优先级队列相对于普通队列,提供了插队功能,每次最先出队的不是最先入队的元素,而是优先级最高的元素。

它的实现采用了标准库提供的heap算法。该系列算法一共提供了四个函数。使用方式如下:

首先,建立一个容器,放入元素:

vector<int> coll;
insertNums(coll, 3, 7);
insertNums(coll, 5, 9);
insertNums(coll, 1, 4); printElems(coll, "all elements: ");

打印结果为:

all elements:
3 4 5 6 7 5 6 7 8 9 1 2 3 4

然后我们调用make_heap,这个算法把[beg, end)内的元素建立成堆

make_heap(coll.begin(), coll.end());

printElems(coll, "after make_heap: ");

打印结果:

after make_heap:
9 8 6 7 7 5 5 3 6 4 1 2 3 4

然后我们调用pop_heap,这个算法必须保证[beg, end)已经是一个heap,然后它将堆顶的元素(其实是begin指向的元素)放到最后,再把[begin. end-1)内的元素重新调整为heap

pop_heap(coll.begin(), coll.end());
coll.pop_back();
printElems(coll, "after pop_heap: ");

打印结果为:

after pop_heap:
8 7 6 7 4 5 5 3 6 4 1 2 3

接下来我们调用push_heap,该算法必须保证[beg, end-1)已经是一个heap,然后将整个[beg, end)调整为heap

coll.push_back(17);
push_heap(coll.begin(), coll.end()); printElems(coll, "after push_heap: ");

打印结果为:

after push_heap:
17 7 8 7 4 5 6 3 6 4 1 2 3 5

最后我们使用sort_heap将[beg, end)由heap转化为有序序列,所以,前提是[beg, end)已经是一个heap

sort_heap(coll.begin(), coll.end());
printElems(coll, "after sort_heap: ");

打印结果为:

after sort_heap:
1 2 3 3 4 4 5 5 6 6 7 7 8 17

完整的测试代码如下:

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std; template <typename T>
void insertNums(T &t, int beg, int end)
{
while(beg <= end)
{
t.insert(t.end(), beg);
++beg;
}
} template <typename T>
void printElems(const T &t, const string &s = "")
{
cout << s << endl;
for(typename T::const_iterator it = t.begin();
it != t.end();
++it)
{
cout << *it << " ";
}
cout << endl;
} int main(int argc, char const *argv[])
{
vector<int> coll;
insertNums(coll, 3, 7);
insertNums(coll, 5, 9);
insertNums(coll, 1, 4); printElems(coll, "all elements: "); //在这个范围内构造heap
make_heap(coll.begin(), coll.end()); printElems(coll, "after make_heap: "); //将堆首放到最后一个位置,其余位置调整成堆
pop_heap(coll.begin(), coll.end());
coll.pop_back();
printElems(coll, "after pop_heap: "); coll.push_back(17);
push_heap(coll.begin(), coll.end()); printElems(coll, "after push_heap: "); sort_heap(coll.begin(), coll.end());
printElems(coll, "after sort_heap: "); return 0;
}

 

根据以上的算法,我们来实现标准库的优先级队列priority_queue,代码如下:

#ifndef PRIORITY_QUEUE_HPP
#define PRIORITY_QUEUE_HPP #include <vector>
#include <algorithm>
#include <functional> template <typename T,
typename Container = std::vector<T>,
typename Compare = std::less<typename Container::value_type> >
class PriorityQueue
{
public:
typedef typename Container::value_type value_type; //不用T
typedef typename Container::size_type size_type;
typedef Container container_type;
typedef value_type &reference;
typedef const value_type &const_reference; PriorityQueue(const Compare& comp = Compare(),
const Container& ctnr = Container());
template <class InputIterator>
PriorityQueue (InputIterator first, InputIterator last,
const Compare& comp = Compare(),
const Container& ctnr = Container());
void push(const value_type &val)
{
cont_.push_back(val);
//调整最后一个元素入堆
std::push_heap(cont_.begin(), cont_.end(), comp_);
} void pop()
{
//第一个元素移出堆,放在最后
std::pop_heap(cont_.begin(), cont_.end(), comp_);
cont_.pop_back();
} bool empty() const { return cont_.empty(); }
size_type size() const { return cont_.size(); }
const_reference top() const { return cont_.front(); } private:
Compare comp_; //比较规则
Container cont_; //内部容器
}; template <typename T, typename Container, typename Compare>
PriorityQueue<T, Container, Compare>::PriorityQueue(const Compare& comp,
const Container& ctnr)
:comp_(comp), cont_(ctnr)
{
std::make_heap(cont_.begin(), cont_.end(), comp_); //建堆
} template <typename T, typename Container, typename Compare>
template <class InputIterator>
PriorityQueue<T, Container, Compare>::PriorityQueue (InputIterator first,
InputIterator last,
const Compare& comp,
const Container& ctnr)
:comp_(comp), cont_(ctnr)
{
cont_.insert(cont_.end(), first, last);
std::make_heap(cont_.begin(), cont_.end(), comp_);
} #endif //PRIORITY_QUEUE_HPP

我们注意到:

测试代码如下:

#include "PriorityQueue.hpp"
#include <iostream>
using namespace std; int main(int argc, char const *argv[])
{
PriorityQueue<float> q;
q.push(66.6);
q.push(22.3);
q.push(44.4); cout << q.top() << endl;
q.pop();
cout << q.top() << endl;
q.pop(); q.push(11.1);
q.push(55.5);
q.push(33.3);
q.pop(); while(!q.empty())
{
cout << q.top() << " ";
q.pop();
}
cout << endl; return 0;
}
05-28 12:08