Очередь приоритетов С++ как двоичная куча

Вы должны попытаться выделить наименьшую проблему, с которой у вас возникли проблемы. Было бы легче помочь, если бы вы могли точно сузить свой вопрос.

Если у вас возникли проблемы с пониманием того, как использовать класс pair из вашего примера в контексте массива, возможно, вам поможет следующий небольшой (автономный) пример:

#include <iostream>
#include <string>

class pair {
public:
    std::string object;
    double key;
};

void print_pair(const pair& p) {
    std::cout << p.object << " = " << p.key << std::endl;
}

int main() {

    // allocated on the stack, dies at the end of the function
    pair p;

    p.object = "question";
    p.key = 42;
    print_pair(p);

    pair* pp = new pair();
    (*pp).object = "6 * 10";  // We need to dereference the pointer, kinda clumsy syntax
    pp->key = 60; // Luckily there's a short hand! pp[0].key = 60; is the same thing
    print_pair(*pp);
    delete pp; // remember to clean up!

    pair* ap = new pair[10]; // allocate 10 pairs
    ap[0].object = "zero"; 
    (*(ap + 0)).key = 0; // same thing, ap[N] is the same as *(ap + N)
    print_pair(ap[0]);
    delete []ap; // remember to use the [] syntax when you new'ed like that!
}

хорошо, наконец-то понял... спасибо errbody :-)

/**
* implementing the priority queue as a binary heap
*
*/

#include <iostream>
#include <istream>
#include <ostream>
#include <sstream>
#include <map>
#include <algorithm>

#include "binary_heap.hpp"

/***********************
 *** inline functions
 ***********************/
inline int left(int i) { return i << 1; }

inline int right(int i) { return i << 1 | 1; }

inline int parent(int i) { return i >> 1; }


/*********************
 *** constructor
 *********************/
priority_queue::priority_queue(int n)  
{
  heapsize = 0;
  size = n;

  // don't forget to allocate the array of size n+1 as we don't use slot zero 
  A = new pair[n+1];
}


/*********************
 *** destructor
 *********************/
priority_queue::~priority_queue()  //delete the array
{
  delete[] A;
}


/*******************************************
 *** heapify * finds max of three things
 *******************************************/
void priority_queue::heapify(int k)
{
  pair smallest = A[k];
  int pos = k;        

  //only treat child as object if it's inside heap
  if (left(k) <= heapsize and A[left(k)].key < A[pos].key) {

    // update variables
    smallest = A[left(k)];
    pos = left(k);
  }

  // identical for right
  if (right(k) <= heapsize and A[right(k)].key < A[pos].key) {

    // update variables
    smallest = A[right(k)];
    pos = right(k);
  }

  // after both if's exectued: smallest is pair with smallest key and
  // pos is index of that pair in A[]

  // only need to do something if pos is NOT the same position
  // that we were passed in originally
  if (pos != k) {

    // swap items
    std::swap(A[k], A[pos]);

    // go recursive to trickle down...
    heapify(pos);
  }
}


/****************
 *** empty
 ****************/
bool priority_queue::empty()
{
  return (heapsize == 0);
}


/****************
 *** insert
 ****************/
void priority_queue::insert(std::string s, double priority)  //add s to the heap with the given priority as its key
{
  if (heapsize == size) {
    throw priority_queue_overflow();
  }

  // make room for insert
  ++heapsize;  
  // assign string arg to object member
  A[heapsize].object = s;
  // assign priority arg to key member
  A[heapsize].key = priority;

  // loop through and trickle up as needed
  int i(heapsize);
  while (i > 1 and A[parent(i)].key > A[i].key) {
    std::swap(A[parent(i)], A[i]);
    i = parent(i);  
  }
}


/*******************
 *** extract_min
 *******************/
std::string priority_queue::extract_min()  //remove the string of lowest key and return that string
{
  if (heapsize == 0) {
    throw priority_queue_underflow();
  }

  std::string ans = A[1].object;
  A[1] = A[heapsize];
  --heapsize;
  // trickle down as needed
  heapify(1);
  return ans;        
}


/**********************************
 *** function operator overload
 **********************************/
priority_queue::operator std::string()
{
  std::stringstream text; 
  int i(1);    

  while (i <= size) { 
    text << A[i].object << std::endl;
    ++i;
  } 
  return text.str(); 
}