vavr/collection/Iterator.java

/*                        __    __  __  __    __  ___
 *                       \  \  /  /    \  \  /  /  __/
 *                        \  \/  /  /\  \  \/  /  /
 *                         \____/__/  \__\____/__/.ɪᴏ
 * ᶜᵒᵖʸʳᶦᵍʰᵗ ᵇʸ ᵛᵃᵛʳ ⁻ ˡᶦᶜᵉⁿˢᵉᵈ ᵘⁿᵈᵉʳ ᵗʰᵉ ᵃᵖᵃᶜʰᵉ ˡᶦᶜᵉⁿˢᵉ ᵛᵉʳˢᶦᵒⁿ ᵗʷᵒ ᵈᵒᵗ ᶻᵉʳᵒ
 */
package io.vavr.collection;

import io.vavr.*;
import io.vavr.collection.IteratorModule.ConcatIterator;
import io.vavr.collection.IteratorModule.DistinctIterator;
import io.vavr.collection.IteratorModule.GroupedIterator;
import io.vavr.control.Option;

import java.math.BigDecimal;
import java.util.*;
import java.util.function.*;

import static java.lang.Double.NEGATIVE_INFINITY;
import static java.lang.Double.POSITIVE_INFINITY;
import static java.math.RoundingMode.HALF_UP;
import static io.vavr.collection.IteratorModule.BigDecimalHelper.areEqual;
import static io.vavr.collection.IteratorModule.BigDecimalHelper.asDecimal;
import static io.vavr.collection.IteratorModule.EmptyIterator;

/**
 * {@code io.vavr.collection.Iterator} is a compositional replacement for {@code java.util.Iterator}
 * whose purpose is to iterate <em>once</em> over a sequence of elements.
 * <p>
 * It is recommended to create instances using {@link AbstractIterator} in favor of {@code Iterator}.
 * <p>
 * <strong>Note:</strong> Iterators encapsulate mutable state.
 * They are not meant to be used concurrently by different threads. Do not reuse Iterators, e.g. after passing to
 * {@linkplain io.vavr.collection.List#ofAll(Iterable)}.
 * <p>
 * There are two abstract methods: {@code hasNext} for checking if there is a next element available,
 * and {@code next} which removes the next element from the iterator and returns it. They can be called
 * an arbitrary amount of times. If {@code hasNext} returns false, a call of {@code next} will throw
 * a {@code NoSuchElementException}.
 * <p>
 * <strong>Caution: Other methods than {@code hasNext} and {@code next} can be called only once (exclusively).
 * More specifically, after calling a method it cannot be guaranteed that the next call will succeed.</strong>
 * <p>
 * An Iterator that can be only used once because it is a traversal pointer into a collection, and not a collection
 * itself.
 *
 * @param <T> Component type
 * @author Daniel Dietrich
 */
// DEV-NOTE: we prefer returning empty() over this if !hasNext() == true in order to free memory.
public interface Iterator<T> extends java.util.Iterator<T>, Traversable<T> {

    /**
     * Creates an Iterator which traverses along the concatenation of the given iterables.
     *
     * @param iterables The iterables
     * @param <T>       Component type.
     * @return A new {@code io.vavr.collection.Iterator}
     */
    @SuppressWarnings("varargs")
    @SafeVarargs
    static <T> Iterator<T> concat(Iterable<? extends T>... iterables) {
        Objects.requireNonNull(iterables, "iterables is null");
        if (iterables.length == 0) {
            return empty();
        } else {
            return new ConcatIterator<>(Stream.of(iterables).map(Iterator::ofAll).iterator());
        }
    }

    /**
     * Creates an Iterator which traverses along the concatenation of the given iterables.
     *
     * @param iterables The iterable of iterables
     * @param <T>       Component type.
     * @return A new {@code io.vavr.collection.Iterator}
     */
    static <T> Iterator<T> concat(Iterable<? extends Iterable<? extends T>> iterables) {
        Objects.requireNonNull(iterables, "iterables is null");
        if (!iterables.iterator().hasNext()) {
            return empty();
        } else {
            return new ConcatIterator<>(Stream.ofAll(iterables).map(Iterator::ofAll).iterator());
        }
    }

    /**
     * Returns the empty Iterator.
     *
     * @param <T> Component type
     * @return The empty Iterator
     */
    @SuppressWarnings("unchecked")
    static <T> Iterator<T> empty() {
        return (Iterator<T>) EmptyIterator.INSTANCE;
    }

    /**
     * Narrows a widened {@code Iterator<? extends T>} to {@code Iterator<T>}
     * by performing a type-safe cast. This is eligible because immutable/read-only
     * collections are covariant.
     *
     * @param iterator An {@code Iterator}.
     * @param <T>      Component type of the {@code Iterator}.
     * @return the given {@code iterator} instance as narrowed type {@code Iterator<T>}.
     */
    @SuppressWarnings("unchecked")
    static <T> Iterator<T> narrow(Iterator<? extends T> iterator) {
        return (Iterator<T>) iterator;
    }

    /**
     * Creates an Iterator which traverses one element.
     *
     * @param element An element
     * @param <T>     Component type.
     * @return A new Iterator
     */
    static <T> Iterator<T> of(T element) {
        return new AbstractIterator<T>() {

            boolean hasNext = true;

            @Override
            public boolean hasNext() {
                return hasNext;
            }

            @Override
            public T getNext() {
                hasNext = false;
                return element;
            }
        };
    }

    /**
     * Creates an Iterator which traverses the given elements.
     *
     * @param elements Zero or more elements
     * @param <T>      Component type
     * @return A new Iterator
     */
    @SafeVarargs
    static <T> Iterator<T> of(T... elements) {
        Objects.requireNonNull(elements, "elements is null");
        if (elements.length == 0) {
            return empty();
        } else {
            return new AbstractIterator<T>() {

                int index = 0;

                @Override
                public boolean hasNext() {
                    return index < elements.length;
                }

                @Override
                public T getNext() {
                    return elements[index++];
                }
            };
        }
    }

    /**
     * Creates an Iterator based on the given Iterable. This is a convenience method for
     * {@code Iterator.ofAll(iterable.iterator()}.
     *
     * @param iterable A {@link Iterable}
     * @param <T>      Component type.
     * @return A new {@code io.vavr.collection.Iterator}
     */
    @SuppressWarnings("unchecked")
    static <T> Iterator<T> ofAll(Iterable<? extends T> iterable) {
        Objects.requireNonNull(iterable, "iterable is null");
        if (iterable instanceof Iterator) {
            return (Iterator<T>) iterable;
        } else {
            return ofAll(iterable.iterator());
        }
    }

    /**
     * Creates an Iterator based on the given Iterator by
     * delegating calls of {@code hasNext()} and {@code next()} to it.
     *
     * @param iterator A {@link java.util.Iterator}
     * @param <T>      Component type.
     * @return A new {@code io.vavr.collection.Iterator}
     */
    @SuppressWarnings("unchecked")
    static <T> Iterator<T> ofAll(java.util.Iterator<? extends T> iterator) {
        Objects.requireNonNull(iterator, "iterator is null");
        if (iterator instanceof Iterator) {
            return (Iterator<T>) iterator;
        } else {
            return new AbstractIterator<T>() {

                @Override
                public boolean hasNext() {
                    return iterator.hasNext();
                }

                @Override
                public T getNext() {
                    return iterator.next();
                }
            };
        }
    }

    /**
     * Creates an Iterator from boolean values.
     *
     * @param elements boolean values
     * @return A new Iterator of Boolean values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Boolean> ofAll(boolean... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Boolean>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Boolean getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Creates an Iterator from byte values.
     *
     * @param elements byte values
     * @return A new Iterator of Byte values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Byte> ofAll(byte... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Byte>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Byte getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Creates an Iterator from char values.
     *
     * @param elements char values
     * @return A new Iterator of Character values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Character> ofAll(char... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Character>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Character getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Creates ann Iterator from double values.
     *
     * @param elements double values
     * @return A new Iterator of Double values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Double> ofAll(double... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Double>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Double getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Creates an Iterator from float values.
     *
     * @param elements float values
     * @return A new Iterator of Float values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Float> ofAll(float... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Float>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Float getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Creates an Iterator from int values.
     *
     * @param elements int values
     * @return A new Iterator of Integer values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Integer> ofAll(int... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Integer>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Integer getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Creates an Iterator from long values.
     *
     * @param elements long values
     * @return A new Iterator of Long values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Long> ofAll(long... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Long>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Long getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Creates an Iterator from short values.
     *
     * @param elements short values
     * @return A new Iterator of Short values
     * @throws NullPointerException if elements is null
     */
    static Iterator<Short> ofAll(short... elements) {
        Objects.requireNonNull(elements, "elements is null");
        return new AbstractIterator<Short>() {
            int i = 0;

            @Override
            public boolean hasNext() {
                return i < elements.length;
            }

            @Override
            public Short getNext() {
                return elements[i++];
            }
        };
    }

    /**
     * Returns an Iterator on a sequence of {@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 Iterator
     * @param n   The number of elements
     * @param f   The Function computing element values
     * @return An Iterator on a sequence of elements {@code f(0),f(1), ..., f(n - 1)}
     * @throws NullPointerException if {@code f} is null
     */
    static <T> Iterator<T> tabulate(int n, Function<? super Integer, ? extends T> f) {
        Objects.requireNonNull(f, "f is null");
        return io.vavr.collection.Collections.tabulate(n, f);
    }

    /**
     * Returns an Iterator on a sequence of {@code n} values supplied by a given Supplier {@code s}.
     *
     * @param <T> Component type of the Iterator
     * @param n   The number of elements
     * @param s   The Supplier computing element values
     * @return An iterator on a sequence of {@code n} elements, where each element contains the result supplied by {@code s}.
     * @throws NullPointerException if {@code s} is null
     */
    static <T> Iterator<T> fill(int n, Supplier<? extends T> s) {
        Objects.requireNonNull(s, "s is null");
        return io.vavr.collection.Collections.fill(n, s);
    }

    /**
     * Creates an Iterator of characters starting from {@code from}, extending to {@code toExclusive - 1}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.range('a', 'c')  // = ('a', 'b')
     * Iterator.range('c', 'a')  // = ()
     * </code>
     * </pre>
     *
     * @param from        the first character
     * @param toExclusive the successor of the last character
     * @return a range of characters as specified or the empty range if {@code from >= toExclusive}
     */
    static Iterator<Character> range(char from, char toExclusive) {
        return rangeBy(from, toExclusive, 1);
    }

    /**
     * Creates an Iterator of characters starting from {@code from}, extending to {@code toExclusive - 1},
     * with {@code step}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeBy('a', 'c', 1)  // = ('a', 'b')
     * Iterator.rangeBy('a', 'd', 2)  // = ('a', 'c')
     * Iterator.rangeBy('d', 'a', -2) // = ('d', 'b')
     * Iterator.rangeBy('d', 'a', 2)  // = ()
     * </code>
     * </pre>
     *
     * @param from        the first character
     * @param toExclusive the successor of the last character if step &gt; 0, the predecessor of the last character if step &lt; 0
     * @param step        the step
     * @return a range of characters as specified or the empty range if {@code signum(step) == signum(from - toExclusive)}.
     * @throws IllegalArgumentException if {@code step} is zero
     */
    static Iterator<Character> rangeBy(char from, char toExclusive, int step) {
        return rangeBy((int) from, (int) toExclusive, step).map(i -> (char) i.shortValue());
    }

    @GwtIncompatible("BigDecimalHelper is GwtIncompatible")
    static Iterator<Double> rangeBy(double from, double toExclusive, double step) {
        final BigDecimal fromDecimal = asDecimal(from), toDecimal = asDecimal(toExclusive), stepDecimal = asDecimal(step);
        return rangeBy(fromDecimal, toDecimal, stepDecimal).map(BigDecimal::doubleValue);
    }

    static Iterator<BigDecimal> rangeBy(BigDecimal from, BigDecimal toExclusive, BigDecimal step) {
        if (step.signum() == 0) {
            throw new IllegalArgumentException("step cannot be 0");
        } else if (areEqual(from, toExclusive) || step.signum() == from.subtract(toExclusive).signum()) {
            return empty();
        } else {
            if (step.signum() > 0) {
                return new AbstractIterator<BigDecimal>() {
                    BigDecimal i = from;

                    @Override
                    public boolean hasNext() {
                        return i.compareTo(toExclusive) < 0;
                    }

                    @Override
                    public BigDecimal getNext() {
                        final BigDecimal next = this.i;
                        this.i = next.add(step);
                        return next;
                    }
                };
            } else {
                return new AbstractIterator<BigDecimal>() {
                    BigDecimal i = from;

                    @Override
                    public boolean hasNext() {
                        return i.compareTo(toExclusive) > 0;
                    }

                    @Override
                    public BigDecimal getNext() {
                        final BigDecimal next = this.i;
                        this.i = next.add(step);
                        return next;
                    }
                };
            }
        }
    }

    /**
     * Creates an Iterator of int numbers starting from {@code from}, extending to {@code toExclusive - 1}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.range(0, 0)  // = ()
     * Iterator.range(2, 0)  // = ()
     * Iterator.range(-2, 2) // = (-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}
     */
    static Iterator<Integer> range(int from, int toExclusive) {
        return rangeBy(from, toExclusive, 1);
    }

    /**
     * Creates an Iterator of int numbers starting from {@code from}, extending to {@code toExclusive - 1},
     * with {@code step}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeBy(1, 3, 1)  // = (1, 2)
     * Iterator.rangeBy(1, 4, 2)  // = (1, 3)
     * Iterator.rangeBy(4, 1, -2) // = (4, 2)
     * Iterator.rangeBy(4, 1, 2)  // = ()
     * </code>
     * </pre>
     *
     * @param from        the first number
     * @param toExclusive the last number + 1 if step &gt; 0, the last number - 1 if step &lt; 0
     * @param step        the step
     * @return a range of long values as specified or the empty range if {@code (from == toExclusive) || (step * (from - toExclusive) > 0)}.
     * @throws IllegalArgumentException if {@code step} is zero
     */
    static Iterator<Integer> rangeBy(int from, int toExclusive, int step) {
        final int toInclusive = toExclusive - (step > 0 ? 1 : -1);
        return rangeClosedBy(from, toInclusive, step);
    }

    /**
     * Creates an Iterator of long numbers starting from {@code from}, extending to {@code toExclusive - 1}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.range(0L, 0L)  // = ()
     * Iterator.range(2L, 0L)  // = ()
     * Iterator.range(-2L, 2L) // = (-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}
     */
    static Iterator<Long> range(long from, long toExclusive) {
        return rangeBy(from, toExclusive, 1);
    }

    /**
     * Creates an Iterator of long numbers starting from {@code from}, extending to {@code toExclusive - 1},
     * with {@code step}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeBy(1L, 3L, 1L)  // = (1L, 2L)
     * Iterator.rangeBy(1L, 4L, 2L)  // = (1L, 3L)
     * Iterator.rangeBy(4L, 1L, -2L) // = (4L, 2L)
     * Iterator.rangeBy(4L, 1L, 2L)  // = ()
     * </code>
     * </pre>
     *
     * @param from        the first number
     * @param toExclusive the last number + 1 if step &gt; 0, the last number - 1 if step &lt; 0
     * @param step        the step
     * @return a range of long values as specified or the empty range if {@code (from == toExclusive) || (step * (from - toExclusive) > 0)}.
     * @throws IllegalArgumentException if {@code step} is zero
     */
    static Iterator<Long> rangeBy(long from, long toExclusive, long step) {
        final long toInclusive = toExclusive - (step > 0 ? 1 : -1);
        return rangeClosedBy(from, toInclusive, step);
    }

    /**
     * Creates an Iterator of characters starting from {@code from}, extending to {@code toInclusive}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeClosed('a', 'c')  // = ('a', 'b', 'c')
     * Iterator.rangeClosed('c', 'a')  // = ()
     * </code>
     * </pre>
     *
     * @param from        the first character
     * @param toInclusive the last character
     * @return a range of characters as specified or the empty range if {@code from > toInclusive}
     */
    static Iterator<Character> rangeClosed(char from, char toInclusive) {
        return rangeClosedBy(from, toInclusive, 1);
    }

    /**
     * Creates an Iterator of characters starting from {@code from}, extending to {@code toInclusive},
     * with {@code step}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeClosedBy('a', 'c', 1)  // = ('a', 'b', 'c')
     * Iterator.rangeClosedBy('a', 'd', 2)  // = ('a', 'c')
     * Iterator.rangeClosedBy('d', 'a', -2) // = ('d', 'b')
     * Iterator.rangeClosedBy('d', 'a', 2)  // = ()
     * </code>
     * </pre>
     *
     * @param from        the first character
     * @param toInclusive the last character
     * @param step        the step
     * @return a range of characters as specified or the empty range if {@code signum(step) == signum(from - toInclusive)}.
     * @throws IllegalArgumentException if {@code step} is zero
     */
    static Iterator<Character> rangeClosedBy(char from, char toInclusive, int step) {
        return rangeClosedBy((int) from, (int) toInclusive, step).map(i -> (char) i.shortValue());
    }

    @GwtIncompatible
    static Iterator<Double> rangeClosedBy(double from, double toInclusive, double step) {
        if (from == toInclusive) {
            return of(from);
        }

        final double toExclusive = (step > 0) ? Math.nextUp(toInclusive) : Math.nextDown(toInclusive);
        return rangeBy(from, toExclusive, step);
    }

    /**
     * Creates an Iterator of int numbers starting from {@code from}, extending to {@code toInclusive}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeClosed(0, 0)  // = (0)
     * Iterator.rangeClosed(2, 0)  // = ()
     * Iterator.rangeClosed(-2, 2) // = (-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}
     */
    static Iterator<Integer> rangeClosed(int from, int toInclusive) {
        return rangeClosedBy(from, toInclusive, 1);
    }

    /**
     * Creates an Iterator of int numbers starting from {@code from}, extending to {@code toInclusive},
     * with {@code step}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeClosedBy(1, 3, 1)  // = (1, 2, 3)
     * Iterator.rangeClosedBy(1, 4, 2)  // = (1, 3)
     * Iterator.rangeClosedBy(4, 1, -2) // = (4, 2)
     * Iterator.rangeClosedBy(4, 1, 2)  // = ()
     * </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 {@code signum(step) == signum(from - toInclusive)}.
     * @throws IllegalArgumentException if {@code step} is zero
     */
    static Iterator<Integer> rangeClosedBy(int from, int toInclusive, int step) {
        if (step == 0) {
            throw new IllegalArgumentException("step cannot be 0");
        } else if (from == toInclusive) {
            return of(from);
        } else if (Integer.signum(step) == Integer.signum(from - toInclusive)) {
            return empty();
        } else {
            final int end = toInclusive - step;
            if (step > 0) {
                return new AbstractIterator<Integer>() {
                    int i = from - step;

                    @Override
                    public boolean hasNext() {
                        return i <= end;
                    }

                    @Override
                    public Integer getNext() {
                        return i += step;
                    }
                };
            } else {
                return new AbstractIterator<Integer>() {
                    int i = from - step;

                    @Override
                    public boolean hasNext() {
                        return i >= end;
                    }

                    @Override
                    public Integer getNext() {
                        return i += step;
                    }
                };
            }
        }
    }

    /**
     * Creates an Iterator of long numbers starting from {@code from}, extending to {@code toInclusive}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeClosed(0L, 0L)  // = (0L)
     * Iterator.rangeClosed(2L, 0L)  // = ()
     * Iterator.rangeClosed(-2L, 2L) // = (-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}
     */
    static Iterator<Long> rangeClosed(long from, long toInclusive) {
        return rangeClosedBy(from, toInclusive, 1L);
    }

    /**
     * Creates an Iterator of long numbers starting from {@code from}, extending to {@code toInclusive},
     * with {@code step}.
     * <p>
     * Examples:
     * <pre>
     * <code>
     * Iterator.rangeClosedBy(1L, 3L, 1L)  // = (1L, 2L, 3L)
     * Iterator.rangeClosedBy(1L, 4L, 2L)  // = (1L, 3L)
     * Iterator.rangeClosedBy(4L, 1L, -2L) // = (4L, 2L)
     * Iterator.rangeClosedBy(4L, 1L, 2L)  // = ()
     * </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 {@code signum(step) == signum(from - toInclusive)}.
     * @throws IllegalArgumentException if {@code step} is zero
     */
    static Iterator<Long> rangeClosedBy(long from, long toInclusive, long step) {
        if (step == 0) {
            throw new IllegalArgumentException("step cannot be 0");
        } else if (from == toInclusive) {
            return of(from);
        } else if (Long.signum(step) == Long.signum(from - toInclusive)) {
            return empty();
        } else {
            final long end = toInclusive - step;
            if (step > 0) {
                return new AbstractIterator<Long>() {
                    long i = from - step;

                    @Override
                    public boolean hasNext() {
                        return i <= end;
                    }

                    @Override
                    public Long getNext() {
                        return i += step;
                    }
                };
            } else {
                return new AbstractIterator<Long>() {
                    long i = from - step;

                    @Override
                    public boolean hasNext() {
                        return i >= end;
                    }

                    @Override
                    public Long getNext() {
                        return i += step;
                    }
                };

            }
        }
    }

    /**
     * Returns an infinite iterator of int values starting from {@code value}.
     * <p>
     * The {@code Iterator} extends to {@code Integer.MIN_VALUE} when passing {@code Integer.MAX_VALUE}.
     *
     * @param value a start int value
     * @return a new {@code Iterator} of int values starting from {@code from}
     */
    static Iterator<Integer> from(int value) {
        return new AbstractIterator<Integer>() {
            private int next = value;

            @Override
            public boolean hasNext() {
                return true;
            }

            @Override
            public Integer getNext() {
                return next++;
            }
        };
    }

    /**
     * Returns an infinite iterator of int values starting from {@code value} and spaced by {@code step}.
     * <p>
     * The {@code Iterator} extends to {@code Integer.MIN_VALUE} when passing {@code Integer.MAX_VALUE}.
     *
     * @param value a start int value
     * @param step  the step by which to advance on each iteration
     * @return a new {@code Iterator} of int values starting from {@code from}
     */
    static Iterator<Integer> from(int value, int step) {
        return new AbstractIterator<Integer>() {
            private int next = value;

            @Override
            public boolean hasNext() {
                return true;
            }

            @Override
            public Integer getNext() {
                final int result = next;
                next += step;
                return result;
            }
        };
    }

    /**
     * Returns an infinite iterator of long values starting from {@code value}.
     * <p>
     * The {@code Iterator} extends to {@code Long.MIN_VALUE} when passing {@code Long.MAX_VALUE}.
     *
     * @param value a start long value
     * @return a new {@code Iterator} of long values starting from {@code from}
     */
    static Iterator<Long> from(long value) {
        return new AbstractIterator<Long>() {
            private long next = value;

            @Override
            public boolean hasNext() {
                return true;
            }

            @Override
            public Long getNext() {
                return next++;
            }
        };
    }

    /**
     * Returns an infinite iterator of long values starting from {@code value} and spaced by {@code step}.
     * <p>
     * The {@code Iterator} extends to {@code Long.MIN_VALUE} when passing {@code Long.MAX_VALUE}.
     *
     * @param value a start long value
     * @param step  the step by which to advance on each iteration
     * @return a new {@code Iterator} of long values starting from {@code from}
     */
    static Iterator<Long> from(long value, long step) {
        return new AbstractIterator<Long>() {
            private long next = value;

            @Override
            public boolean hasNext() {
                return true;
            }

            @Override
            public Long getNext() {
                final long result = next;
                next += step;
                return result;
            }
        };
    }

    /**
     * Generates an infinite iterator using a value Supplier.
     *
     * @param supplier A Supplier of iterator values
     * @param <T>      value type
     * @return A new {@code Iterator}
     */
    static <T> Iterator<T> continually(Supplier<? extends T> supplier) {
        Objects.requireNonNull(supplier, "supplier is null");
        return new AbstractIterator<T>() {
            @Override
            public boolean hasNext() {
                return true;
            }

            @Override
            public T getNext() {
                return supplier.get();
            }
        };
    }

    /**
     * Generates an infinite iterator using a function to calculate the next value
     * based on the previous.
     *
     * @param seed The first value in the iterator
     * @param f    A function to calculate the next value based on the previous
     * @param <T>  value type
     * @return A new {@code Iterator}
     */
    static <T> Iterator<T> iterate(T seed, Function<? super T, ? extends T> f) {
        Objects.requireNonNull(f, "f is null");
        return new AbstractIterator<T>() {
            Function<? super T, ? extends T> nextFunc = s -> {
                nextFunc = f;
                return seed;
            };
            T current = null;

            @Override
            public boolean hasNext() {
                return true;
            }

            @Override
            public T getNext() {
                current = nextFunc.apply(current);
                return current;
            }
        };
    }

    /**
     * Creates an infinite iterator returning the given element.
     *
     * @param t   An element
     * @param <T> Element type
     * @return A new Iterator containing infinite {@code t}'s.
     */
    static <T> Iterator<T> continually(T t) {
        return new AbstractIterator<T>() {
            @Override
            public boolean hasNext() {
                return true;
            }

             @Override
             public T getNext() {
                 return t;
             }
         };
     }

     // -- Additional methods of Iterator

     @Override
     default <R> Iterator<R> collect(PartialFunction<? super T, ? extends R> partialFunction) {
         Objects.requireNonNull(partialFunction, "partialFunction is null");
         return filter(partialFunction::isDefinedAt).map(partialFunction::apply);
     }

     // DEV-NOTE: cannot use arg Iterable, it would be ambiguous
     default Iterator<T> concat(java.util.Iterator<? extends T> that) {
         Objects.requireNonNull(that, "that is null");
         if (!that.hasNext()) {
             return this;
         } else if (!hasNext()) {
             return ofAll(that);
         } else {
             return concat(this, ofAll(that));
         }
     }

     /**
      * Inserts an element between all elements of this Iterator.
      *
      * @param element An element.
      * @return an interspersed version of this
      */
     default Iterator<T> intersperse(T element) {
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {

                 boolean insertElement = false;

                 @Override
                 public boolean hasNext() {
                     return that.hasNext();
                 }

                 @Override
                 public T getNext() {
                     if (insertElement) {
                         insertElement = false;
                         return element;
                     } else {
                         insertElement = true;
                         return that.next();
                     }
                 }
             };
         }
     }

     /**
      * Transforms this {@code Iterator}.
      *
      * @param f   A transformation
      * @param <U> Type of transformation result
      * @return An instance of type {@code U}
      * @throws NullPointerException if {@code f} is null
      */
     default <U> U transform(Function<? super Iterator<T>, ? extends U> f) {
         Objects.requireNonNull(f, "f is null");
         return f.apply(this);
     }

     @Override
     default <U> Iterator<Tuple2<T, U>> zip(Iterable<? extends U> that) {
         return zipWith(that, Tuple::of);
     }

     @Override
     default <U, R> Iterator<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");
         if (isEmpty()) {
             return empty();
         } else {
             final Iterator<T> it1 = this;
             final java.util.Iterator<? extends U> it2 = that.iterator();
             return new AbstractIterator<R>() {
                 @Override
                 public boolean hasNext() {
                     return it1.hasNext() && it2.hasNext();
                 }

                 @Override
                 public R getNext() {
                     return mapper.apply(it1.next(), it2.next());
                 }
             };
         }
     }

     @Override
     default <U> Iterator<Tuple2<T, U>> zipAll(Iterable<? extends U> that, T thisElem, U thatElem) {
         Objects.requireNonNull(that, "that is null");
         final java.util.Iterator<? extends U> thatIt = that.iterator();
         if (isEmpty() && !thatIt.hasNext()) {
             return empty();
         } else {
             final Iterator<T> thisIt = this;
             return new AbstractIterator<Tuple2<T, U>>() {
                 @Override
                 public boolean hasNext() {
                     return thisIt.hasNext() || thatIt.hasNext();
                 }

                 @Override
                 public Tuple2<T, U> getNext() {
                     final T v1 = thisIt.hasNext() ? thisIt.next() : thisElem;
                     final U v2 = thatIt.hasNext() ? thatIt.next() : thatElem;
                     return Tuple.of(v1, v2);
                 }
             };
         }
     }

     @Override
     default Iterator<Tuple2<T, Integer>> zipWithIndex() {
         return zipWithIndex(Tuple::of);
     }

     @Override
     default <U> Iterator<U> zipWithIndex(BiFunction<? super T, ? super Integer, ? extends U> mapper) {
         Objects.requireNonNull(mapper, "mapper is null");
         if (isEmpty()) {
             return empty();
         } else {
             final Iterator<T> it1 = this;
             return new AbstractIterator<U>() {
                 private int index = 0;

                 @Override
                 public boolean hasNext() {
                     return it1.hasNext();
                 }

                 @Override
                 public U getNext() {
                     return mapper.apply(it1.next(), index++);
                 }
             };
         }
     }

     @Override
     default <T1, T2> Tuple2<Iterator<T1>, Iterator<T2>> unzip(
             Function<? super T, Tuple2<? extends T1, ? extends T2>> unzipper) {
         Objects.requireNonNull(unzipper, "unzipper is null");
         if (!hasNext()) {
             return Tuple.of(empty(), empty());
         } else {
             final Stream<Tuple2<? extends T1, ? extends T2>> source = Stream.ofAll(this.map(unzipper));
             return Tuple.of(source.map(t -> (T1) t._1).iterator(), source.map(t -> (T2) t._2).iterator());
         }
     }

     @Override
     default <T1, T2, T3> Tuple3<Iterator<T1>, Iterator<T2>, Iterator<T3>> unzip3(
             Function<? super T, Tuple3<? extends T1, ? extends T2, ? extends T3>> unzipper) {
         Objects.requireNonNull(unzipper, "unzipper is null");
         if (!hasNext()) {
             return Tuple.of(empty(), empty(), empty());
         } else {
             final Stream<Tuple3<? extends T1, ? extends T2, ? extends T3>> source = Stream.ofAll(this.map(unzipper));
             return Tuple.of(source.map(t -> (T1) t._1).iterator(), source.map(t -> (T2) t._2).iterator(), source.map(t -> (T3) t._3).iterator());
         }
     }

     /**
      * Creates an iterator from a seed value and a function.
      * The function takes the seed at first.
      * The function should return {@code None} when it's
      * done generating elements, otherwise {@code Some} {@code Tuple}
      * of the value to add to the resulting iterator and
      * the element for the next call.
      * <p>
      * Example:
      * <pre>
      * <code>
      * Iterator.unfold(10, x -&gt; x == 0
      *                 ? Option.none()
      *                 : Option.of(new Tuple2&lt;&gt;(x-1, x)));
      * // List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
      * </code>
      * </pre>
      *
      * @param <T>  type of seeds and unfolded values
      * @param seed the start value for the iteration
      * @param f    the function to get the next step of the iteration
      * @return a list with the values built up by the iteration
      * @throws NullPointerException if {@code f} is null
      */
     static <T> Iterator<T> unfold(T seed, Function<? super T, Option<Tuple2<? extends T, ? extends T>>> f) {
         return unfoldLeft(seed, f);
     }

     /**
      * Creates an iterator from a seed value and a function.
      * The function takes the seed at first.
      * The function should return {@code None} when it's
      * done generating elements, otherwise {@code Some} {@code Tuple}
      * of the value to add to the resulting iterator and
      * the element for the next call.
      * <p>
      * Example:
      * <pre>
      * <code>
      * Iterator.unfoldLeft(10, x -&gt; x == 0
      *                    ? Option.none()
      *                    : Option.of(new Tuple2&lt;&gt;(x-1, x)));
      * // List(1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
      * </code>
      * </pre>
      *
      * @param <T>  type of seeds
      * @param <U>  type of unfolded values
      * @param seed the start value for the iteration
      * @param f    the function to get the next step of the iteration
      * @return a list with the values built up by the iteration
      * @throws NullPointerException if {@code f} is null
      */
     static <T, U> Iterator<U> unfoldLeft(T seed, Function<? super T, Option<Tuple2<? extends T, ? extends U>>> f) {
         Objects.requireNonNull(f, "f is null");
         return Stream.<U> ofAll(
                 unfoldRight(seed, f.andThen(tupleOpt -> tupleOpt.map(t -> Tuple.of(t._2, t._1)))))
                 .reverse().iterator();
     }

     /**
      * Creates an iterator from a seed value and a function.
      * The function takes the seed at first.
      * The function should return {@code None} when it's
      * done generating elements, otherwise {@code Some} {@code Tuple}
      * of the element for the next call and the value to add to the
      * resulting iterator.
      * <p>
      * Example:
      * <pre>
      * <code>
      * Iterator.unfoldRight(10, x -&gt; x == 0
      *             ? Option.none()
      *             : Option.of(new Tuple2&lt;&gt;(x, x-1)));
      * // List(10, 9, 8, 7, 6, 5, 4, 3, 2, 1))
      * </code>
      * </pre>
      *
      * @param <T>  type of seeds
      * @param <U>  type of unfolded values
      * @param seed the start value for the iteration
      * @param f    the function to get the next step of the iteration
      * @return a list with the values built up by the iteration
      * @throws NullPointerException if {@code f} is null
      */
     static <T, U> Iterator<U> unfoldRight(T seed, Function<? super T, Option<Tuple2<? extends U, ? extends T>>> f) {
         Objects.requireNonNull(f, "the unfold iterating function is null");
         return new AbstractIterator<U>() {
             private Option<Tuple2<? extends U, ? extends T>> nextVal = f.apply(seed);

             @Override
             public boolean hasNext() {
                 return nextVal.isDefined();
             }

             @Override
             public U getNext() {
                 final U result = nextVal.get()._1;
                 nextVal = f.apply(nextVal.get()._2);
                 return result;
             }
         };
     }

     // -- Overridden methods of Traversable

     @Override
     default Iterator<T> distinct() {
         if (!hasNext()) {
             return empty();
         } else {
             return new DistinctIterator<>(this, io.vavr.collection.HashSet.empty(), Function.identity());
         }
     }

     @Override
     default Iterator<T> distinctBy(Comparator<? super T> comparator) {
         Objects.requireNonNull(comparator, "comparator is null");
         if (!hasNext()) {
             return empty();
         } else {
             return new DistinctIterator<>(this, TreeSet.empty(comparator), Function.identity());
         }
     }

     @Override
     default <U> Iterator<T> distinctBy(Function<? super T, ? extends U> keyExtractor) {
         Objects.requireNonNull(keyExtractor, "keyExtractor is null");
         if (!hasNext()) {
             return empty();
         } else {
             return new DistinctIterator<>(this, io.vavr.collection.HashSet.empty(), keyExtractor);
         }
     }

     /**
      * Removes up to n elements from this iterator.
      *
      * @param n A number
      * @return The empty iterator, if {@code n <= 0} or this is empty, otherwise a new iterator without the first n elements.
      */
     @Override
     default Iterator<T> drop(int n) {
         if (n <= 0) {
             return this;
         } else if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {

                 long count = n;

                 @Override
                 public boolean hasNext() {
                     while (count > 0 && that.hasNext()) {
                         that.next(); // discarded
                         count--;
                     }
                     return that.hasNext();
                 }

                 @Override
                 public T getNext() {
                     return that.next();
                 }
             };
         }
     }

     @Override
     default Iterator<T> dropRight(int n) {
         if (n <= 0) {
             return this;
         } else if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {
                 private io.vavr.collection.Queue<T> queue = io.vavr.collection.Queue.empty();

                 @Override
                 public boolean hasNext() {
                     while (queue.length() < n && that.hasNext()) {
                         queue = queue.append(that.next());
                     }
                     return queue.length() == n && that.hasNext();
                 }

                 @Override
                 public T getNext() {
                     final Tuple2<T, io.vavr.collection.Queue<T>> t = queue.append(that.next()).dequeue();
                     queue = t._2;
                     return t._1;
                 }
             };
         }
     }

     @Override
     default Iterator<T> dropUntil(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         return dropWhile(predicate.negate());
     }

     @Override
     default Iterator<T> dropWhile(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {

                 private T next;
                 private boolean cached = false;
                 private boolean first = true;

                 @Override
                 public boolean hasNext() {
                     if (cached) {
                         return true;
                     } else if (first) {
                         first = false;
                         while (that.hasNext()) {
                             next = that.next();
                             if (!predicate.test(next)) {
                                 cached = true;
                                 return true;
                             }
                         }
                         return false;
                     } else if (that.hasNext()) {
                         next = that.next();
                         cached = true;
                         return true;
                     } else {
                         return false;
                     }
                 }

                 @Override
                 public T getNext() {
                     cached = false;
                     return next;
                 }
             };
         }
     }

     /**
      * Returns an Iterator that contains elements that satisfy the given {@code predicate}.
      *
      * @param predicate A predicate
      * @return A new Iterator
      */
     @Override
     default Iterator<T> filter(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {

                 Option<T> next = Option.none();

                 @Override
                 public boolean hasNext() {
                     while (next.isEmpty() && that.hasNext()) {
                         final T candidate = that.next();
                         if (predicate.test(candidate)) {
                             next = Option.some(candidate);
                         }
                     }
                     return next.isDefined();
                 }

                 @Override
                 public T getNext() {
                     final T result = next.get();
                     next = Option.none();
                     return result;
                 }
             };
         }
     }

     @Override
     default Option<T> findLast(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         T last = null;
         while (hasNext()) {
             final T elem = next();
             if (predicate.test(elem)) {
                 last = elem;
             }
         }
         return Option.of(last);
     }

     /**
      * FlatMaps the elements of this Iterator to Iterables, which are iterated in the order of occurrence.
      *
      * @param mapper A mapper
      * @param <U>    Component type
      * @return A new Iterable
      */
     @Override
     default <U> Iterator<U> flatMap(Function<? super T, ? extends Iterable<? extends U>> mapper) {
         Objects.requireNonNull(mapper, "mapper is null");
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<U>() {

                 final Iterator<? extends T> inputs = that;
                 java.util.Iterator<? extends U> current = java.util.Collections.emptyIterator();

                 @Override
                 public boolean hasNext() {
                     boolean currentHasNext;
                     while (!(currentHasNext = current.hasNext()) && inputs.hasNext()) {
                         current = mapper.apply(inputs.next()).iterator();
                     }
                     return currentHasNext;
                 }

                 @Override
                 public U getNext() {
                     return current.next();
                 }
             };
         }
     }

     @Override
     default <U> U foldRight(U zero, BiFunction<? super T, ? super U, ? extends U> f) {
         Objects.requireNonNull(f, "f is null");
         return Stream.ofAll(this).foldRight(zero, f);
     }

     @Override
     default T get() {
         return head();
     }

     @Override
     default <C> Map<C, Iterator<T>> groupBy(Function<? super T, ? extends C> classifier) {
         return io.vavr.collection.Collections.groupBy(this, classifier, Iterator::ofAll);
     }

     @Override
     default Iterator<Seq<T>> grouped(int size) {
         return new GroupedIterator<>(this, size, size);
     }

     @Override
     default boolean hasDefiniteSize() {
         return false;
     }

     @Override
     default T head() {
         if (!hasNext()) {
             throw new NoSuchElementException("head() on empty iterator");
         }
         return next();
     }

     @Override
     default Iterator<T> init() {
         if (!hasNext()) {
             throw new UnsupportedOperationException();
         } else {
             return dropRight(1);
         }
     }

     @Override
     default Option<Iterator<T>> initOption() {
         return hasNext() ? Option.some(init()) : Option.none();
     }

     /**
      * An {@code Iterator} is computed synchronously.
      *
      * @return false
      */
     @Override
     default boolean isAsync() {
         return false;
     }

     @Override
     default boolean isEmpty() {
         return !hasNext();
     }

     /**
      * An {@code Iterator} is computed lazily.
      *
      * @return true
      */
     @Override
     default boolean isLazy() {
         return true;
     }

     @Override
     default boolean isTraversableAgain() {
         return false;
     }

     @Override
     default boolean isSequential() {
         return true;
     }

     @Override
     default Iterator<T> iterator() {
         return this;
     }

     @Override
     default int length() {
         return foldLeft(0, (n, ignored) -> n + 1);
     }

     /**
      * Maps the elements of this Iterator lazily using the given {@code mapper}.
      *
      * @param mapper A mapper.
      * @param <U>    Component type
      * @return A new Iterator
      */
     @Override
     default <U> Iterator<U> map(Function<? super T, ? extends U> mapper) {
         Objects.requireNonNull(mapper, "mapper is null");
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<U>() {

                 @Override
                 public boolean hasNext() {
                     return that.hasNext();
                 }

                 @Override
                 public U getNext() {
                     return mapper.apply(that.next());
                 }
             };
         }
     }

     @Override
     default Iterator<T> orElse(Iterable<? extends T> other) {
         return isEmpty() ? ofAll(other) : this;
     }

     @Override
     default Iterator<T> orElse(Supplier<? extends Iterable<? extends T>> supplier) {
         return isEmpty() ? ofAll(supplier.get()) : this;
     }

     @Override
     default Tuple2<Iterator<T>, Iterator<T>> partition(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         if (!hasNext()) {
             return Tuple.of(empty(), empty());
         } else {
             final Stream<T> that = Stream.ofAll(this);
             final Iterator<T> first = that.iterator().filter(predicate);
             final Iterator<T> second = that.iterator().filter(predicate.negate());
             return Tuple.of(first, second);
         }
     }

     @Override
     default Iterator<T> peek(Consumer<? super T> action) {
         Objects.requireNonNull(action, "action is null");
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {
                 @Override
                 public boolean hasNext() {
                     return that.hasNext();
                 }

                 @Override
                 public T getNext() {
                     final T next = that.next();
                     action.accept(next);
                     return next;
                 }
             };
         }
     }

     @Override
     default T reduceLeft(BiFunction<? super T, ? super T, ? extends T> op) {
         Objects.requireNonNull(op, "op is null");
         if (isEmpty()) {
             throw new NoSuchElementException("reduceLeft on Nil");
         } else {
             final Stream<T> stream = Stream.ofAll(this);
             return stream.tail().foldLeft(stream.head(), op);
         }
     }

     @Override
     default T reduceRight(BiFunction<? super T, ? super T, ? extends T> op) {
         Objects.requireNonNull(op, "op is null");
         if (isEmpty()) {
             throw new NoSuchElementException("reduceRight on Nil");
         } else {
             final Stream<T> reversed = Stream.ofAll(this).reverse();
             return reversed.reduceLeft((xs, x) -> op.apply(x, xs));
         }
     }

     @Override
     default Iterator<T> replace(T currentElement, T newElement) {
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {
                 boolean isFirst = true;

                 @Override
                 public boolean hasNext() {
                     return that.hasNext();
                 }

                 @Override
                 public T getNext() {
                     final T elem = that.next();
                     if (isFirst && Objects.equals(currentElement, elem)) {
                         isFirst = false;
                         return newElement;
                     } else {
                         return elem;
                     }
                 }
             };
         }
     }

     @Override
     default Iterator<T> replaceAll(T currentElement, T newElement) {
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {

                 @Override
                 public boolean hasNext() {
                     return that.hasNext();
                 }

                 @Override
                 public T getNext() {
                     final T elem = that.next();
                     if (Objects.equals(currentElement, elem)) {
                         return newElement;
                     } else {
                         return elem;
                     }
                 }
             };
         }
     }

     @Override
     default Iterator<T> retainAll(Iterable<? extends T> elements) {
         return io.vavr.collection.Collections.retainAll(this, elements);
     }

     @Override
     default Traversable<T> scan(T zero, BiFunction<? super T, ? super T, ? extends T> operation) {
         return scanLeft(zero, operation);
     }

     @Override
     default <U> Iterator<U> scanLeft(U zero, BiFunction<? super U, ? super T, ? extends U> operation) {
         Objects.requireNonNull(operation, "operation is null");
         if (isEmpty()) {
             return of(zero);
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<U>() {

                 boolean isFirst = true;
                 U acc = zero;

                 @Override
                 public boolean hasNext() {
                     return isFirst || that.hasNext();
                 }

                 @Override
                 public U getNext() {
                     if (isFirst) {
                         isFirst = false;
                         return acc;
                     } else {
                         acc = operation.apply(acc, that.next());
                         return acc;
                     }
                 }
             };
         }
     }

     // not lazy!
     @Override
     default <U> Iterator<U> scanRight(U zero, BiFunction<? super T, ? super U, ? extends U> operation) {
         Objects.requireNonNull(operation, "operation is null");
         if (isEmpty()) {
             return of(zero);
         } else {
             return io.vavr.collection.Collections.scanRight(this, zero, operation, Function.identity());
         }
     }

     @Override
     default Iterator<Seq<T>> slideBy(Function<? super T, ?> classifier) {
         Objects.requireNonNull(classifier, "classifier is null");
         if (!hasNext()) {
             return empty();
         } else {
             final Stream<T> source = Stream.ofAll(this);
             return new AbstractIterator<Seq<T>>() {
                 private Stream<T> that = source;
                 private Stream<T> next = null;

                 @Override
                 public boolean hasNext() {
                     while (next == null && !that.isEmpty()) {
                         final Object key = classifier.apply(that.head());
                         final Tuple2<Stream<T>, Stream<T>> split = that.splitAt(e -> !key.equals(classifier.apply(e)));
                         next = split._1;
                         that = split._2;
                     }
                     return next != null;
                 }

                 @Override
                 public Stream<T> getNext() {
                     final Stream<T> result = next;
                     next = null;
                     return result;
                 }
             };
         }
     }

     @Override
     default Iterator<Seq<T>> sliding(int size) {
         return sliding(size, 1);
     }

     @Override
     default Iterator<Seq<T>> sliding(int size, int step) {
         return new GroupedIterator<>(this, size, step);
     }

     @Override
     default Tuple2<Iterator<T>, Iterator<T>> span(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         if (!hasNext()) {
             return Tuple.of(empty(), empty());
         } else {
             final Stream<T> that = Stream.ofAll(this);
             return Tuple.of(that.iterator().takeWhile(predicate), that.iterator().dropWhile(predicate));
         }
     }

     @Override
     default String stringPrefix() {
         return "Iterator";
     }

     @Override
     default Iterator<T> tail() {
         if (!hasNext()) {
             throw new UnsupportedOperationException();
         } else {
             next(); // remove first element
             return this;
         }
     }

     @Override
     default Option<Iterator<T>> tailOption() {
         if (hasNext()) {
             next();
             return Option.some(this);
         } else {
             return Option.none();
         }
     }

     /**
      * Take the first n elements from this iterator.
      *
      * @param n A number
      * @return The empty iterator, if {@code n <= 0} or this is empty, otherwise a new iterator without the first n elements.
      */
     @Override
     default Iterator<T> take(int n) {
         if (n <= 0 || !hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {

                 long count = n;

                 @Override
                 public boolean hasNext() {
                     return count > 0 && that.hasNext();
                 }

                 @Override
                 public T getNext() {
                     count--;
                     return that.next();
                 }
             };
         }
     }

     @Override
     default Iterator<T> takeRight(int n) {
         if (n <= 0) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {
                 private io.vavr.collection.Queue<T> queue = io.vavr.collection.Queue.empty();

                 @Override
                 public boolean hasNext() {
                     while (that.hasNext()) {
                         queue = queue.enqueue(that.next());
                         if (queue.length() > n) {
                             queue = queue.dequeue()._2;
                         }
                     }
                     return queue.length() > 0;
                 }

                 @Override
                 public T getNext() {
                     final Tuple2<T, io.vavr.collection.Queue<T>> t = queue.dequeue();
                     queue = t._2;
                     return t._1;
                 }
             };
         }
     }

     @Override
     default Iterator<T> takeUntil(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         return takeWhile(predicate.negate());
     }

     @Override
     default Iterator<T> takeWhile(Predicate<? super T> predicate) {
         Objects.requireNonNull(predicate, "predicate is null");
         if (!hasNext()) {
             return empty();
         } else {
             final Iterator<T> that = this;
             return new AbstractIterator<T>() {

                 private T next;
                 private boolean cached = false;
                 private boolean finished = false;

                 @Override
                 public boolean hasNext() {
                     if (cached) {
                         return true;
                     } else if (finished) {
                         return false;
                     } else if (that.hasNext()) {
                         next = that.next();
                         if (predicate.test(next)) {
                             cached = true;
                             return true;
                         }
                     }
                     finished = true;
                     return false;
                 }

                 @Override
                 public T getNext() {
                     cached = false;
                     return next;
                 }
             };
         }
     }
 }

 interface IteratorModule {

     final class ConcatIterator<T> extends AbstractIterator<T> {

         private final Iterator<? extends Iterator<? extends T>> iterators;
         private Iterator<? extends T> current = Iterator.empty();

         ConcatIterator(Iterator<? extends Iterator<? extends T>> iterators) {
             this.iterators = iterators;
         }

         @Override
         public boolean hasNext() {
             while (!current.hasNext() && !iterators.isEmpty()) {
                 current = iterators.next();
             }
             return current.hasNext();
         }

         @Override
         public T getNext() {
             return current.next();
         }
     }

     final class DistinctIterator<T, U> extends AbstractIterator<T> {

         private final Iterator<? extends T> that;
         private io.vavr.collection.Set<U> known;
         private final Function<? super T, ? extends U> keyExtractor;
         private T next = null;

         DistinctIterator(Iterator<? extends T> that, io.vavr.collection.Set<U> set, Function<? super T, ? extends U> keyExtractor) {
             this.that = that;
             this.known = set;
             this.keyExtractor = keyExtractor;
         }

         @Override
         public boolean hasNext() {
             while (next == null && that.hasNext()) {
                 final T elem = that.next();
                 final U key = keyExtractor.apply(elem);
                 if (!known.contains(key)) {
                     known = known.add(key);
                     next = elem;
                 }
             }
             return next != null;
         }

         @Override
         public T getNext() {
             final T result = next;
             next = null;
             return result;
         }
     }

     final class EmptyIterator implements Iterator<Object> {

         static final EmptyIterator INSTANCE = new EmptyIterator();

         @Override
         public boolean hasNext() { return false; }

         @Override
         public Object next() { throw new NoSuchElementException(stringPrefix() + ".next()"); }

         @Override
         public String stringPrefix() {
             return "EmptyIterator";
         }

         @Override
         public String toString() {
             return stringPrefix() + "()";
         }
     }

     final class GroupedIterator<T> implements Iterator<Seq<T>> {

         private final Iterator<T> that;
         private final int size;
         private final int step;
         private final int gap;
         private final int preserve;

         private Object[] buffer;

         GroupedIterator(Iterator<T> that, int size, int step) {
             if (size < 1 || step < 1) {
                 throw new IllegalArgumentException("size (" + size + ") and step (" + step + ") must both be positive");
             }
             this.that = that;
             this.size = size;
             this.step = step;
             this.gap = Math.max(step - size, 0);
             this.preserve = Math.max(size - step, 0);
             this.buffer = take(that, new Object[size], 0, size);
         }

         @Override
         public boolean hasNext() {
             return buffer.length > 0;
         }

         @Override
         public Seq<T> next() {
             if (buffer.length == 0) {
                 throw new NoSuchElementException();
             }
             final Object[] result = buffer;
             if (that.hasNext()) {
                 buffer = new Object[size];
                 if (preserve > 0) {
                     System.arraycopy(result, step, buffer, 0, preserve);
                 }
                 if (gap > 0) {
                     drop(that, gap);
                     buffer = take(that, buffer, preserve, size);
                 } else {
                     buffer = take(that, buffer, preserve, step);
                 }
             } else {
                 buffer = new Object[0];
             }
             return Array.wrap(result);
         }

         private static void drop(Iterator<?> source, int count) {
             for (int i = 0; i < count && source.hasNext(); i++) {
                 source.next();
             }
         }

         private static Object[] take(Iterator<?> source, Object[] target, int offset, int count) {
             int i = offset;
             while (i < count + offset && source.hasNext()) {
                 target[i] = source.next();
                 i++;
             }
             if (i < target.length) {
                 final Object[] result = new Object[i];
                 System.arraycopy(target, 0, result, 0, i);
                 return result;
             } else {
                 return target;
             }
         }
     }

     final class BigDecimalHelper {

         @GwtIncompatible("Math::nextDown is not implemented")
         private static final Lazy<BigDecimal> INFINITY_DISTANCE = Lazy.of(() -> {
             final BigDecimal two = BigDecimal.valueOf(2);
             final BigDecimal supremum = BigDecimal.valueOf(Math.nextDown(Double.POSITIVE_INFINITY));
             BigDecimal lowerBound = supremum;
             BigDecimal upperBound = two.pow(Double.MAX_EXPONENT + 1);
             while (true) {
                 final BigDecimal magicValue = lowerBound.add(upperBound).divide(two, HALF_UP);
                 if (Double.isInfinite(magicValue.doubleValue())) {
                     if (areEqual(magicValue, upperBound)) {
                         return magicValue.subtract(supremum);
                     }
                     upperBound = magicValue;
                 } else {
                     lowerBound = magicValue;
                 }
             }
         });

         /* scale-independent equality */
         static boolean areEqual(BigDecimal from, BigDecimal toExclusive) {
             return from.compareTo(toExclusive) == 0;
         }

         /* parse infinite values also */
         @GwtIncompatible("Math::nextUp is not implemented")
         static BigDecimal asDecimal(double number) {
             if (number == NEGATIVE_INFINITY) {
                 final BigDecimal result = BigDecimal.valueOf(Math.nextUp(NEGATIVE_INFINITY));
                 return result.subtract(INFINITY_DISTANCE.get());
             } else if (number == POSITIVE_INFINITY) {
                 final BigDecimal result = BigDecimal.valueOf(Math.nextDown(POSITIVE_INFINITY));
                 return result.add(INFINITY_DISTANCE.get());
             } else {
                 return BigDecimal.valueOf(number);
             }
         }
     }
 }