优先级队列(Priority Queue)
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优先级队列(Priority Queue)
注:队列是一种特征为FIFO的数据结构,每次从队列中取出的是最早加入队列中的元素。但是,许多应用需要另一种队列,每次从队列中取出的应是具有最高优先权的元素,这种队列就是优先级队列(Priority Queue),也称为优先权队列。
1. 优先级队列的概念
1.1 优先级队列的定义
- 优先级队列是不同于先进先出队列的另一种队列。每次从队列中取出的是具有最高优先权的元素。
1.2 优先级队列的特点
- 优先级队列是0个或多个元素的集合,每个元素都有一个优先权或值。
- 当给每个元素分配一个数字来标记其优先级时,可设较小的数字具有较高的优先级,这样更方便地在一个集合中访问优先级最高的元素,并对其进行查找和删除操作。
- 对优先级队列,执行的操作主要有:(1)查找,(2)插入,(3)删除。
- 在最小优先级队列(min Priority Queue)中,查找操作用来搜索优先权最小的元素,删除操作用来删除该元素。
- 在最大优先级队列(max Priority Queue)中,查找操作用来搜索优先权最大的元素,删除操作用来删除该元素。
- 插入操作均只是简单地把一个新的元素加入到队列中。
- 注:每个元素的优先级根据问题的要求而定。当从优先级队列中删除一个元素时,可能出现多个元素具有相同的优先权。在这种情况下,把这些具有相同优先权的元素视为一个先来先服务的队列,按他们的入队顺序进行先后处理。
2. 最小优先级队列的实现——基于一维数组的存储表示
2.1 最小优先级队列的类定义及其操作的实现
文件:PriorityQueue.h
#ifndef PRIORITY_QUEUE_H_#define PRIORITY_QUEUE_H_#include <iostream>#include <string>#include <strstream>using namespace std;const int defaultSize = 50;template <class T>class PriorityQueue{public: PriorityQueue(int sz = defaultSize); //构造函数 ~PriorityQueue(); //析构函数public: bool getHead(T& x) const; //读取队头(具最小优先权)的值 bool Insert(const T& x); //将新元素x插入到队尾 bool RemoveMin(T& x); //将队头元素删除 bool IsEmpty() const; //判断队列是否为空 bool IsFull() const; //判断队列是否为满 void MakeEmpty(); //置优先级队列为空 int getSize() const; //求优先级队列中元素个数public: template <class T> friend ostream& operator<<(ostream& os, const PriorityQueue<T>& q); //输出队列元素的重载操作<<private: void adjust(); //队列调整private: T *pqelements; //存放队列元素的队列数组 int maxSize; //队列最大可容纳元素个数 int count; //当前元素个数(长度)};//构造函数template <class T>PriorityQueue<T>::PriorityQueue(int sz){ cout << "$ 执行构造函数" << endl; if (sz >= 0) { maxSize = sz; count = 0; pqelements = new T[maxSize]; }} //析构函数template <class T>PriorityQueue<T>::~PriorityQueue(){ cout << "$ 执行析构函数" << endl; delete[] pqelements; pqelements = NULL;} //读取队头(具最小优先权)的值template <class T>bool PriorityQueue<T>::getHead(T& x) const{ if (true == IsEmpty()) { return false; } x = pqelements[0]; return true;}//将新元素x插入到队尾template <class T>bool PriorityQueue<T>::Insert(const T& x){ if (true == IsFull()) { return false; } pqelements[count++] = x; adjust(); //按优先权进行调整 return true;}//将队头元素删除template <class T>bool PriorityQueue<T>::RemoveMin(T& x){ if (true == IsEmpty()) { return false; } x = pqelements[0]; for (int i = 1; i < count; i++) { pqelements[i - 1] = pqelements[i]; } count--; return true;}//判断队列是否为空template <class T>bool PriorityQueue<T>::IsEmpty() const{ return (0 == count) ? true : false;}//判断队列是否为满template <class T>bool PriorityQueue<T>::IsFull() const{ return (maxSize == count) ? true : false;}//置优先级队列为空template <class T>void PriorityQueue<T>::MakeEmpty(){ delete[] pqelements; count = 0; pqelements = new T[maxSize];}//求优先级队列中元素个数template <class T>int PriorityQueue<T>::getSize() const{ return count;}//输出队列元素的重载操作<<template <class T>ostream& operator<<(ostream& os, const PriorityQueue<T>& q){ for (int i = 0; i < q.count; i++) { os << "[" << i << "]" << " : " << q.pqelements[i] << endl; } return os;}//队列调整template <class T>void PriorityQueue<T>::adjust(){ int i = 0; T temp = pqelements[count - 1]; for (i = count - 2; i >= 0; i--) { if (pqelements[i] <= temp) { break; } pqelements[i + 1] = pqelements[i]; } pqelements[i + 1] = temp;}#endif /* PRIORITY_QUEUE_H_ */
2.2 主函数(main函数)的实现
文件:main.cpp
#include "PriorityQueue.h"#define EXIT 0 //退出#define GETHEAD 1 //读取队头(具最小优先权)的值#define INSERT 2 //将新元素x插入到队尾#define REMOVEMIN 3 //将队头元素删除#define ISEMPTY 4 //判断队列是否为空#define ISFULL 5 //判断队列是否为满#define MAKEEMPTY 6 //置优先级队列为空#define GETSIZE 7 //求优先级队列中元素个数#define OPERATOR_OSTREAM 8 //输出队列元素的重载操作<<void print_description(){ cout << "------------------------------>优先级队列<------------------------------" << endl; cout << "功能选项说明:" << endl; cout << "#0: 退出" << endl; cout << "#1: 读取队头(具最小优先权)的值" << endl; cout << "#2: 将新元素x插入到队尾" << endl; cout << "#3: 将队头元素删除" << endl; cout << "#4: 判断队列是否为空" << endl; cout << "#5: 判断队列是否为满" << endl; cout << "#6: 置优先级队列为空" << endl; cout << "#7: 求优先级队列中元素个数" << endl; cout << "#8: 输出队列元素的重载操作<<" << endl; cout << "--------------------------------------------------------------------" << endl;}//判断输入的字符串每个字符是否都是数值0~9bool IsNumber(const string& s_num){ for (size_t i = 0; i < s_num.size(); i++) { if ((s_num[i] < '0') || (s_num[i] > '9')) { return false; } } return true;}//类型转换——将string型转为模板类型Ttemplate <class T>T StrToTtype(const string& s_num){ T n_num; strstream ss_num; ss_num << s_num; ss_num >> n_num; return n_num;}//输入数据值template <class T>T get_data(){ cout << "> 请输入数据值,data = "; string s_data; cin >> s_data; return StrToTtype<T>(s_data);}//输入数组的最大长度template <class T>int get_maxsize(){ cout << "> 请输入数组的最大长度,maxsize = "; string s_maxsize; cin >> s_maxsize; while (false == IsNumber(s_maxsize)) { cout << "* 输入有误,请重新输入:"; cin >> s_maxsize; } return atoi(s_maxsize.c_str());}//构造优先级队列template <class T>PriorityQueue<T>* construct_priorityqueue(){ cout << "\n==> 创建优先级队列" << endl; int n_maxsize = get_maxsize<T>(); PriorityQueue<T> *priorityQueue = new PriorityQueue<T>(n_maxsize); return priorityQueue;}//析构优先级队列template <class T>void destory_priorityqueue(PriorityQueue<T>* priorityQueue){ cout << "\n==> 释放优先级队列在堆中申请的空间,并将指向该空间的指针变量置为空" << endl; delete priorityQueue; priorityQueue = NULL;}//读取队头(具最小优先权)的值template <class T>void gethead(PriorityQueue<T>* priorityQueue){ cout << "$ 执行读取队头(具最小优先权)的值函数" << endl; T data; if (false == priorityQueue->getHead(data)) { cout << "* 读取队头元素失败" << endl; return; } cout << "* 读取队头元素成功,data = " << data << endl;}//将新元素x插入到队尾template <class T> void insert(PriorityQueue<T>* priorityQueue){ cout << "$ 执行将新元素x插入到队尾函数" << endl; T data = get_data<T>(); if (false == priorityQueue->Insert(data)) { cout << "* 入队失败" << endl; return; } cout << "* 入队成功,data = " << data << endl;}//将队头元素删除template <class T> void removemin(PriorityQueue<T>* priorityQueue){ cout << "$ 执行将队头元素删除函数" << endl; T data; if (false == priorityQueue->RemoveMin(data)) { cout << "* 出队失败" << endl; return; } cout << "* 出队成功,data = " << data << endl;}//判断队列是否为空template <class T> void isempty(PriorityQueue<T>* priorityQueue){ cout << "$ 执行判断队列是否为空函数,IsEmpty = " << priorityQueue->IsEmpty() << endl;}//判断队列是否为满template <class T> void isfull(PriorityQueue<T>* priorityQueue){ cout << "$ 执行判断队列是否为满函数,IsFull = " << priorityQueue->IsFull() << endl;}//置优先级队列为空template <class T>void makeempty(PriorityQueue<T>* priorityQueue){ cout << "$ 执行置优先级队列为空函数" << endl; priorityQueue->MakeEmpty();}//求优先级队列中元素个数template <class T> void getsize(PriorityQueue<T>* priorityQueue){ cout << "$ 执行求优先级队列中元素个数函数,Size = " << priorityQueue->getSize() << endl;}//输出队列元素的重载操作<<template <class T>void operator_ostream(PriorityQueue<T>* priorityQueue){ cout << "$ 执行输出队列元素的重载操作<<函数" << endl; cout << *priorityQueue;//或operator<<(cout, *priorityQueue);}//优先级队列操作选择template <class T>void select_operation(PriorityQueue<T>* priorityQueue){ if (NULL == priorityQueue) { cout << "* 没有构造优先级队列,请先构造优先级队列。" << endl; return; } string s_operation; while (s_operation != "0") { cout << "\n==> 请输入功能选项编号(按\"0\"退出程序):"; cin >> s_operation; while (false == IsNumber(s_operation)) { cout << "* 输入有误,请重新输入:"; cin >> s_operation; } int n_operation = atoi(s_operation.c_str()); switch (n_operation) { case EXIT://退出 { cout << "$ 退出程序" << endl; break; } case GETHEAD://读取队头(具最小优先权)的值 { gethead(priorityQueue); break; } case INSERT://将新元素x插入到队尾 { insert(priorityQueue); break; } case REMOVEMIN://将队头元素删除 { removemin(priorityQueue); break; } case ISEMPTY://判断队列是否为空 { isempty(priorityQueue); break; } case ISFULL://判断队列是否为满 { isfull(priorityQueue); break; } case MAKEEMPTY://置优先级队列为空 { makeempty(priorityQueue); break; } case GETSIZE://求优先级队列中元素个数 { getsize(priorityQueue); break; } case OPERATOR_OSTREAM://输出队列元素的重载操作<< { operator_ostream(priorityQueue); break; } default: { cout << "* 请输入正确的功能选项编号" << endl; break; } } }}int main(int argc, char* argv[]){ print_description(); PriorityQueue<int> *priorityQueue = construct_priorityqueue<int>(); select_operation(priorityQueue); destory_priorityqueue(priorityQueue); system("pause"); return 0;}
3. 最小优先级队列的实现——基于单链表的存储表示
3.1 最小优先级队列的类定义及其操作的实现
文件:PriorityQueue.h
#ifndef PRIORITY_QUEUE_H_#define PRIORITY_QUEUE_H_#include <iostream>#include <string>#include <strstream>using namespace std;template <class T>struct LinkNode //链表结点类的定义{ T data; //数据域 LinkNode<T> *link; //指针域——后继指针 //仅初始化指针成员的构造函数 LinkNode(LinkNode<T>* ptr = NULL){ link = ptr; } //初始化数据与指针成员的构造函数 LinkNode(const T& value, LinkNode<T>* ptr = NULL){ data = value; link = ptr; }};template <class T>class PriorityQueue{public: PriorityQueue(); //构造函数 ~PriorityQueue(); //析构函数public: bool getHead(T& x) const; //读取队头(具最小优先权)的值 bool Insert(const T& x); //将新元素x插入到队尾 bool RemoveMin(T& x); //将队头元素删除 bool IsEmpty() const; //判断队列是否为空 bool IsFull() const; //判断队列是否为满 void MakeEmpty(); //置优先级队列为空 int getSize() const; //求优先级队列中元素个数public: template <class T> friend ostream& operator<<(ostream& os, const PriorityQueue<T>& q); //输出队列中元素的重载操作<<private: void adjust(LinkNode<T> *newNode); //队列调整private: LinkNode<T> *front; //队头指针,即链头指针};//构造函数template <class T>PriorityQueue<T>::PriorityQueue(): front(NULL){ cout << "$ 执行构造函数" << endl;} //析构函数template <class T>PriorityQueue<T>::~PriorityQueue(){ cout << "$ 执行析构函数" << endl; MakeEmpty();} //读取队头(具最小优先权)的值template <class T>bool PriorityQueue<T>::getHead(T& x) const{ if (true == IsEmpty()) { return false; } x = front->data; return true;}//将新元素x插入到队尾template <class T>bool PriorityQueue<T>::Insert(const T& x){ LinkNode<T> *newNode = new LinkNode<T>(x); if (NULL == newNode) { return false; } if (NULL == front) { front = newNode; return true; } adjust(newNode); return true;}//将队头元素删除template <class T>bool PriorityQueue<T>::RemoveMin(T& x){ if (true == IsEmpty()) { return false; } LinkNode<T> *curNode = front; front = front->link; x = curNode->data; delete curNode; return true;}//判断队列是否为空template <class T>bool PriorityQueue<T>::IsEmpty() const{ return (NULL == front) ? true : false;}//判断队列是否为满template <class T>bool PriorityQueue<T>::IsFull() const{ return false;}//置优先级队列为空template <class T>void PriorityQueue<T>::MakeEmpty(){ LinkNode<T> *curNode = NULL; while (NULL != front) //当链表不为空时,删去链表中所有结点 { curNode = front; //保存被删结点 front = curNode->link; //被删结点的下一个结点成为头结点 delete curNode; //从链表上摘下被删结点 }}//求优先级队列中元素个数template <class T>int PriorityQueue<T>::getSize() const{ int count = 0; LinkNode<T> *curNode = front; while (NULL != curNode) { curNode = curNode->link; count++; } return count;}//输出队列中元素的重载操作<<template <class T>ostream& operator<<(ostream& os, const PriorityQueue<T>& q){ int i = 0; LinkNode<T> *curNode = q.front; while (NULL != curNode) { os << "[" << i++ << "]" << " : " << curNode->data << endl; curNode = curNode->link; } return os;}//队列调整template <class T>void PriorityQueue<T>::adjust(LinkNode<T> *newNode){ LinkNode<T> *preNode = NULL; LinkNode<T> *curNode = front; while (NULL != curNode) { if (curNode->data > newNode->data) { break; } preNode = curNode; curNode = curNode->link; } if (preNode == NULL) { newNode->link = curNode; front = newNode; } else { preNode->link = newNode; newNode->link = curNode; }}#endif /* PRIORITY_QUEUE_H_ */
3.2 主函数(main函数)的实现
文件:main.cpp
#include "PriorityQueue.h"#define EXIT 0 //退出#define GETHEAD 1 //读取队头(具最小优先权)的值#define INSERT 2 //将新元素x插入到队尾#define REMOVEMIN 3 //将队头元素删除#define ISEMPTY 4 //判断队列是否为空#define ISFULL 5 //判断队列是否为满#define MAKEEMPTY 6 //置优先级队列为空#define GETSIZE 7 //求优先级队列中元素个数#define OPERATOR_OSTREAM 8 //输出队列元素的重载操作<<void print_description(){ cout << "------------------------------>优先级队列<------------------------------" << endl; cout << "功能选项说明:" << endl; cout << "#0: 退出" << endl; cout << "#1: 读取队头(具最小优先权)的值" << endl; cout << "#2: 将新元素x插入到队尾" << endl; cout << "#3: 将队头元素删除" << endl; cout << "#4: 判断队列是否为空" << endl; cout << "#5: 判断队列是否为满" << endl; cout << "#6: 置优先级队列为空" << endl; cout << "#7: 求优先级队列中元素个数" << endl; cout << "#8: 输出队列元素的重载操作<<" << endl; cout << "--------------------------------------------------------------------" << endl;}//判断输入的字符串每个字符是否都是数值0~9bool IsNumber(const string& s_num){ for (size_t i = 0; i < s_num.size(); i++) { if ((s_num[i] < '0') || (s_num[i] > '9')) { return false; } } return true;}//类型转换——将string型转为模板类型Ttemplate <class T>T StrToTtype(const string& s_num){ T n_num; strstream ss_num; ss_num << s_num; ss_num >> n_num; return n_num;}//输入数据值template <class T>T get_data(){ cout << "> 请输入数据值,data = "; string s_data; cin >> s_data; return StrToTtype<T>(s_data);}//构造优先级队列template <class T>PriorityQueue<T>* construct_priorityqueue(){ cout << "\n==> 创建优先级队列" << endl; PriorityQueue<T> *priorityQueue = new PriorityQueue<T>; return priorityQueue;}//析构优先级队列template <class T>void destory_priorityqueue(PriorityQueue<T>* priorityQueue){ cout << "\n==> 释放优先级队列在堆中申请的空间,并将指向该空间的指针变量置为空" << endl; delete priorityQueue; priorityQueue = NULL;}//读取队头(具最小优先权)的值template <class T>void gethead(PriorityQueue<T>* priorityQueue){ cout << "$ 执行读取队头(具最小优先权)的值函数" << endl; T data; if (false == priorityQueue->getHead(data)) { cout << "* 读取队头元素失败" << endl; return; } cout << "* 读取队头元素成功,data = " << data << endl;}//将新元素x插入到队尾template <class T>void insert(PriorityQueue<T>* priorityQueue){ cout << "$ 执行将新元素x插入到队尾函数" << endl; T data = get_data<T>(); if (false == priorityQueue->Insert(data)) { cout << "* 入队失败" << endl; return; } cout << "* 入队成功,data = " << data << endl;}//将队头元素删除template <class T>void removemin(PriorityQueue<T>* priorityQueue){ cout << "$ 执行将队头元素删除函数" << endl; T data; if (false == priorityQueue->RemoveMin(data)) { cout << "* 出队失败" << endl; return; } cout << "* 出队成功,data = " << data << endl;}//判断队列是否为空template <class T>void isempty(PriorityQueue<T>* priorityQueue){ cout << "$ 执行判断队列是否为空函数,IsEmpty = " << priorityQueue->IsEmpty() << endl;}//判断队列是否为满template <class T>void isfull(PriorityQueue<T>* priorityQueue){ cout << "$ 执行判断队列是否为满函数,IsFull = " << priorityQueue->IsFull() << endl;}//置优先级队列为空template <class T>void makeempty(PriorityQueue<T>* priorityQueue){ cout << "$ 执行置优先级队列为空函数" << endl; priorityQueue->MakeEmpty();}//求优先级队列中元素个数template <class T>void getsize(PriorityQueue<T>* priorityQueue){ cout << "$ 执行求优先级队列中元素个数函数,Size = " << priorityQueue->getSize() << endl;}//输出队列元素的重载操作<<template <class T>void operator_ostream(PriorityQueue<T>* priorityQueue){ cout << "$ 执行输出队列元素的重载操作<<函数" << endl; cout << *priorityQueue;//或operator<<(cout, *priorityQueue);}//优先级队列操作选择template <class T>void select_operation(PriorityQueue<T>* priorityQueue){ if (NULL == priorityQueue) { cout << "* 没有构造优先级队列,请先构造优先级队列。" << endl; return; } string s_operation; while (s_operation != "0") { cout << "\n==> 请输入功能选项编号(按\"0\"退出程序):"; cin >> s_operation; while (false == IsNumber(s_operation)) { cout << "* 输入有误,请重新输入:"; cin >> s_operation; } int n_operation = atoi(s_operation.c_str()); switch (n_operation) { case EXIT://退出 { cout << "$ 退出程序" << endl; break; } case GETHEAD://读取队头(具最小优先权)的值 { gethead(priorityQueue); break; } case INSERT://将新元素x插入到队尾 { insert(priorityQueue); break; } case REMOVEMIN://将队头元素删除 { removemin(priorityQueue); break; } case ISEMPTY://判断队列是否为空 { isempty(priorityQueue); break; } case ISFULL://判断队列是否为满 { isfull(priorityQueue); break; } case MAKEEMPTY://置优先级队列为空 { makeempty(priorityQueue); break; } case GETSIZE://求优先级队列中元素个数 { getsize(priorityQueue); break; } case OPERATOR_OSTREAM://输出队列元素的重载操作<< { operator_ostream(priorityQueue); break; } default: { cout << "* 请输入正确的功能选项编号" << endl; break; } } }}int main(int argc, char* argv[]){ print_description(); PriorityQueue<int> *priorityQueue = construct_priorityqueue<int>(); select_operation(priorityQueue); destory_priorityqueue(priorityQueue); system("pause"); return 0;}
参考文献:
[1]《数据结构(用面向对象方法与C++语言描述)(第2版)》殷人昆——第三章
[2] 百度搜索关键字:优先级队列
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