1. 概要
线性表是一种线性结构,它是具有相同类型的n(n≥0)个数据元素组成的有限序列。本章先介绍线性表的几个基本组成部分:数组、单向链表、双向链表;随后给出双向链表的C、C++和Java三种语言的实现
2. 数组
数组有上界和下界,数组的元素在上下界内是连续的。存储10,20,30,40,50的数组的示意图如下
数组的特点是:数据是连续的;随机访问速度快。
数组中稍微复杂一点的是多维数组和动态数组。对于C语言而言,多维数组本质上也是通过一维数组实现的。至于动态数组,是指数组的容量能动态增长的数组;对于C语言而言,若要提供动态数组,需要手动实现;而对于C++而言,STL提供了Vector;对于Java而言,Collection集合中提供了ArrayList和Vector。
3. 单向链表
单向链表(单链表)是链表的一种,它由节点组成,每个节点都包含下一个节点的指针。
单链表的示意图如下:
表头为空,表头的后继节点是”节点10”(数据为10的节点),”节点10”的后继节点是”节点20”(数据为10的节点)
3.1 单链表删除节点
删除”节点30”
删除之前:”节点20” 的后继节点为”节点30”,而”节点30” 的后继节点为”节点40”。
删除之后:”节点20” 的后继节点为”节点40”。
3.2 单链表添加节点
在”节点10”与”节点20”之间添加”节点15”
添加之前:”节点10” 的后继节点为”节点20”。
添加之后:”节点10” 的后继节点为”节点15”,而”节点15” 的后继节点为”节点20”。
单链表的特点是:节点的链接方向是单向的;相对于数组来说,单链表的的随机访问速度较慢,但是单链表删除/添加数据的效率很高。
4. 双向链表
双向链表(双链表)是链表的一种。和单链表一样,双链表也是由节点组成,它的每个数据结点中都有两个指针,分别指向直接后继和直接前驱。所以,从双向链表中的任意一个结点开始,都可以很方便地访问它的前驱结点和后继结点。一般我们都构造双向循环链表。
双链表的示意图如下:
表头为空,表头的后继节点为”节点10”(数据为10的节点);”节点10”的后继节点是”节点20”(数据为10的节点),”节点20”的前继节点是”节点10”;”节点20”的后继节点是”节点30”,”节点30”的前继节点是”节点20”;…;末尾节点的后继节点是表头。
4.1 双链表删除节点
删除”节点30”
删除之前:”节点20”的后继节点为”节点30”,”节点30” 的前继节点为”节点20”。”节点30”的后继节点为”节点40”,”节点40” 的前继节点为”节点30”。
删除之后:”节点20”的后继节点为”节点40”,”节点40” 的前继节点为”节点20”。
4.2 双链表添加节点
在”节点10”与”节点20”之间添加”节点15”
添加之前:”节点10”的后继节点为”节点20”,”节点20” 的前继节点为”节点10”。
添加之后:”节点10”的后继节点为”节点15”,”节点15” 的前继节点为”节点10”。”节点15”的后继节点为”节点20”,”节点20” 的前继节点为”节点15”。
5. Java实现双链表
/**
* Java 实现的双向链表。
* 注:java自带的集合包中有实现双向链表,路径是:java.util.LinkedList
*
* @author skywang
* @date 2013/11/07
*/
public class DoubleLink<T> {
// 表头
private DNode<T> mHead;
// 节点个数
private int mCount;
// 双向链表“节点”对应的结构体
private class DNode<T> {
public DNode prev;
public DNode next;
public T value;
public DNode(T value, DNode prev, DNode next) {
this.value = value;
this.prev = prev;
this.next = next;
}
}
// 构造函数
public DoubleLink() {
// 创建“表头”。注意:表头没有存储数据!
mHead = new DNode<T>(null, null, null);
mHead.prev = mHead.next = mHead;
// 初始化“节点个数”为0
mCount = 0;
}
// 返回节点数目
public int size() {
return mCount;
}
// 返回链表是否为空
public boolean isEmpty() {
return mCount==0;
}
// 获取第index位置的节点
private DNode<T> getNode(int index) {
if (index<0 || index>=mCount)
throw new IndexOutOfBoundsException();
// 正向查找
if (index <= mCount/2) {
DNode<T> node = mHead.next;
for (int i=0; i<index; i++)
node = node.next;
return node;
}
// 反向查找
DNode<T> rnode = mHead.prev;
int rindex = mCount - index -1;
for (int j=0; j<rindex; j++)
rnode = rnode.prev;
return rnode;
}
// 获取第index位置的节点的值
public T get(int index) {
return getNode(index).value;
}
// 获取第1个节点的值
public T getFirst() {
return getNode(0).value;
}
// 获取最后一个节点的值
public T getLast() {
return getNode(mCount-1).value;
}
// 将节点插入到第index位置之前
public void insert(int index, T t) {
if (index==0) {
DNode<T> node = new DNode<T>(t, mHead, mHead.next);
mHead.next.prev = node;
mHead.next = node;
mCount++;
return ;
}
DNode<T> inode = getNode(index);
DNode<T> tnode = new DNode<T>(t, inode.prev, inode);
inode.prev.next = tnode;
inode.next = tnode;
mCount++;
return ;
}
// 将节点插入第一个节点处。
public void insertFirst(T t) {
insert(0, t);
}
// 将节点追加到链表的末尾
public void appendLast(T t) {
DNode<T> node = new DNode<T>(t, mHead.prev, mHead);
mHead.prev.next = node;
mHead.prev = node;
mCount++;
}
// 删除index位置的节点
public void del(int index) {
DNode<T> inode = getNode(index);
inode.prev.next = inode.next;
inode.next.prev = inode.prev;
inode = null;
mCount--;
}
// 删除第一个节点
public void deleteFirst() {
del(0);
}
// 删除最后一个节点
public void deleteLast() {
del(mCount-1);
}
}
测试程序(DlinkTest.java)
/**
* Java 实现的双向链表。
* 注:java自带的集合包中有实现双向链表,路径是:java.util.LinkedList
*
* @author skywang
* @date 2013/11/07
*/
public class DlinkTest {
// 双向链表操作int数据
private static void int_test() {
int[] iarr = {10, 20, 30, 40};
System.out.println("\n----int_test----");
// 创建双向链表
DoubleLink<Integer> dlink = new DoubleLink<Integer>();
dlink.insert(0, 20); // 将 20 插入到第一个位置
dlink.appendLast(10); // 将 10 追加到链表末尾
dlink.insertFirst(30); // 将 30 插入到第一个位置
// 双向链表是否为空
System.out.printf("isEmpty()=%b\n", dlink.isEmpty());
// 双向链表的大小
System.out.printf("size()=%d\n", dlink.size());
// 打印出全部的节点
for (int i=0; i<dlink.size(); i++)
System.out.println("dlink("+i+")="+ dlink.get(i));
}
private static void string_test() {
String[] sarr = {"ten", "twenty", "thirty", "forty"};
System.out.println("\n----string_test----");
// 创建双向链表
DoubleLink<String> dlink = new DoubleLink<String>();
dlink.insert(0, sarr[1]); // 将 sarr中第2个元素 插入到第一个位置
dlink.appendLast(sarr[0]); // 将 sarr中第1个元素 追加到链表末尾
dlink.insertFirst(sarr[2]); // 将 sarr中第3个元素 插入到第一个位置
// 双向链表是否为空
System.out.printf("isEmpty()=%b\n", dlink.isEmpty());
// 双向链表的大小
System.out.printf("size()=%d\n", dlink.size());
// 打印出全部的节点
for (int i=0; i<dlink.size(); i++)
System.out.println("dlink("+i+")="+ dlink.get(i));
}
// 内部类
private static class Student {
private int id;
private String name;
public Student(int id, String name) {
this.id = id;
this.name = name;
}
@Override
public String toString() {
return "["+id+", "+name+"]";
}
}
private static Student[] students = new Student[]{
new Student(10, "sky"),
new Student(20, "jody"),
new Student(30, "vic"),
new Student(40, "dan"),
};
private static void object_test() {
System.out.println("\n----object_test----");
// 创建双向链表
DoubleLink<Student> dlink = new DoubleLink<Student>();
dlink.insert(0, students[1]); // 将 students中第2个元素 插入到第一个位置
dlink.appendLast(students[0]); // 将 students中第1个元素 追加到链表末尾
dlink.insertFirst(students[2]); // 将 students中第3个元素 插入到第一个位置
// 双向链表是否为空
System.out.printf("isEmpty()=%b\n", dlink.isEmpty());
// 双向链表的大小
System.out.printf("size()=%d\n", dlink.size());
// 打印出全部的节点
for (int i=0; i<dlink.size(); i++) {
System.out.println("dlink("+i+")="+ dlink.get(i));
}
}
public static void main(String[] args) {
int_test(); // 演示向双向链表操作“int数据”。
string_test(); // 演示向双向链表操作“字符串数据”。
object_test(); // 演示向双向链表操作“对象”。
}
}
运行结果
----int_test----
isEmpty()=false
size()=3
dlink(0)=30
dlink(1)=20
dlink(2)=10
----string_test----
isEmpty()=false
size()=3
dlink(0)=thirty
dlink(1)=twenty
dlink(2)=ten
----object_test----
isEmpty()=false
size()=3
dlink(0)=[30, vic]
dlink(1)=[20, jody]
dlink(2)=[10, sky]
6. 双链表实现2
public class MyDoubleLink implements Iterable<Object>{
private class Node{
public Node(Object data){
this.data = data;
}
Node next;
Node prev;
Object data;
}
private Node head;
private Node rear;
public void add(Object data){
Node node = new Node(data);
if (head == null){
head = node;
rear = node;
} else {
rear.next = node;
node.prev = rear;
rear = node;
}
}
public boolean contains(Object data){
Node node = find(data);
return node != null;
}
public void print(){
Node temp = head;
while(temp != null){
System.out.print(temp.data + ",");
temp = temp.next;
}
System.out.println();
}
private Node find(Object data){
Node node = head;
while (node != null){
if (node.data.equals(data) && node.data.hashCode() == data.hashCode()){
break;
} else {
node = node.next;
}
}
return node;
}
public void remove(Object data){
Node node = find(data);
if (node != null){
if (node == head && node == rear){//只有一个节点
head = null;
rear = null;
} else if (node == head){ //头节点
head = head.next;
head.prev = null;
} else if (node == rear){ //尾节点
rear = rear.prev;
rear.next = null;
} else { //中间节点
node.prev.next = node.next;
node.next.prev = node.prev;
}
}
}
@Override
public Iterator<Object> iterator() {
Iterator<Object> ite = new Iterator<Object>() {
private Node temp = head;
@Override
public boolean hasNext() {
return temp != null;
}
@Override
public Object next() {
// TODO Auto-generated method stub
Object data = temp.data;
temp = temp.next;
return data;
}
@Override
public void remove() {
// TODO Auto-generated method stub
}
};
return ite;
}
}
6.1 测试双链表
public class Test {
public static class Instance{
public Instance(int i){
}
public Instance(){
}
}
public static void main(String[] args) {
Instance in = new Instance(){
};
MyDoubleLink datas = new MyDoubleLink();
datas.add("aaa");
datas.add("bbb");
datas.add("ccc");
datas.print();
datas.remove("ccc");
datas.print();
for (Object d : datas) {
System.out.println(d);
}
}
}
7. 双链表
import java.util.Iterator;
public class MyDoubleLink implements Iterable<Object>{
private class Node{
public Node(Object data){
this.data = data;
}
Node next;
Node prev;
Object data;
}
private Node head;
private Node rear;
public void add(Object data){
Node node = new Node(data);
if (head == null){
head = node;
rear = node;
} else {
rear.next = node;
node.prev = rear;
rear = node;
}
}
public boolean contains(Object data){
Node node = find(data);
return node != null;
}
public void print(){
Node temp = head;
while(temp != null){
System.out.print(temp.data + ",");
temp = temp.next;
}
System.out.println();
}
private Node find(Object data){
Node node = head;
while (node != null){
if (node.data.equals(data) && node.data.hashCode() == data.hashCode()){
break;
} else {
node = node.next;
}
}
return node;
}
public void remove(Object data){
Node node = find(data);
if (node != null){
if (node == head && node == rear){//只有一个节点
head = null;
rear = null;
} else if (node == head){ //头节点
head = head.next;
head.prev = null;
} else if (node == rear){ //尾节点
rear = rear.prev;
rear.next = null;
} else { //中间节点
node.prev.next = node.next;
node.next.prev = node.prev;
}
}
}
@Override
public Iterator<Object> iterator() {
Iterator<Object> ite = new Iterator<Object>() {
private Node temp = head;
@Override
public boolean hasNext() {
return temp != null;
}
@Override
public Object next() {
// TODO Auto-generated method stub
Object data = temp.data;
temp = temp.next;
return data;
}
@Override
public void remove() {
// TODO Auto-generated method stub
}
};
return ite;
}
}
public class TEst {
public static class Instance{
public Instance(int i){
}
public Instance(){
}
}
/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
Instance in = new Instance(){
};
MyDoubleLink datas = new MyDoubleLink();
datas.add("aaa");
datas.add("bbb");
datas.add("ccc");
datas.print();
datas.remove("ccc");
datas.print();
for (Object d : datas) {
System.out.println(d);
}
}
}
7.1 单链表的实现
// linkList2.java
// demonstrates linked list
// to run this program: C>java LinkList2App
////////////////////////////////////////////////////////////////
class Link
{
public int iData; // data item (key)
public double dData; // data item
public Link next; // next link in list
// -------------------------------------------------------------
public Link(int id, double dd) // constructor
{
iData = id;
dData = dd;
}
// -------------------------------------------------------------
public void displayLink() // display ourself
{
System.out.print("{" + iData + ", " + dData + "} ");
}
} // end class Link
////////////////////////////////////////////////////////////////
class LinkList
{
private Link first; // ref to first link on list
// -------------------------------------------------------------
public LinkList() // constructor
{
first = null; // no links on list yet
}
// -------------------------------------------------------------
public void insertFirst(int id, double dd)
{ // make new link
Link newLink = new Link(id, dd);
newLink.next = first; // it points to old first link
first = newLink; // now first points to this
}
// -------------------------------------------------------------
public Link find(int key) // find link with given key
{ // (assumes non-empty list)
Link current = first; // start at 'first'
while(current.iData != key) // while no match,
{
if(current.next == null) // if end of list,
return null; // didn't find it
else // not end of list,
current = current.next; // go to next link
}
return current; // found it
}
// -------------------------------------------------------------
public Link delete(int key) // delete link with given key
{ // (assumes non-empty list)
Link current = first; // search for link
Link previous = first;
while(current.iData != key)
{
if(current.next == null)
return null; // didn't find it
else
{
previous = current; // go to next link
current = current.next;
}
} // found it
if(current == first) // if first link,
first = first.next; // change first
else // otherwise,
previous.next = current.next; // bypass it
return current;
}
// -------------------------------------------------------------
public void displayList() // display the list
{
System.out.print("List (first-->last): ");
Link current = first; // start at beginning of list
while(current != null) // until end of list,
{
current.displayLink(); // print data
current = current.next; // move to next link
}
System.out.println("");
}
// -------------------------------------------------------------
} // end class LinkList
////////////////////////////////////////////////////////////////
class LinkList2App
{
public static void main(String[] args)
{
LinkList theList = new LinkList(); // make list
theList.insertFirst(22, 2.99); // insert 4 items
theList.insertFirst(44, 4.99);
theList.insertFirst(66, 6.99);
theList.insertFirst(88, 8.99);
theList.displayList(); // display list
Link f = theList.find(44); // find item
if( f != null)
System.out.println("Found link with key " + f.iData);
else
System.out.println("Can't find link");
Link d = theList.delete(66); // delete item
if( d != null )
System.out.println("Deleted link with key " + d.iData);
else
System.out.println("Can't delete link");
theList.displayList(); // display list
} // end main()
} // end class LinkList2App
////////////////////////////////////////////////////////////////
7.2 有序链表
// sortedList.java
// demonstrates sorted list
// to run this program: C>java SortedListApp
////////////////////////////////////////////////////////////////
class Link
{
public long dData; // data item
public Link next; // next link in list
// -------------------------------------------------------------
public Link(long dd) // constructor
{ dData = dd; }
// -------------------------------------------------------------
public void displayLink() // display this link
{ System.out.print(dData + " "); }
} // end class Link
////////////////////////////////////////////////////////////////
class SortedList
{
private Link first; // ref to first item
// -------------------------------------------------------------
public SortedList() // constructor
{ first = null; }
// -------------------------------------------------------------
public boolean isEmpty() // true if no links
{ return (first==null); }
// -------------------------------------------------------------
public void insert(long key) // insert, in order
{
Link newLink = new Link(key); // make new link
Link previous = null; // start at first
Link current = first;
// until end of list,
while(current != null && key > current.dData)
{ // or key > current,
previous = current;
current = current.next; // go to next item
}
if(previous==null) // at beginning of list
first = newLink; // first --> newLink
else // not at beginning
previous.next = newLink; // old prev --> newLink
newLink.next = current; // newLink --> old currnt
} // end insert()
// -------------------------------------------------------------
public Link remove() // return & delete first link
{ // (assumes non-empty list)
Link temp = first; // save first
first = first.next; // delete first
return temp; // return value
}
// -------------------------------------------------------------
public void displayList()
{
System.out.print("List (first-->last): ");
Link current = first; // start at beginning of list
while(current != null) // until end of list,
{
current.displayLink(); // print data
current = current.next; // move to next link
}
System.out.println("");
}
} // end class SortedList
////////////////////////////////////////////////////////////////
class SortedListApp
{
public static void main(String[] args)
{ // create new list
SortedList theSortedList = new SortedList();
theSortedList.insert(20); // insert 2 items
theSortedList.insert(40);
theSortedList.displayList(); // display list
theSortedList.insert(10); // insert 3 more items
theSortedList.insert(30);
theSortedList.insert(50);
theSortedList.displayList(); // display list
theSortedList.remove(); // remove an item
theSortedList.displayList(); // display list
} // end main()
} // end class SortedListApp
////////////////////////////////////////////////////////////////
7.3 双向链表
// doublyLinked.java
// demonstrates doubly-linked list
// to run this program: C>java DoublyLinkedApp
////////////////////////////////////////////////////////////////
class Link
{
public long dData; // data item
public Link next; // next link in list
public Link previous; // previous link in list
// -------------------------------------------------------------
public Link(long d) // constructor
{ dData = d; }
// -------------------------------------------------------------
public void displayLink() // display this link
{ System.out.print(dData + " "); }
// -------------------------------------------------------------
} // end class Link
////////////////////////////////////////////////////////////////
class DoublyLinkedList
{
private Link first; // ref to first item
private Link last; // ref to last item
// -------------------------------------------------------------
public DoublyLinkedList() // constructor
{
first = null; // no items on list yet
last = null;
}
// -------------------------------------------------------------
public boolean isEmpty() // true if no links
{ return first==null; }
// -------------------------------------------------------------
public void insertFirst(long dd) // insert at front of list
{
Link newLink = new Link(dd); // make new link
if( isEmpty() ) // if empty list,
last = newLink; // newLink <-- last
else
first.previous = newLink; // newLink <-- old first
newLink.next = first; // newLink --> old first
first = newLink; // first --> newLink
}
// -------------------------------------------------------------
public void insertLast(long dd) // insert at end of list
{
Link newLink = new Link(dd); // make new link
if( isEmpty() ) // if empty list,
first = newLink; // first --> newLink
else
{
last.next = newLink; // old last --> newLink
newLink.previous = last; // old last <-- newLink
}
last = newLink; // newLink <-- last
}
// -------------------------------------------------------------
public Link deleteFirst() // delete first link
{ // (assumes non-empty list)
Link temp = first;
if(first.next == null) // if only one item
last = null; // null <-- last
else
first.next.previous = null; // null <-- old next
first = first.next; // first --> old next
return temp;
}
// -------------------------------------------------------------
public Link deleteLast() // delete last link
{ // (assumes non-empty list)
Link temp = last;
if(first.next == null) // if only one item
first = null; // first --> null
else
last.previous.next = null; // old previous --> null
last = last.previous; // old previous <-- last
return temp;
}
// -------------------------------------------------------------
// insert dd just after key
public boolean insertAfter(long key, long dd)
{ // (assumes non-empty list)
Link current = first; // start at beginning
while(current.dData != key) // until match is found,
{
current = current.next; // move to next link
if(current == null)
return false; // didn't find it
}
Link newLink = new Link(dd); // make new link
if(current==last) // if last link,
{
newLink.next = null; // newLink --> null
last = newLink; // newLink <-- last
}
else // not last link,
{
newLink.next = current.next; // newLink --> old next
// newLink <-- old next
current.next.previous = newLink;
}
newLink.previous = current; // old current <-- newLink
current.next = newLink; // old current --> newLink
return true; // found it, did insertion
}
// -------------------------------------------------------------
public Link deleteKey(long key) // delete item w/ given key
{ // (assumes non-empty list)
Link current = first; // start at beginning
while(current.dData != key) // until match is found,
{
current = current.next; // move to next link
if(current == null)
return null; // didn't find it
}
if(current==first) // found it; first item?
first = current.next; // first --> old next
else // not first
// old previous --> old next
current.previous.next = current.next;
if(current==last) // last item?
last = current.previous; // old previous <-- last
else // not last
// old previous <-- old next
current.next.previous = current.previous;
return current; // return value
}
// -------------------------------------------------------------
public void displayForward()
{
System.out.print("List (first-->last): ");
Link current = first; // start at beginning
while(current != null) // until end of list,
{
current.displayLink(); // display data
current = current.next; // move to next link
}
System.out.println("");
}
// -------------------------------------------------------------
public void displayBackward()
{
System.out.print("List (last-->first): ");
Link current = last; // start at end
while(current != null) // until start of list,
{
current.displayLink(); // display data
current = current.previous; // move to previous link
}
System.out.println("");
}
// -------------------------------------------------------------
} // end class DoublyLinkedList
////////////////////////////////////////////////////////////////
class DoublyLinkedApp
{
public static void main(String[] args)
{ // make a new list
DoublyLinkedList theList = new DoublyLinkedList();
theList.insertFirst(22); // insert at front
theList.insertFirst(44);
theList.insertFirst(66);
theList.insertLast(11); // insert at rear
theList.insertLast(33);
theList.insertLast(55);
theList.displayForward(); // display list forward
theList.displayBackward(); // display list backward
theList.deleteFirst(); // delete first item
theList.deleteLast(); // delete last item
theList.deleteKey(11); // delete item with key 11
theList.displayForward(); // display list forward
theList.insertAfter(22, 77); // insert 77 after 22
theList.insertAfter(33, 88); // insert 88 after 33
theList.displayForward(); // display list forward
} // end main()
} // end class DoublyLinkedApp
////////////////////////////////////////////////////////////////