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.\n"); else printf("Test failed.\n"); } 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.