         return Collections.equals(this, o);
     }
 
     @Override
     public int hashCode() {
         return Collections.hashUnordered(this);
     }
 
     @Override
     public String stringPrefix() {
         return "HashSet";
     }
 
     @Override
     public String toString() {
         return mkString(stringPrefix() + "(", ", ", ")");
     }
 
     private static <T> HashArrayMappedTrie<T, T> addAll(HashArrayMappedTrie<T, T> initial,
             Iterable<? extends T> additional) {
         HashArrayMappedTrie<T, T> that = initial;
         for (T t : additional) {
             that = that.put(t, t);
         }
         return that;
     }
 
     // -- Serialization
 
     /**
      * {@code writeReplace} method for the serialization proxy pattern.
      * <p>
      * The presence of this method causes the serialization system to emit a SerializationProxy instance instead of
      * an instance of the enclosing class.
      *
      * @return A SerializationProxy for this enclosing class.
      */
     @GwtIncompatible("The Java serialization protocol is explicitly not supported")
     private Object writeReplace() {
         return new SerializationProxy<>(this.tree);
     }
 
     /**
      * {@code readObject} method for the serialization proxy pattern.
      * <p>
      * Guarantees that the serialization system will never generate a serialized instance of the enclosing class.
      *
      * @param stream An object serialization stream.
      * @throws java.io.InvalidObjectException This method will throw with the message "Proxy required".
      */
     @GwtIncompatible("The Java serialization protocol is explicitly not supported")
     private void readObject(ObjectInputStream stream) throws InvalidObjectException {
         throw new InvalidObjectException("Proxy required");
     }
 
     /**
      * A serialization proxy which, in this context, is used to deserialize immutable, linked Lists with final
      * instance fields.
      *
      * @param <T> The component type of the underlying list.
      */
     // DEV NOTE: The serialization proxy pattern is not compatible with non-final, i.e. extendable,
     // classes. Also, it may not be compatible with circular object graphs.
     @GwtIncompatible("The Java serialization protocol is explicitly not supported")
     private static final class SerializationProxy<T> implements Serializable {
 
         private static final long serialVersionUID = 1L;
 
         // the instance to be serialized/deserialized
         private transient HashArrayMappedTrie<T, T> tree;
 
         /**
          * Constructor for the case of serialization, called by {@link HashSet#writeReplace()}.
          * <p/>
          * The constructor of a SerializationProxy takes an argument that concisely represents the logical state of
          * an instance of the enclosing class.
          *
          * @param tree a Cons
          */
         SerializationProxy(HashArrayMappedTrie<T, T> tree) {
             this.tree = tree;
         }
 
         /**
          * Write an object to a serialization stream.
          *
          * @param s An object serialization stream.
          * @throws java.io.IOException If an error occurs writing to the stream.
          */
         private void writeObject(ObjectOutputStream s) throws IOException {
             s.defaultWriteObject();
             s.writeInt(tree.size());
             for (Tuple2<T, T> e : tree) {
                 s.writeObject(e._1);
             }
         }
 
         /**
          * Read an object from a deserialization stream.
          *
          * @param s An object deserialization stream.
          * @throws ClassNotFoundException If the object's class read from the stream cannot be found.
          * @throws InvalidObjectException If the stream contains no list elements.
          * @throws IOException            If an error occurs reading from the stream.
          */
         private void readObject(ObjectInputStream s) throws ClassNotFoundException, IOException {
             s.defaultReadObject();
             final int size = s.readInt();
             if (size < 0) {
                 throw new InvalidObjectException("No elements");
             }
             HashArrayMappedTrie<T, T> temp = HashArrayMappedTrie.empty();
             for (int i = 0; i < size; i++) {
                 @SuppressWarnings("unchecked")
                 final T element = (T) s.readObject();
                 temp = temp.put(element, element);
             }
             tree = temp;
         }
 
         /**
          * {@code readResolve} method for the serialization proxy pattern.
          * <p>
          * Returns a logically equivalent instance of the enclosing class. The presence of this method causes the
          * serialization system to translate the serialization proxy back into an instance of the enclosing class
          * upon deserialization.
          *
          * @return A deserialized instance of the enclosing class.
          */
         private Object readResolve() {
             return tree.isEmpty() ? HashSet.empty() : new HashSet<>(tree);
         }
     }
 }