This is a small demo showing the usage of priority queues and standalone heap

priority_queue_demo.cpp

#include <iostream>
#include <queue>
#include <vector>
#include <functional>
#include <algorithm>

using namespace std;

class Compare {
public:
    bool operator()(const int& v1, const int& v2)
    {
        return v1 > v2; // min heap
    }
};

// standalone min heap
void vector_min_heap(vector<int> v)
{
    make_heap(begin(v), end(v), [](const int& i1, const int& i2) {return i1 > i2;}); // rearrange the elements to form a heap

    v.push_back(21); push_heap(begin(v), end(v), [](const int& i1, const int& i2) {return i1 > i2;});

    for_each(begin(v), end(v), [](const int& i) { cout << i << ' '; });
    cout << endl;
}

// standalone max heap
void vector_max_heap(vector<int> v)
{
    // make_heap(begin(v), end(v)); // same as below
    make_heap(begin(v), end(v), [](const int& i1, const int& i2) {return i1 < i2;}); // rearrange the elements to form a heap

    // v.push_back(21); push_heap(begin(v), end(v)); // same as below
    v.push_back(21); push_heap(begin(v), end(v), [](const int& i1, const int& i2) {return i1 < i2;});

    for_each(begin(v), end(v), [](const int& i) { cout << i << ' '; });
    cout << endl;
}

int main()
{
    int data[] = {23,56,78,77,21};
    
    priority_queue<int, vector<int>, greater<int>> pq_min_heap (begin(data), end(data)); // also makes a heap
    priority_queue<int, vector<int>, less<int>> pq_max_heap (begin(data), end(data)); // also makes a heap
    priority_queue<int> pq_default (begin(data), end(data)); // also makes a heap
    
    priority_queue<int, vector<int>, Compare> pq_func_obj (begin(data), end(data)); // also makes a heap

    pq_min_heap.push(7);
    pq_min_heap.push(100);

    cout << "Expecting top(pq_min_heap) 7: " << pq_min_heap.top() << endl;
    
    pq_min_heap.pop();
    cout << "Expecting top(pop(pq_min_heap)) 21: " << pq_min_heap.top() << endl;

    vector<int> v {1,7,4,8,10,17,8};

    vector_min_heap(v);
    vector_max_heap(v);
}