用两个栈实现队列（C++ 和 Python 实现）

（说明：本博客中的题目、题目详细说明及参考代码均摘自 “何海涛《剑指Offer：名企面试官精讲典型编程题》2012年”）

题目

　　用两个栈实现一个队列。队列的声明如下，请实现它的两个函数 appendTail 和 deleteHead，分别完成在队列尾部插入结点和在队列头部删除结点功能。

template <typename T> class CQueue
{
public:
    CQueue(void);
    ~CQueue(void);

    void appendTail(const T& node);
    T deleteHead();     
};

进一步详细说明：

　　在上述队列的声明中可以看出，一个队列包含两个栈 stack1 和 stack2，因此这道题的意图是要求我们操作这两个 “先进后出” 的栈实现一个 “先进先出” 的队列 CQueue。

 

算法设计思想

　　因为栈是后进先出的数据结构，当将数据依次压入第一个栈后，再依次从这个栈弹出，压入第二个栈，如果此时从第二个栈中获取数据，表现正好像一个 “先进先出” 的队列数据结构。

　　具体来说，使用两个栈实现一个队列，可以考虑用第一个栈（stack1）存放输入的元素（队尾元素），从第二个栈（stack2）获取队头元素。当第一栈（stack1）为空时，将第二个栈（stack2）中的全部元素依次弹出，再依次压入第一个栈中。其过程如图 2.8 所示，

 

C++ 实现

#include <iostream>
#include <stack>
#include <exception>


template <typename T> class CQueue
{
public:
    CQueue(void);
    ~CQueue(void);

    void appendTail(const T& node);
    T deleteHead();

private:
    std::stack<T> stack1;
    std::stack<T> stack2;
};

// Declare queue empty exception when try to pop when the queue is empty.
class QEmptyException: public std::exception {
    virtual const char* what() const throw()
    {
        return "Error: Queue is empty!";
    }
} popException;

// stack1 as input stack, stack2 as output stack
template <typename T>
void CQueue<T>::appendTail(const T& node)
{
    stack1.push(node);
}

template <class T>
T CQueue<T>::deleteHead()
{
    // Check if there are elements in stack2
    if (stack2.empty())
    {
        // Pop all the elements from stack1, then push them onto stack2
        if (stack1.size() > 0)
        {
            while (!stack1.empty())
            {
                T elem = stack1.top();
                stack1.pop();
                stack2.push(elem);
            }
        }
        else
            throw popException;
    }

    // Get the top element from stack2, then delete it from stack2
    T elem = stack2.top();
    stack2.pop();

    return elem;
}

template <typename T>
CQueue<T>::CQueue(void)
{
}

template <typename T>
CQueue<T>::~CQueue(void)
{
}

void unitest()
{
    CQueue<int> que;

    std::cout << "Push 1, 2, 3 successively into CQueue." << std::endl;
    que.appendTail(1);
    que.appendTail(2);
    que.appendTail(3);
    std::cout << "Pop the head of the queue: " << que.deleteHead() << std::endl;
    std::cout << "Pop the head of the queue: " << que.deleteHead() << std::endl;
    std::cout << "Push 4, 5, 6 successively into CQueue." << std::endl;
    que.appendTail(4);
    que.appendTail(5);
    que.appendTail(6);
    // Pop the rest elements in the queue, until the queue empty exception happens
    for (int i = 0; i < 4; ++i)
    {
        std::cout << "Pop the head of the queue: " << que.deleteHead() << std::endl;
    }

}

int main()
{
    unitest();

    return 0;
}

 

Python 实现

#!/usr/bin/python
# -*- coding: utf8 -*-

class CQueue:
    def __init__(self):
        self.stack1 = []
        self.stack2 = []

    def append_tail(self, elem):
        self.stack1.append(elem)

    def delete_head(self):
        if not self.stack2:
            if self.stack1:
                while self.stack1:
                    elem = self.stack1.pop()
                    self.stack2.append(elem)
            else:
                raise Exception("Queue is empty.")
            
        elem = self.stack2.pop()
        return elem


def unitest():
    # Create an instance of class CQueue
    que = CQueue()
    print "Push 1, 2, 3 successively into CQueue."
    for i in range(1, 4):
        que.append_tail(i)
    print "Pop the head of the queue:", que.delete_head()
    print "Pop the head of the queue:", que.delete_head()
    print "Push 4, 5, 6 successively into CQueue."
    for i in range(4, 7):
        que.append_tail(i)
    # Pop the rest elements in the queue
    for i in range(4):
        print "Pop the head of the queue:", que.delete_head()
        

if __name__ == '__main__':
    unitest()

 

参考代码

1. targetver.h

#pragma once

// The following macros define the minimum required platform.  The minimum required platform
// is the earliest version of Windows, Internet Explorer etc. that has the necessary features to run 
// your application.  The macros work by enabling all features available on platform versions up to and 
// including the version specified.

// Modify the following defines if you have to target a platform prior to the ones specified below.
// Refer to MSDN for the latest info on corresponding values for different platforms.
#ifndef _WIN32_WINNT            // Specifies that the minimum required platform is Windows Vista.
#define _WIN32_WINNT 0x0600     // Change this to the appropriate value to target other versions of Windows.
#endif

2. stdafx.h

// stdafx.h : include file for standard system include files,
// or project specific include files that are used frequently, but
// are changed infrequently
//

#pragma once

#include "targetver.h"

#include <stdio.h>
#include <tchar.h>



// TODO: reference additional headers your program requires here

3. stdafx.cpp

// stdafx.cpp : source file that includes just the standard includes
// QueueWithTwoStacks.pch will be the pre-compiled header
// stdafx.obj will contain the pre-compiled type information

#include "stdafx.h"

// TODO: reference any additional headers you need in STDAFX.H
// and not in this file

4. Queue.h

#pragma once
#include <stack>
#include <exception>

using namespace std;

template <typename T> class CQueue
{
public:
    CQueue(void);
    ~CQueue(void);
    
    // 在队列末尾添加一个结点
    void appendTail(const T& node);

    // 删除队列的头结点
    T deleteHead();

private:
    stack<T> stack1;
    stack<T> stack2;
};

template <typename T> CQueue<T>::CQueue(void)
{
}

template <typename T> CQueue<T>::~CQueue(void)
{
}

template<typename T> void CQueue<T>::appendTail(const T& element)
{
    stack1.push(element);
} 

template<typename T> T CQueue<T>::deleteHead()
{
    if(stack2.size()<= 0)
    {
        while(stack1.size()>0)
        {
            T& data = stack1.top();
            stack1.pop();
            stack2.push(data);
        }
    }

    if(stack2.size() == 0)
        throw new exception("queue is empty");

    T head = stack2.top();
    stack2.pop();

    return head;
}

5. Queue.cpp

#include "StdAfx.h"
#include "Queue.h"
#include <queue>

6. QueueWithTwoStacks.cpp

// QueueWithTwoStacks.cpp : Defines the entry point for the console application.
//

// 《剑指Offer——名企面试官精讲典型编程题》代码
// 著作权所有者：何海涛

#include "stdafx.h"
#include "Queue.h"

void Test(char actual, char expected)
{
    if(actual == expected)
        printf("Test passed.
");
    else
        printf("Test failed.
");
}

int _tmain(int argc, _TCHAR* argv[])
{
    CQueue<char> queue;

    queue.appendTail('a');
    queue.appendTail('b');
    queue.appendTail('c');

    char head = queue.deleteHead();
    Test(head, 'a');

    head = queue.deleteHead();
    Test(head, 'b');

    queue.appendTail('d');
    head = queue.deleteHead();
    Test(head, 'c');

    queue.appendTail('e');
    head = queue.deleteHead();
    Test(head, 'd');

    head = queue.deleteHead();
    Test(head, 'e');

    return 0;
}

7. 参考代码下载

项目 07_QueueWithTwoStacks 下载： 百度网盘

何海涛《剑指Offer：名企面试官精讲典型编程题》 所有参考代码下载：百度网盘

 

参考资料

[1]  何海涛. 剑指 Offer：名企面试官精讲典型编程题 [M]. 北京：电子工业出版社，2012. 58-62.