数据结构与算法之队列（基于数组）讲解

淡淡的烟草味﹌ 2024-04-18 15:15 89阅读 0赞

1，队列是一致先进先出结构（first in first out）FIFO

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2，基于数据的方法实现队列，数组的具体类

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   <td> <pre><code>package com.dream21th.algorithmicdatastructure.quene;

/**
 * @Auther: hp
 * @Date: 2019/9/7 15:42
 * @Description:
 */
public class MyExtendArray&lt;E&gt; {

private E[] datas;

private int size;

/**
     * 创建有参构造函数，初始化数组容量
     * @param capacity
     */
    public MyExtendArray(int capacity){
        datas=(E[])new Object[capacity];
        size=0;
    }

/**
     * 构造无参函数，初始化数组容量
     */
    public MyExtendArray(){
        this(10);
    }

public int getSize(){
        return this.size;
    }

public boolean isEmpty(){
        return this.size==0;
    }

/**
     * 在指定索引位置加值
     * @param index
     * @param e
     */
    public void add(int index,E e){
        if(index&lt;0 || index&gt;this.size){
            throw new IllegalArgumentException("index must between 0 and size");
        }
        if(this.size==datas.length){
            resize(2*datas.length);
        }
        for(int position=size-1;position&gt;=index;position--){
            this.datas[position+1]=this.datas[position];
        }
        this.datas[index]=e;
        this.size++;
    }

private void resize(int newCapacity) {

E[] newDatas= (E[]) new Object[newCapacity];

for(int i=0;i&lt;this.size;i++){
            newDatas[i]=this.datas[i];
        }
        this.datas=newDatas;
    }

/**
     * 在第一个位置加入元素
     * @param e
     */
    public void addFirst(E e){
        this.add(0,e);
    }

/**
     * 在最后一个位置添加元素
     * @param e
     */
    public void addLast(E e){
        this.add(size,e);
    }

public E get(int index){
        if(index&lt;0 || index&gt;=this.size){
            throw new IllegalArgumentException("index must between 0 and size");
        }
        return this.datas[index];
    }

public void set(int index,E e){
        if(index&lt;0 || index&gt;=this.size){
            throw new IllegalArgumentException("index must between 0 and size");
        }
        this.datas[index]=e;
    }

public boolean contain(E e){
        for(int i=0;i&lt;size;i++){
            if(this.datas[i].equals(e)){
                return true;
            }
        }
        return false;
    }

public int find(int e){
        for(int i=0;i&lt;size;i++){
            if(this.datas[i].equals(e)){
                return i;
            }
        }
        return -1;
    }

public E remove(int index){
        if(index&lt;0 || index&gt;=this.size){
            throw new IllegalArgumentException("index must between 0 and size");
        }
        E ret=this.datas[index];
        for(int i=index+1;i&lt;size;i++){
            this.datas[i-1]=this.datas[i];
        }
        size--;
        this.datas[size]=null;
        if(this.size==this.datas.length/4 &amp;&amp; this.datas.length/2!=0){
            resize(this.datas.length/2);
        }
        return ret;
    }

public E removeFirst(){
        return remove(0);
    }

public E removeLast(){
        return remove(size-1);
    }

public E getLast(){
       return  get(this.size-1);
    }

public E getFirst(){
        return get(0);
    }

public int getCapacity(){
        return this.datas.length;
    }
    @Override
    public String toString() {

StringBuilder builder=new StringBuilder();
        builder.append(String.format("Array: size = %d,capacity = %d \n",this.size,this.datas.length));
        builder.append("[");
        for(int i=0;i&lt;size;i++){
            builder.append(this.datas[i]);
            if(i!=size-1){
                builder.append(",");
            }
        }
        builder.append("]");
        return builder.toString();
    }
}
</code></pre> </td> 
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3，数组实现队列

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   <td> <pre><code>package com.dream21th.algorithmicdatastructure.quene;

/**
 * @Auther: hp
 * @Date: 2019/9/8 15:40
 * @Description:
 */
public interface Queue&lt;E&gt; {

int getSize();

void enquene(E e);

E dequene();

E getfornt();

boolean isEmpty();
}
</code></pre> </td> 
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</table>

<table> 
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  <tr> 
   <td> <pre><code>package com.dream21th.algorithmicdatastructure.quene;

/**
 * @Auther: hp
 * @Date: 2019/9/8 15:42
 * @Description:
 */
public class ArrayQuene&lt;E&gt; implements Queue&lt;E&gt; {

private MyExtendArray&lt;E&gt; myExtendArray;

public ArrayQuene(int capacity){
        myExtendArray=new MyExtendArray();
    }

public ArrayQuene(){
        this(10);
    }

@Override
    public int getSize() {
        return myExtendArray.getSize();
    }

@Override
    public void enquene(E e) {
       myExtendArray.addLast(e);
    }

@Override
    public E dequene() {
        return myExtendArray.removeFirst();
    }

@Override
    public E getfornt() {
        return myExtendArray.getFirst();
    }

@Override
    public boolean isEmpty() {
        return myExtendArray.isEmpty();
    }

public int getCapacity(){
        return myExtendArray.getCapacity();
    }

@Override
    public String toString() {

StringBuilder builder=new StringBuilder();
        builder.append(String.format("Stack: size = %d, capacity = %d \n",getSize(),getCapacity()));
        builder.append("fornt [");
        for(int i=0;i&lt;getSize();i++){
            builder.append(myExtendArray.get(i));
            if(i!=getSize()-1){
                builder.append(",");
            }
        }
        builder.append("] tail");

return builder.toString();
    }
}
</code></pre> </td> 
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4，复杂度分析

进入队列从末尾进入，复杂度为O(1)

出队列从头部出，后面数据都要向前移动一位，复杂度为O(n)

5,基于环形数组实现队列

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM2MzA1MDI3_size_16_color_FFFFFF_t_70 1][]

<table> 
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   <td> <pre><code>package com.dream21th.algorithmicdatastructure.quene;

/**
 * @Auther: hp
 * @Date: 2019/9/8 16:20
 * @Description:
 */
public class LoopQueue&lt;E&gt; implements Queue&lt;E&gt; {
    private E[] datas;
    private int front;
    private int tail;
    private int size;

public LoopQueue(int capacity){
        datas= (E[]) new Object[capacity+1];
        front=0;
        tail=0;
        size=0;
    }

public LoopQueue(){
        this(10);
    }
    @Override
    public int getSize() {
        return this.size;
    }

public int getCapacity(){
        return this.datas.length-1;
    }

@Override
    public void enquene(E e) {
        if((tail+1)%this.datas.length==front){
            resize(getCapacity()*2);
        }
        this.datas[tail]=e;
        tail++;
        size++;
    }

private void resize(int capacity){
        E[] newDatas= (E[]) new Object[capacity+1];

/* for(int i=0;i&lt;size;i++){
            newDatas[i]=datas[(front+i)%datas.length];
        }*/
        int j=0;
        for(int i=front;i!=tail;i=(i+1)%this.datas.length){
            newDatas[j++]=this.datas[i];
        }
        datas=newDatas;
        front=0;
        tail=size;
    }

@Override
    public E dequene() {
        if(isEmpty()){
            throw new IllegalArgumentException("queue is empty");
        }
        E data = this.datas[front];
        if(this.size==this.getCapacity()/4 &amp;&amp; this.getCapacity()/2!=0){
            resize(this.getCapacity()/2);
        }
        this.datas[front]=null;
        front++;
        size--;
        return data;
    }

@Override
    public E getfornt() {
        return this.datas[front];
    }

@Override
    public boolean isEmpty() {
        return front==tail;
    }

@Override
    public String toString() {

StringBuilder builder=new StringBuilder();
        builder.append(String.format("Stack: size = %d, capacity = %d \n",getSize(),getCapacity()));
        builder.append("Queue front [");
        for(int i=front;i!=tail;i=(i+1)%this.datas.length){
            builder.append(this.datas[i]);
            if((i+1)%this.datas.length!=tail){
                builder.append(",");
            }
        }
        builder.append("] tail");

return builder.toString();
    }
}
</code></pre> </td> 
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6，复杂度分析

出队列和入队列复杂度都为O（1）

7，两种方式对比

<table> 
 <tbody> 
  <tr> 
   <td> <pre><code>package com.dream21th.algorithmicdatastructure.quene;

/**
 * @Auther: hp
 * @Date: 2019/9/8 15:48
 * @Description:
 */
public class Test {

public static void main(String[] args) {
        /*ArrayQuene&lt;Integer&gt; arrayQuene=new ArrayQuene&lt;&gt;();

for(int i=0;i&lt;10;i++){
            arrayQuene.enquene(i);
            System.out.println(arrayQuene);
            if(i%3==2){
                arrayQuene.dequene();
                System.out.println(arrayQuene);
            }
        }*/

/* LoopQueue&lt;Integer&gt; arrayQuene=new LoopQueue&lt;&gt;();

for(int i=0;i&lt;20;i++){
            arrayQuene.enquene(i);
            System.out.println(arrayQuene);
        }

for(int i=0;i&lt;16;i++){
            arrayQuene.dequene();
            System.out.println(arrayQuene);
        }*/

ArrayQuene&lt;Integer&gt; arrayQuene=new ArrayQuene&lt;&gt;();

System.out.println(testTime(arrayQuene,100000));
        LoopQueue&lt;Integer&gt; loopQuene=new LoopQueue&lt;&gt;();
        System.out.println(testTime(loopQuene,100000));
    }

public static double testTime(Queue&lt;Integer&gt; queue,int total){
        long beginTime=System.nanoTime();

for(int i=0;i&lt;total;i++){
            queue.enquene(i);
        }

for (int i=0;i&lt;total;i++){
            queue.dequene();
        }

long endTime=System.nanoTime();

return (endTime-beginTime)/1000000000.0;
    }
}
</code></pre> </td> 
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结果

13.559065063  
0.013770266

相差1000倍

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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM2MzA1MDI3_size_16_color_FFFFFF_t_70 1]: https://image.dandelioncloud.cn/pgy_files/images/2024/04/18/49544c697ac34f94ad24a0d5e5eb2f68.png