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Add Skip List (#3154)
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Artem Boiarshinov
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package com.thealgorithms.datastructures.lists;
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import java.util.*;
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import java.util.stream.Collectors;
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import java.util.stream.IntStream;
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/**
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* Skip list is a data structure that allows {@code O(log n)} search complexity
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* as well as {@code O(log n)} insertion complexity within an ordered sequence
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* of {@code n} elements. Thus it can get the best features of a sorted array
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* (for searching) while maintaining a linked list-like structure that allows
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* insertion, which is not possible with a static array.
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* <p>
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* A skip list is built in layers. The bottom layer is an ordinary ordered
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* linked list. Each higher layer acts as an "express lane" for the lists
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* below.
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* <pre>
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* [ ] ------> [ ] --> [ ]
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* [ ] --> [ ] [ ] --> [ ]
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* [ ] [ ] [ ] [ ] [ ] [ ]
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* H 0 1 2 3 4
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* </pre>
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*
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* @param <E> type of elements
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* @see <a href="https://en.wikipedia.org/wiki/Skip_list">Wiki. Skip list</a>
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*/
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public class SkipList<E extends Comparable<E>> {
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/**
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* Node before first node.
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*/
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private final Node<E> head;
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/**
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* Maximum layers count.
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* Calculated by {@link #heightStrategy}.
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*/
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private final int height;
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/**
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* Function for determining height of new nodes.
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* @see HeightStrategy
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*/
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private final HeightStrategy heightStrategy;
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/**
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* Current count of elements in list.
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*/
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private int size;
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private static final int DEFAULT_CAPACITY = 100;
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public SkipList() {
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this(DEFAULT_CAPACITY, new BernoulliHeightStrategy());
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}
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public SkipList(int expectedCapacity, HeightStrategy heightStrategy) {
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this.heightStrategy = heightStrategy;
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this.height = heightStrategy.height(expectedCapacity);
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this.head = new Node<>(null, this.height);
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this.size = 0;
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}
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public void add(E e) {
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Objects.requireNonNull(e);
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Node<E> current = head;
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int layer = height;
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Node<E>[] toFix = new Node[height + 1];
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while (layer >= 0) {
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Node<E> next = current.next(layer);
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if (next == null || next.getValue().compareTo(e) > 0) {
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toFix[layer] = current;
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layer--;
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} else {
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current = next;
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}
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}
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int nodeHeight = heightStrategy.nodeHeight(height);
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Node<E> node = new Node<>(e, nodeHeight);
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for (int i = 0; i <= nodeHeight; i++) {
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if (toFix[i].next(i) != null) {
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node.setNext(i, toFix[i].next(i));
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toFix[i].next(i).setPrevious(i, node);
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}
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toFix[i].setNext(i, node);
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node.setPrevious(i, toFix[i]);
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}
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size++;
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}
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public E get(int index) {
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int counter = -1; // head index
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Node<E> current = head;
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while (counter != index) {
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current = current.next(0);
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counter++;
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}
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return current.value;
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}
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public void remove(E e) {
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Objects.requireNonNull(e);
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Node<E> current = head;
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int layer = height;
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while (layer >= 0) {
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Node<E> next = current.next(layer);
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if (e.equals(current.getValue())) {
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break;
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} else if (next == null || next.getValue().compareTo(e) > 0) {
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layer--;
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} else {
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current = next;
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}
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}
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for (int i = 0; i <= layer; i++) {
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current.previous(i).setNext(i, current.next(i));
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current.next(i).setPrevious(i, current.previous(i));
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}
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size--;
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}
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/**
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* A search for a target element begins at the head element in the top
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* list, and proceeds horizontally until the current element is greater
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* than or equal to the target. If the current element is equal to the
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* target, it has been found. If the current element is greater than the
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* target, or the search reaches the end of the linked list, the procedure
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* is repeated after returning to the previous element and dropping down
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* vertically to the next lower list.
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*
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* @param e element whose presence in this list is to be tested
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* @return true if this list contains the specified element
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*/
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public boolean contains(E e) {
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Objects.requireNonNull(e);
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Node<E> current = head;
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int layer = height;
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while (layer >= 0) {
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Node<E> next = current.next(layer);
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if (e.equals(current.getValue())) {
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return true;
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} else if (next == null || next.getValue().compareTo(e) > 0) {
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layer--;
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} else {
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current = next;
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}
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}
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return false;
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}
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public int size() {
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return size;
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}
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/**
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* Print height distribution of the nodes in a manner:
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* <pre>
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* [ ] --- --- [ ] --- [ ]
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* [ ] --- [ ] [ ] --- [ ]
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* [ ] [ ] [ ] [ ] [ ] [ ]
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* H 0 1 2 3 4
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* </pre>
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* Values of nodes is not presented.
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*
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* @return string representation
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*/
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@Override
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public String toString() {
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List<boolean[]> layers = new ArrayList<>();
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int sizeWithHeader = size + 1;
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for (int i = 0; i <= height; i++) {
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layers.add(new boolean[sizeWithHeader]);
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}
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Node<E> current = head;
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int position = 0;
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while (current != null) {
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for (int i = 0; i <= current.height; i++) {
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layers.get(i)[position] = true;
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}
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current = current.next(0);
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position++;
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}
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Collections.reverse(layers);
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String result = layers.stream()
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.map(layer -> {
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StringBuilder acc = new StringBuilder();
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for (boolean b : layer) {
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if (b) {
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acc.append("[ ]");
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} else {
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acc.append("---");
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}
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acc.append(" ");
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}
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return acc.toString();
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})
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.collect(Collectors.joining("\n"));
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String positions = IntStream.range(0, sizeWithHeader - 1)
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.mapToObj(i -> String.format("%3d", i))
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.collect(Collectors.joining(" "));
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return result + String.format("%n H %s%n", positions);
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}
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/**
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* Value container.
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* Each node have pointers to the closest nodes left and right from current
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* on each layer of nodes height.
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* @param <E> type of elements
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*/
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private static class Node<E> {
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private final E value;
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private final int height;
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private final List<Node<E>> forward;
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private final List<Node<E>> backward;
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@SuppressWarnings("unchecked")
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public Node(E value, int height) {
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this.value = value;
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this.height = height;
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// predefined size lists with null values in every cell
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this.forward = Arrays.asList(new Node[height + 1]);
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this.backward = Arrays.asList(new Node[height + 1]);
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}
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public Node<E> next(int layer) {
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checkLayer(layer);
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return forward.get(layer);
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}
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public void setNext(int layer, Node<E> node) {
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forward.set(layer, node);
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}
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public void setPrevious(int layer, Node<E> node) {
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backward.set(layer, node);
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}
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public Node<E> previous(int layer) {
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checkLayer(layer);
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return backward.get(layer);
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}
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public E getValue() {
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return value;
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}
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private void checkLayer(int layer) {
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if (layer < 0 || layer > height) {
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throw new IllegalArgumentException();
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}
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}
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}
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/**
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* Height strategy is a way of calculating maximum height for skip list
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* and height for each node.
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* @see BernoulliHeightStrategy
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*/
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public interface HeightStrategy {
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int height(int expectedSize);
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int nodeHeight(int heightCap);
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}
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/**
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* In most common skip list realisation element in layer {@code i} appears
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* in layer {@code i+1} with some fixed probability {@code p}.
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* Two commonly used values for {@code p} are 1/2 and 1/4.
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* Probability of appearing element in layer {@code i} could be calculated
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* with <code>P = p<sup>i</sup>(1 - p)</code>
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* <p>
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* Maximum height that would give the best search complexity
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* calculated by <code>log<sub>1/p</sub>n</code>
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* where {@code n} is an expected count of elements in list.
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*/
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public static class BernoulliHeightStrategy implements HeightStrategy {
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private final double probability;
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private static final double DEFAULT_PROBABILITY = 0.5;
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private static final Random RANDOM = new Random();
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public BernoulliHeightStrategy() {
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this.probability = DEFAULT_PROBABILITY;
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}
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public BernoulliHeightStrategy(double probability) {
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if (probability <= 0 || probability >= 1) {
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throw new IllegalArgumentException("Probability should be from 0 to 1. But was: " + probability);
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}
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this.probability = probability;
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}
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@Override
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public int height(int expectedSize) {
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long height = Math.round(Math.log10(expectedSize) / Math.log10(1 / probability));
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if (height > Integer.MAX_VALUE) {
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throw new IllegalArgumentException();
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}
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return (int) height;
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}
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@Override
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public int nodeHeight(int heightCap) {
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int level = 0;
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double border = 100 * (1 - probability);
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while (((RANDOM.nextInt(Integer.MAX_VALUE) % 100) + 1) > border) {
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if (level + 1 >= heightCap) {
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return level;
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}
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level++;
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}
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return level;
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}
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}
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}
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