算法导论 顺序循环双向队列

顺序循环双向队列

1. 什么是双向队列？

算法导论原题：

10.1-5

Whereas a stack allows insertion and deletion of elements at only one end, and a queue allows insertion at one end and deletion at the other end, a deque (double-ended queue) allows insertion and deletion at both ends. Write four O(1) time procedures to insert elements into and delete elements from both ends of a deque implemented by an array.

译：栈只允许在一端插入和删除元素，队列只允许在一端插入和在另一端删除，一个deque（double-ended queue，双向队列）允许在两端插入和删除。写出4个运行时间为O(1)的过程，分别在两端插入和删除元素，该列队是用一个数组实现的。

2. 双向队列如何实现？

顺序双向循环队列只是在原来的顺序循环队列基础上，增加了队列头的插入和队列尾的删除操作。只要写过普通队列的操作，双向队列的操作也是不难写的，并没有多大难度。建议读者们自己尝试动手写一下。

3. 双向队列的实现（C++代码）

//SequeDeQueue.h
#pragma once

#include <assert.h>

template<typename ElemType>
class SequeDeQueue
{
public:
    SequeDeQueue(unsigned int size);
    bool HeadDeQueue(ElemType* elem);
    bool TailDeQueue(ElemType* elem);
    bool HeadEnQueue(const ElemType& elem);
    bool TailEnQueue(const ElemType& elem);
    bool Empty();
    bool Visit(ElemType* elem, unsigned int pos) const;
private:
    ElemType* m_array;
    unsigned int m_tail;
    unsigned int m_head;
    unsigned int m_size;
};

template<typename ElemType>
bool SequeDeQueue<ElemType>::TailEnQueue(const ElemType& elem)
{
    if ( (m_tail + 1 + m_size) % m_size == m_head)
    {
        assert(false && "Error: SequeDeQueue is overflow!");
        return false;
    }
    else
    {
        m_array[m_tail] = elem;
        m_tail = (m_tail + 1 + m_size) % m_size;
        return true;
    }
}

template<typename ElemType>
bool SequeDeQueue<ElemType>::HeadEnQueue(const ElemType& elem)
{
    if ( (m_head - 1 + m_size) % m_size == m_head)
    {
        assert(false && "Error: SequeDeQueue is overflow!");
        return false;
    }
    else
    {
        m_array[m_head] = elem;
        m_head = (m_head - 1 + m_size) % m_size;
        return true;
    }
}

template<typename ElemType>
bool SequeDeQueue<ElemType>::TailDeQueue(ElemType* elem)
{
    if (Empty())
    {
        assert(false && "Error: SequeDeQueue is underflow!");
        return false;
    }
    else
    {
        m_tail = (m_tail - 1 + m_size) % m_size;
        *elem = m_array[m_tail];
        return true;
    }
}

template<typename ElemType>
bool SequeDeQueue<ElemType>::HeadDeQueue(ElemType* elem)
{
    if (Empty())
    {
        assert(false && "Error: SequeDeQueue is underflow!");
        return false;
    }
    else
    {
        m_head = (m_head + 1 + m_size) % m_size;
        *elem = m_array[m_head];
        return true;
    }
}

template<typename ElemType>
bool SequeDeQueue<ElemType>::Visit(ElemType* elem, unsigned int pos) const
{
    if (pos >= m_size || pos < 0)
    {
        assert(false && "Error: Visit Pos is out range of array!");
        return false;
    }
    *elem = m_array[pos];
    return true;
}

template<typename ElemType>
bool SequeDeQueue<ElemType>::Empty()
{
    return ((m_head + 1 + m_size) % m_size == m_tail) ? true : false;
}

template<typename ElemType>
SequeDeQueue<ElemType>::SequeDeQueue(unsigned int size)
    :m_array(new ElemType[size]),m_tail(0),m_head(size-1),m_size(size)
{
    memset(m_array,0,sizeof(ElemType)*size);
}

//Util.h
#pragma once

namespace Util
{
    template<typename T>
    void PrintMemory(const T& dateStruct, unsigned int size)
    {
        cout << "PrintMemory: ";
        for (int i = 0; i != size; i++)
        {
            ElemType tempElem;
            dateStruct.Visit(&tempElem,i);
            printf("%d ",tempElem);
        }
        printf("\n");
        printf("\n");
    }
}

//main.cpp
#include "Util.h"
#include "SequeDeQueue.h"
#include <iostream>

using namespace std;

typedef int ElemType;

int main()
{

    const int QUEUE_SIZE = 10;
    SequeDeQueue<int> testSequeDeQueue(QUEUE_SIZE);

    cout << "testSequeDeQueue is " << (testSequeDeQueue.Empty() ? "Empty." : "Not Empty.") << endl;
    Util::PrintMemory(testSequeDeQueue,QUEUE_SIZE);

    for (int i = 1; i != 4; i++)
    {
        testSequeDeQueue.HeadEnQueue(i);
        cout << "HeadEnQueue:" << i << endl;
        cout << "testSequeDeQueue is " << (testSequeDeQueue.Empty() ? "Empty." : "Not Empty.") << endl;
        Util::PrintMemory(testSequeDeQueue,QUEUE_SIZE);
    }

    for (int i = 4; i != 7; i++)
    {
        testSequeDeQueue.TailEnQueue(i);
        cout << "TailEnQueue:" << i << endl;
        cout << "testSequeDeQueue is " << (testSequeDeQueue.Empty() ? "Empty." : "Not Empty.") << endl;
        Util::PrintMemory(testSequeDeQueue,QUEUE_SIZE);
    }

    for (int i = 0; i != 2; i++)
    {
        ElemType tempElem;
        testSequeDeQueue.HeadDeQueue(&tempElem);
        cout << "HeadDeQueue:" << tempElem << endl;
        cout << "testSequeDeQueue is " << (testSequeDeQueue.Empty() ? "Empty." : "Not Empty.") << endl;
        Util::PrintMemory(testSequeDeQueue,QUEUE_SIZE);
    }

    for (int i = 0; i != 4; i++)
    {
        ElemType tempElem;
        testSequeDeQueue.TailDeQueue(&tempElem);
        cout << "TailDeQueue:" << tempElem << endl;
        cout << "testSequeDeQueue is " << (testSequeDeQueue.Empty() ? "Empty." : "Not Empty.") << endl;
        Util::PrintMemory(testSequeDeQueue,QUEUE_SIZE);
    }

    return 0;
}

4. 程序运行结果

testSequeDeQueue is Empty.

PrintMemory: 0 0 0 0 0 0 0 0 0 0


HeadEnQueue:1

testSequeDeQueue is Not Empty.

PrintMemory: 0 0 0 0 0 0 0 0 0 1


HeadEnQueue:2

testSequeDeQueue is Not Empty.

PrintMemory: 0 0 0 0 0 0 0 0 2 1


HeadEnQueue:3

testSequeDeQueue is Not Empty.

PrintMemory: 0 0 0 0 0 0 0 3 2 1


TailEnQueue:4

testSequeDeQueue is Not Empty.

PrintMemory: 4 0 0 0 0 0 0 3 2 1


TailEnQueue:5

testSequeDeQueue is Not Empty.

PrintMemory: 4 5 0 0 0 0 0 3 2 1


TailEnQueue:6

testSequeDeQueue is Not Empty.

PrintMemory: 4 5 6 0 0 0 0 3 2 1


HeadDeQueue:3

testSequeDeQueue is Not Empty.

PrintMemory: 4 5 6 0 0 0 0 3 2 1


HeadDeQueue:2

testSequeDeQueue is Not Empty.

PrintMemory: 4 5 6 0 0 0 0 3 2 1


TailDeQueue:6

testSequeDeQueue is Not Empty.

PrintMemory: 4 5 6 0 0 0 0 3 2 1


TailDeQueue:5

testSequeDeQueue is Not Empty.

PrintMemory: 4 5 6 0 0 0 0 3 2 1


TailDeQueue:4

testSequeDeQueue is Not Empty.

PrintMemory: 4 5 6 0 0 0 0 3 2 1


TailDeQueue:1

testSequeDeQueue is Empty.

PrintMemory: 4 5 6 0 0 0 0 3 2 1