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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 implements IList {
/**
* size
*/
private int size = 0;
/**
* head node
*/
private Node head;
/**
* tail node
*/
private Node 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 last = tail;
Node 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 prev = null;
Node x = head;
for (int i = 0; i < index; i++) {
prev = x;
x = x.next;
}
// current node
Node current = x;
// new node
Node 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 prev = null;
Node 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 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 prev = null;
Node x = head;
for (int i = 0; i < index; i++) {
prev = x;
x = x.next;
}
// if linked is empty
if (x == null) {
return null;
}
Node 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 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 node = node(index);
return node == null ? null : node.element;
}
/**
* get element by index
*
* @param index
* @return
*/
private Node node(int index) {
checkPositionIndex(index);
Node 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 x = head; x != null; ) {
Node 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 x = head; x != null; x = x.next) {
if (x.element == null) {
return true;
}
}
} else {
for (Node 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
*/
private class Node {
private Node next;
private T element;
public Node(Node 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
* @author https://wangwei.one
* @date 2018/04/28
*/
public class DoublyLinkedList implements IList {
/**
* size
*/
private int size = 0;
/**
* head element
*/
private Node head = null;
/**
* tail element
*/
private Node 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 last = tail;
Node 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 target) {
Node prev = target.prev;
Node 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 x = head; x != null; x = x.next) {
if (x.element == null) {
unlink(x);
return true;
}
}
} else {
for (Node 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 node(int index) {
checkPositionIndex(index);
if (index < (size >> 1)) {
Node x = head;
for (int i = 0; i < index; i++) {
x = x.next;
}
return x;
} else {
Node x = tail;
for (int i = size - 1; i > index; i--) {
x = x.prev;
}
return x;
}
}
/**
* unlink node
*
* @param node
*/
private T unlink(Node node) {
final T element = node.element;
final Node prev = node.prev;
final Node 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 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 node = node(index);
return node == null ? null : node.element;
}
/**
* clear list
*/
@Override
public void clear() {
for (Node x = head; x != null; ) {
Node 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 x = head; x != null; x = x.next) {
if (x.element == null) {
return true;
}
}
} else {
for (Node 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
*/
private class Node {
private T element;
private Node prev;
private Node next;
public Node(Node prev, T element, Node 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
* @author https://wangwei.one
* @date 2018/05/03
*/
public class SinglyCircularLinkedList implements IList {
/**
* size
*/
private int size = 0;
/**
* head node
*/
private Node head = null;
/**
* tail node
*/
private Node 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 last = tail;
Node 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 prev = tail;
Node x = head;
for (int i = 0; i < index; i++) {
prev = x;
x = x.next;
}
// current node
Node current = x;
// new node
Node 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 prev = tail;
// start with head
Node 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 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 prev = tail;
Node x = head;
for (int i = 0; i < index; i++) {
prev = x;
x = x.next;
}
// if linked is empty
if (x == null) {
return null;
}
Node 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 node(int index) {
checkPositionIndex(index);
Node 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 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 x = head; x != null; ) {
Node 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 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
*/
private class Node {
private T element;
private Node next;
public Node(T element, Node 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 implements IList {
/**
* size
*/
private int size;
/**
* head node
*/
private Node head;
/**
* tail node
*/
private Node 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 last = tail;
Node 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 target = node(index);
Node prev = target.prev;
Node 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 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 prev = x.prev;
Node 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 x = head;
for (int i = 0; i < index; i++) {
x = x.next;
}
// if linked is empty
if (x == null) {
return null;
}
Node prev = x.prev;
Node 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 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 node(int index) {
checkPositionIndex(index);
if (index < (size >> 1)) {
Node x = head;
for (int i = 0; i < index; i++) {
x = x.next;
}
return x;
} else {
Node x = tail;
for (int i = size - 1; i > index; i--) {
x = x.prev;
}
return x;
}
}
/**
* clear list
*/
@Override
public void clear() {
for (Node x = head; x != null; ) {
Node 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 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
*/
private class Node {
private T element;
private Node prev;
private Node next;
public Node(T element, Node prev, Node 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& 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》