数据结构基础(7) --循环队列的设计与实现

队列

队列简称队, 也是一种操作受限的线性表, 只允许在表的一端进行插入, 而在表的另一端进行删除.其特点为”先进先出(FIFO)”,故又称为先进先出的线性表,简单队列如图所示:



循环队列

顺序队列有一个先天不足, 那就是空间利用率不高, 会产生”假溢出”现象,即:其实队列中还有空闲的空间以存储元素, 但我们在判断队列是否还有空间时, 队列告诉我们队列已经满了, 因此这种溢出并不是真正的溢出, 在data数组中依然存在可以放置元素的空位置, 所以说这是一种”假溢出”;

于是我们就引入了循环队列的概念, 将顺序队列臆造为一个环状的空间, 即把存储队列元素的表从逻辑上看成一个环, 称为循环队列,其示意图如下:



注意:如图中所示,我们的循环队列为了在实现上的便利, 会有一个位置的空闲, m_front(如图中的front)指针总会指向一个元素值为空的位置,因此(m_front+1)%capacity才真正的指向队首元素, 而m_rear(图中为rear)才指向一个真实存在的队尾元素;

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//循环队列的实现与解析
template <typename Type>
class MyQueue
{
template <typename T>
friend ostream &operator<<(std::ostream &os, const MyQueue<T> &queue);
public:
MyQueue(int queueSize = 64);
~MyQueue();

void push(const Type &item);
void pop() throw (std::range_error);
const Type &front() const throw (std::range_error);
const Type &rear() const throw (std::range_error);
bool isEmpty() const;

private:
Type *m_queue;
int m_front; //队首指针(其实(m_front+1)%capacity才真正的指向队首元素)
int m_rear; //队尾指针
int capacity; //队列的内存大小, 但实际可用的大小为capacity-1
};

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template <typename Type>
MyQueue<Type>::MyQueue(int queueSize): capacity(queueSize)
{
if (queueSize < 1)
throw std::range_error("queueSize must >= 1");

m_queue = new Type[capacity];
if (m_queue == NULL)
throw std::bad_alloc();

m_front = m_rear = 0;
}

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template <typename Type>
MyQueue<Type>::~MyQueue()
{
delete []m_queue;
m_queue = NULL;
m_front = m_rear = 0;
capacity = -1;
}

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template <typename Type>
inline bool MyQueue<Type>::isEmpty() const
{
return m_front == m_rear;
}

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template <typename Type>
inline void MyQueue<Type>::push(const Type &item)
{
if ((m_rear+1)%capacity == m_front) //队列已满
{
Type *newQueue = new Type[2 * capacity]; //新队列的长度为原队列的2倍
if (newQueue == NULL)
throw std::bad_alloc();

int start = (m_front+1)%capacity; //数据序列的起始地址
if (start <= 1) //队列指针尚未回绕
{
//只需拷贝一次:从start所指向的元素直到m_rear所指向的元素
//std::copy(m_queue+start, m_queue+start+capacity-1, newQueue);
std::copy(m_queue+start, m_queue+m_rear+1, newQueue);
}
else
{
//需要拷贝两次
//1:从start所指向的元素直到数组(不是队列)末尾
std::copy(m_queue+start, m_queue+capacity, newQueue);
//2:从数组(不是队列)起始直到队列末尾
std::copy(m_queue, m_queue+m_rear+1, newQueue+capacity-start);
}

//重新设置指针位置:详细信息请看下面图解
m_front = 2*capacity-1;
m_rear = capacity-2;
capacity *= 2;

delete []m_queue;
m_queue = newQueue;
}

//队尾指针后移
//注意:此处m_front+1可能需要回绕
m_rear = (m_rear+1)%capacity;
m_queue[m_rear] = item;
}

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template <typename Type>
inline const Type &MyQueue<Type>::front() const
throw (std::range_error)
{
if (isEmpty())
throw range_error("queue is empty");
//注意:此处m_front+1可能需要回绕
return m_queue[(m_front+1)%capacity];
}

template <typename Type>
inline const Type &MyQueue<Type>::rear() const
throw (std::range_error)
{
if (isEmpty())
throw range_error("queue is empty");

return m_queue[m_rear];
}

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template <typename Type>
inline void MyQueue<Type>::pop()
throw (std::range_error)
{
if (isEmpty())
throw range_error("queue is empty");

//注意:此处m_front+1可能需要回绕
m_front = (m_front+1)%capacity;
m_queue[m_front].~Type(); //显示调用析构函数以销毁(析构)对象
}

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//输出队列所有内容以做测试
template <typename Type>
ostream &operator<<(ostream &os, const MyQueue<Type> &queue)
{
for (int i = (queue.m_front+1)%(queue.capacity);
i <= queue.m_rear; /**空**/ )
{
os << queue.m_queue[i] << ' ';
if (i == queue.m_rear)
break;
else
i = (i+1)%(queue.capacity);
}

return os;
}

补充说明

当队列已满时的两类扩充操作:



扩充之后的内存布局:






附-测试代码:

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int main()
{
MyQueue<char> cQueue(3);
cQueue.push('A');
cQueue.push('B');

//因为cQueue实际能够用的大小为2, 所以此处会对数组进行放大
cQueue.push('C');
cout << cQueue << endl;
cout << "front = " << cQueue.front() << ", rear = "
<< cQueue.rear() << endl;

cQueue.pop();
cQueue.pop();
cQueue.push('D');
cQueue.push('E');
cQueue.push('F');

//此时queue的m_rear会进行回绕
cQueue.push('G');
cQueue.pop();
cQueue.push('H');

//此时队列已满, 再添加元素则会进行对队列扩张
//此时m_rear已经回绕, 则会触发两次拷贝操作
cQueue.push('I');

//验证是否能够正常工作
cout << cQueue << endl;
cout << "front = " << cQueue.front() << ", rear = "
<< cQueue.rear() << endl;

for (char ch = '1'; ch <= '9'; ++ch)
cQueue.push(ch);
for (int i = 0; i < 4; ++i)
cQueue.pop();

cout << cQueue << endl;
cout << "front = " << cQueue.front() << ", rear = "
<< cQueue.rear() << endl;

return 0;
}

原文地址：/article/1333401.html