数据结构与算法 | 线性表 —— 链表

pexels-photo-1322185

原文链接：https://wangwei.one/posts/java-data-structures-and-algorithms-linkedlist.html

链表

定义

逻辑结构上一个挨一个的数据，在实际存储时，并没有像顺序表那样也相互紧挨着。恰恰相反，数据随机分布在内存中的各个位置，这种存储结构称为线性表的链式存储。

由于分散存储，为了能够体现出数据元素之间的逻辑关系，每个数据元素在存储的同时，要配备一个指针，用于指向它的直接后继元素，即每一个数据元素都指向下一个数据元素（最后一个指向NULL(空)）。这种结构成为 "单向链表"。

SingleLinkedList

在单向链表的基础上，给各个结点额外配备一个指针变量，用于指向每个结点的直接前趋元素。这样的链表被称为“双向链表”或者“双链表”。

DoublyLinkedList

当单向链表的尾部数据指向头部数据时，就构成了单向循环链表。

SinglyCircularLinkedList

当双向链表的头部和尾部相互指向时，就构成了双向循环链表。

DoublyCircularLinkedList

单向链表

单向链表在插入元素、删除元素时，需要获取前驱元素，需要从head开始遍历，时间复杂度为O(n)。

根据index查询对应元素，也需要从head开始遍历，时间复杂度为O(n)。

代码实现

package one.wangwei.algorithms.datastructures.list.impl;

import one.wangwei.algorithms.datastructures.list.IList;

/**
 * Single Linked List
 *
 * @author https://wangwei.one
 * @date 2018/12/25
 */
public class SingleLinkedList<T> implements IList<T> {

    /**
     * size
     */
    private int size = 0;
    /**
     * head node
     */
    private Node<T> head;
    /**
     * tail node
     */
    private Node<T> tail;

    /**
     * add element
     *
     * @param element
     * @return
     */
    @Override
    public boolean add(T element) {
        return addLast(element);
    }

    /**
     * add element at index
     *
     * @param index
     * @param element
     * @return
     */
    @Override
    public boolean add(int index, T element) {
        if (index < 0 || index > size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
        if (index == size) {
            return add(element);
        } else {
            return addBefore(index, element);
        }
    }

    /**
     * Add Last element
     *
     * @param element
     * @return
     */
    private boolean addLast(T element) {
        Node<T> last = tail;
        Node<T> newNode = new Node<>(null, element);
        tail = newNode;
        // if linked list is empty
        if (last == null) {
            head = newNode;
        } else {
            last.next = newNode;
        }
        size++;
        return true;
    }

    /**
     * add element before certain element
     *
     * @param index
     * @param element
     * @return
     */
    private boolean addBefore(int index, T element) {
        checkPositionIndex(index);
        // prev node
        Node<T> prev = null;
        Node<T> x = head;
        for (int i = 0; i < index; i++) {
            prev = x;
            x = x.next;
        }
        // current node
        Node<T> current = x;
        // new node
        Node<T> newNode = new Node<>(current, element);
        // if current node is head
        if (prev == null) {
            head = newNode;
        } else {
            prev.next = newNode;
        }
        size++;
        return true;
    }

    /**
     * remove element
     *
     * @param element
     * @return
     */
    @Override
    public boolean remove(T element) {
        Node<T> prev = null;
        Node<T> x = head;
        if (element == null) {
            while (x != null && x.element != null) {
                prev = x;
                x = x.next;
            }
        } else {
            while (x != null && !x.element.equals(element)) {
                prev = x;
                x = x.next;
            }
        }

        // if this linked is null OR don't find element
        if (x == null) {
            return false;
        }

        Node<T> next = x.next;

        // if delete node is head
        if (prev == null) {
            head = next;
        } else {
            prev.next = next;
        }
        // if delete node is tail
        if (next == null) {
            tail = prev;
        }

        // for GC
        x.element = null;
        x = null;

        size--;
        return true;
    }

    /**
     * remove element by index
     *
     * @param index
     * @return
     */
    @Override
    public T remove(int index) {
        checkPositionIndex(index);
        Node<T> prev = null;
        Node<T> x = head;
        for (int i = 0; i < index; i++) {
            prev = x;
            x = x.next;
        }

        // if linked is empty
        if (x == null) {
            return null;
        }

        Node<T> next = x.next;

        // if delete node is head
        if (prev == null) {
            head = next;
        } else {
            prev.next = next;
        }

        // if delete node is tail
        if (next == null) {
            tail = prev;
        }
        size--;
        return x.element;
    }

    /**
     * set element by index
     *
     * @param index
     * @param element
     * @return old element
     */
    @Override
    public T set(int index, T element) {
        checkPositionIndex(index);
        Node<T> node = node(index);
        T oldElement = node.element;
        node.element = element;
        return oldElement;
    }
    
    /**
     * get element by index
     *
     * @param index
     * @return
     */
    @Override
    public T get(int index) {
        Node<T> node = node(index);
        return node == null ? null : node.element;
    }

    /**
     * get element by index
     *
     * @param index
     * @return
     */
    private Node<T> node(int index) {
        checkPositionIndex(index);
        Node<T> x = head;
        for (int i = 0; i < index; i++) {
            x = x.next;
        }
        return x;
    }

    /**
     * check index
     *
     * @param index
     */
    private void checkPositionIndex(int index) {
        if (index < 0 || index >= size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
    }

    /**
     * clear list
     */
    @Override
    public void clear() {
        for (Node<T> x = head; x != null; ) {
            Node<T> next = x.next;
            x.element = null;
            x.next = null;
            x = next;
        }
        head = tail = null;
        size = 0;
    }

    /**
     * contain certain element
     *
     * @param element
     */
    @Override
    public boolean contains(T element) {
        if (element == null) {
            for (Node<T> x = head; x != null; x = x.next) {
                if (x.element == null) {
                    return true;
                }
            }
        } else {
            for (Node<T> x = head; x != null; x = x.next) {
                if (x.element.equals(element)) {
                    return true;
                }
            }
        }
        return false;
    }

    /**
     * get list size
     *
     * @return
     */
    @Override
    public int size() {
        return size;
    }

    /**
     * Linked List Node
     *
     * @param <T>
     */
    private class Node<T> {
        private Node<T> next;
        private T element;

        public Node(Node<T> next, T element) {
            this.next = next;
            this.element = element;
        }
    }
}

源代码

双向链表

相比于单向链表，双向链表多了一个前驱指针，在查找前驱节点时，时间复杂度降低为了O(1)。

通过index查询，删除某个node节点，时间复杂度都降为了O(1)。代码如下：

代码实现

package one.wangwei.algorithms.datastructures.list.impl;

import one.wangwei.algorithms.datastructures.list.IList;

/**
 * Doubly Linked List
 *
 * @param <T>
 * @author https://wangwei.one
 * @date 2018/04/28
 */
public class DoublyLinkedList<T> implements IList<T> {

    /**
     * size
     */
    private int size = 0;
    /**
     * head element
     */
    private Node<T> head = null;
    /**
     * tail element
     */
    private Node<T> tail = null;

    /**
     * add element
     *
     * @param element
     * @return
     */
    @Override
    public boolean add(T element) {
        return addLast(element);
    }

    /**
     * add element at index
     *
     * @param index
     * @param element
     * @return
     */
    @Override
    public boolean add(int index, T element) {
        if (index < 0 || index > size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
        if (index == size) {
            return add(element);
        } else {
            return addBefore(element, node(index));
        }
    }

    /**
     * Add Last element
     *
     * @param element
     * @return
     */
    private boolean addLast(T element) {
        final Node<T> last = tail;
        Node<T> newNode = new Node<>(last, element, null);
        tail = newNode;
        if (last == null) {
            head = newNode;
        } else {
            last.next = newNode;
        }
        size++;
        return true;
    }

    /**
     * add element before certain element
     *
     * @param element
     * @param target
     * @return
     */
    private boolean addBefore(T element, Node<T> target) {
        Node<T> prev = target.prev;
        Node<T> newNode = new Node<>(prev, element, target);
        target.prev = newNode;
        if (prev == null) {
            head = newNode;
        } else {
            prev.next = newNode;
        }
        size++;
        return true;
    }

    /**
     * remove node by element
     *
     * @param element
     * @return
     */
    @Override
    public boolean remove(T element) {
        if (element == null) {
            for (Node<T> x = head; x != null; x = x.next) {
                if (x.element == null) {
                    unlink(x);
                    return true;
                }
            }
        } else {
            for (Node<T> x = head; x != null; x = x.next) {
                if (element.equals(x.element)) {
                    unlink(x);
                    return true;
                }
            }
        }
        return false;
    }

    /**
     * remove node by index
     *
     * @param index
     * @return
     */
    @Override
    public T remove(int index) {
        return unlink(node(index));
    }

    /**
     * get element by index
     *
     * @param index
     * @return
     */
    private Node<T> node(int index) {
        checkPositionIndex(index);
        if (index < (size >> 1)) {
            Node<T> x = head;
            for (int i = 0; i < index; i++) {
                x = x.next;
            }
            return x;
        } else {
            Node<T> x = tail;
            for (int i = size - 1; i > index; i--) {
                x = x.prev;
            }
            return x;
        }
    }

    /**
     * unlink node
     *
     * @param node
     */
    private T unlink(Node<T> node) {
        final T element = node.element;
        final Node<T> prev = node.prev;
        final Node<T> next = node.next;

        // if unlink is head
        if (prev == null) {
            head = next;
        } else {
            prev.next = next;
            // clear prev
            node.prev = null;
        }

        // if unlink is tail
        if (next == null) {
            tail = prev;
        } else {
            next.prev = prev;
            node.next = null;
        }

        node.element = null;
        size--;
        return element;
    }

    private void checkPositionIndex(int index) {
        if (index < 0 || index >= size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
    }

    /**
     * set element by index
     *
     * @param index
     * @param element
     * @return
     */
    @Override
    public T set(int index, T element) {
        checkPositionIndex(index);
        Node<T> oldNode = node(index);
        T oldElement = oldNode.element;
        oldNode.element = element;
        return oldElement;
    }

    /**
     * get element by index
     *
     * @param index
     * @return
     */
    @Override
    public T get(int index) {
        Node<T> node = node(index);
        return node == null ? null : node.element;
    }

    /**
     * clear list
     */
    @Override
    public void clear() {
        for (Node<T> x = head; x != null; ) {
            Node<T> next = x.next;
            x.element = null;
            x.next = null;
            x.prev = null;
            x = next;
        }
        head = tail = null;
        size = 0;
    }

    /**
     * contain certain element
     *
     * @param element
     */
    @Override
    public boolean contains(T element) {
        if (element == null) {
            for (Node<T> x = head; x != null; x = x.next) {
                if (x.element == null) {
                    return true;
                }
            }
        } else {
            for (Node<T> x = head; x != null; x = x.next) {
                if (element.equals(x.element)) {
                    return true;
                }
            }
        }
        return false;
    }

    /**
     * get list size
     *
     * @return
     */
    @Override
    public int size() {
        return size;
    }

    /**
     * node
     *
     * @param <T>
     */
    private class Node<T> {

        private T element;
        private Node<T> prev;
        private Node<T> next;

        public Node(Node<T> prev, T element, Node<T> next) {
            this.element = element;
            this.prev = prev;
            this.next = next;
        }
    }

}

源代码

单向循环链表

与单向链表一样，在寻找前驱节点时，需要遍历整个链表，时间复杂度为O(n).

在第一次添加元素时，特别注意，head与tail为同一节点，并且需要自指向。

package one.wangwei.algorithms.datastructures.list.impl;

import one.wangwei.algorithms.datastructures.list.IList;

/**
 * Singly Circular Linked List
 *
 * @param <T>
 * @author https://wangwei.one
 * @date 2018/05/03
 */
public class SinglyCircularLinkedList<T> implements IList<T> {

    /**
     * size
     */
    private int size = 0;
    /**
     * head node
     */
    private Node<T> head = null;
    /**
     * tail node
     */
    private Node<T> tail = null;

    /**
     * add element
     *
     * @param element
     * @return
     */
    @Override
    public boolean add(T element) {
        return addLast(element);
    }

    /**
     * add element at index
     *
     * @param index
     * @param element
     * @return
     */
    @Override
    public boolean add(int index, T element) {
        if (index < 0 || index > size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
        if (index == size) {
            return add(element);
        } else {
            return addBefore(index, element);
        }
    }

    /**
     * Add Last element
     *
     * @param element
     * @return
     */
    private boolean addLast(T element) {
        final Node<T> last = tail;
        Node<T> newElement = new Node<>(element, head);
        tail = newElement;
        if (last == null) {
            head = newElement;
            // we need linked itself when add an element first
            tail.next = head;
        } else {
            last.next = newElement;
        }
        size++;
        return true;
    }

    /**
     * add element before certain element
     *
     * @param element
     * @param element
     * @return
     */
    private boolean addBefore(int index, T element) {
        checkPositionIndex(index);
        // prev node, start with tail
        Node<T> prev = tail;
        Node<T> x = head;
        for (int i = 0; i < index; i++) {
            prev = x;
            x = x.next;
        }
        // current node
        Node<T> current = x;
        // new node
        Node<T> newNode = new Node<>(element, current);
        if (index == 0) {
            head = newNode;
        }
        prev.next = newNode;
        size++;
        return true;
    }

    /**
     * remove node by element
     *
     * @param element
     * @return
     */
    @Override
    public boolean remove(T element) {
        // start with tail
        Node<T> prev = tail;
        // start with head
        Node<T> x = head;
        // start with index -1
        int prevIndex = -1;

        for (int i = 0; i < size; i++) {
            if (element == null && x.element == null) {
                break;
            }
            if (element != null && element.equals(x.element)) {
                break;
            }
            prev = x;
            x = x.next;
            prevIndex = i;
        }

        // if this linked list is empty
        if (x == null) {
            return false;
        }

        // if don't match element
        if (prevIndex == size - 1) {
            return false;
        }

        Node<T> next = x.next;

        // if delete node is head
        if (prevIndex == -1) {
            head = next;
        }

        // if delete node is tail
        if (prevIndex == size - 2) {
            tail = prev;
        }

        prev.next = next;

        size--;

        if (size == 0) {
            head = tail = null;
        }

        // for GC
        x = null;

        return true;
    }

    /**
     * remove element by index
     *
     * @param index
     * @return
     */
    @Override
    public T remove(int index) {
        checkPositionIndex(index);
        Node<T> prev = tail;
        Node<T> x = head;
        for (int i = 0; i < index; i++) {
            prev = x;
            x = x.next;
        }

        // if linked is empty
        if (x == null) {
            return null;
        }

        Node<T> next = x.next;

        // if delete node is head
        if (index == 0) {
            head = next;
        }

        // if delete node is tail
        if (index == size - 1) {
            tail = prev;
        }

        prev.next = next;

        size--;

        if (size == 0) {
            head = tail = null;
        }

        return x.element;
    }

    /**
     * get element by index
     *
     * @param index
     * @return
     */
    private Node<T> node(int index) {
        checkPositionIndex(index);
        Node<T> x = head;
        for (int i = 0; i < index; i++) {
            x = x.next;
        }
        return x;
    }

    private void checkPositionIndex(int index) {
        if (index < 0 || index >= size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
    }

    /**
     * set element by index
     *
     * @param index
     * @param element
     * @return
     */
    @Override
    public T set(int index, T element) {
        checkPositionIndex(index);
        Node<T> oldNode = node(index);
        T oldElement = oldNode.element;
        oldNode.element = element;
        return oldElement;
    }

    /**
     * get element by index
     *
     * @param index
     * @return
     */
    @Override
    public T get(int index) {
        return node(index).element;
    }

    /**
     * clear list element
     */
    @Override
    public void clear() {
        for (Node<T> x = head; x != null; ) {
            Node<T> next = x.next;
            x.element = null;
            x.next = null;
            x = next;
        }
        head = tail = null;
        size = 0;
    }

    /**
     * contain certain element
     *
     * @param element
     */
    @Override
    public boolean contains(T element) {
        if (head == null) {
            return false;
        }
        Node<T> x = head;
        for (int i = 0; i < size; i++) {
            if (element == null && x.element == null) {
                return true;
            }
            if (element != null && element.equals(x.element)) {
                return true;
            }
            x = x.next;
        }
        return false;
    }

    /**
     * get list size
     *
     * @return
     */
    @Override
    public int size() {
        return size;
    }

    /**
     * Node
     *
     * @param <T>
     */
    private class Node<T> {

        private T element;
        private Node<T> next;

        public Node(T element, Node<T> next) {
            this.element = element;
            this.next = next;
        }
    }
}

源代码

双向循环链表

双向循环链表相比单向循环链表，降低了查找前驱节点的复杂度，时间复杂度为O(1).

同样第一次添加元素时，head与tail为同一元素，需要自指向。

package one.wangwei.algorithms.datastructures.list.impl;

import one.wangwei.algorithms.datastructures.list.IList;

/**
 * Doubly circular linked list
 *
 * @author https://wangwei.one
 * @date 2018/12/21
 */
public class DoublyCircularLinkedList<T> implements IList<T> {

    /**
     * size
     */
    private int size;
    /**
     * head node
     */
    private Node<T> head;
    /**
     * tail node
     */
    private Node<T> tail;

    /**
     * add element
     *
     * @param element
     * @return
     */
    @Override
    public boolean add(T element) {
        return addLast(element);
    }

    /**
     * add element at index
     *
     * @param index
     * @param element
     * @return
     */
    @Override
    public boolean add(int index, T element) {
        if (index < 0 || index > size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
        if (index == size) {
            return add(element);
        } else {
            return addBefore(index, element);
        }
    }

    /**
     * Add last element
     *
     * @param element
     * @return
     */
    private boolean addLast(T element) {
        Node<T> last = tail;
        Node<T> newNode = new Node<>(element, last, head);
        tail = newNode;
        // add element at first
        if (last == null) {
            head = newNode;
            tail.next = head;
        } else {
            last.next = newNode;
        }
        head.prev = tail;
        size++;
        return true;
    }

    /**
     * add element before certain element
     *
     * @param index
     * @param element
     * @return
     */
    private boolean addBefore(int index, T element) {
        Node<T> target = node(index);
        Node<T> prev = target.prev;
        Node<T> newNode = new Node<>(element, prev, target);

        prev.next = newNode;
        target.prev = newNode;

        if (index == 0) {
            head = newNode;
        }

        size++;
        return true;
    }

    /**
     * remove element
     *
     * @param element
     * @return
     */
    @Override
    public boolean remove(T element) {
        // start with head
        Node<T> x = head;
        // start with index -1
        int prevIndex = -1;

        for (int i = 0; i < size; i++) {
            if (element == null && x.element == null) {
                break;
            }
            if (element != null && element.equals(x.element)) {
                break;
            }
            x = x.next;
            prevIndex = i;
        }

        // if this linked list is empty
        if (x == null) {
            return false;
        }

        // if don't match element
        if (prevIndex == size - 1) {
            return false;
        }

        Node<T> prev = x.prev;
        Node<T> next = x.next;

        // if delete node is head
        if (prevIndex == -1) {
            head = next;
        }

        // if delete node is tail
        if (prevIndex == size - 2) {
            tail = prev;
        }

        prev.next = next;
        next.prev = prev;

        size--;

        if (size == 0) {
            head = tail = null;
        }

        // for GC
        x = null;

        return true;
    }

    /**
     * remove element by index
     *
     * @param index
     * @return
     */
    @Override
    public T remove(int index) {
        checkPositionIndex(index);
        Node<T> x = head;
        for (int i = 0; i < index; i++) {
            x = x.next;
        }

        // if linked is empty
        if (x == null) {
            return null;
        }

        Node<T> prev = x.prev;
        Node<T> next = x.next;

        // if delete node is head
        if (index == 0) {
            head = next;
        }

        // if delete node is tail
        if (index == size - 1) {
            tail = prev;
        }

        prev.next = next;
        next.prev = prev;

        size--;

        if (size == 0) {
            head = tail = null;
        }

        return x.element;
    }

    private void checkPositionIndex(int index) {
        if (index < 0 || index >= size) {
            throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size);
        }
    }

    /**
     * set element by index
     *
     * @param index
     * @param element
     * @return old element
     */
    @Override
    public T set(int index, T element) {
        Node<T> oldNode = node(index);
        T oldElement = oldNode.element;
        oldNode.element = element;
        return oldElement;
    }

    /**
     * get element by index
     *
     * @param index
     * @return
     */
    @Override
    public T get(int index) {
        return node(index).element;
    }

    /**
     * get element by index
     *
     * @param index
     * @return
     */
    private Node<T> node(int index) {
        checkPositionIndex(index);
        if (index < (size >> 1)) {
            Node<T> x = head;
            for (int i = 0; i < index; i++) {
                x = x.next;
            }
            return x;
        } else {
            Node<T> x = tail;
            for (int i = size - 1; i > index; i--) {
                x = x.prev;
            }
            return x;
        }
    }

    /**
     * clear list
     */
    @Override
    public void clear() {
        for (Node<T> x = head; x != null; ) {
            Node<T> next = x.next;
            x.element = null;
            x.next = null;
            x = next;
        }
        head = tail = null;
        size = 0;
    }

    /**
     * contain certain element
     *
     * @param element
     * @return
     */
    @Override
    public boolean contains(T element) {
        if (head == null) {
            return false;
        }
        Node<T> x = head;
        for (int i = 0; i < size; i++) {
            if (element == null && x.element == null) {
                return true;
            }
            if (element != null && element.equals(x.element)) {
                return true;
            }
            x = x.next;
        }
        return false;
    }

    /**
     * get list size
     *
     * @return
     */
    @Override
    public int size() {
        return size;
    }

    /**
     * Node
     *
     * @param <T>
     */
    private class Node<T> {
        private T element;
        private Node<T> prev;
        private Node<T> next;

        public Node(T element, Node<T> prev, Node<T> next) {
            this.element = element;
            this.prev = prev;
            this.next = next;
        }
    }

}

源代码

总结

写链表代码特别需要注意边界条件的处理：

• 如果链表为空，代码能否正常工作？
• 如果链表只有一个节点时，代码能否正常工作？
• 如果链表只有两个节点时，代码能否正常工作？
• 代码在删除或插入Head和Tail节点时，这四种的链表结构是否

ArrayList vs LinkedList

	ArrayList	LinkedList
插入&<br />删除	O(n)	O(1)
随机访问	O(1)	O(n)
优点	连续的内存空间，可以借助CPU的预取机制	内存不连续，天然支持动态扩容
缺点	无法存储大数据，数组扩容耗性能	频繁地插入删除操作，会导致内存碎片的增加，导致频繁的GC

相关练习

• 链表反转
• 链表环检测
• 有序链表合并

参考资料

• http://data.biancheng.net/view/5.html
• https://github.com/phishman3579/java-algorithms-implementation
• 《数据结构与算法之美》