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Showing content from https://cplusplus.com/reference/algorithm/push_heap/ below:

function template

std::push_heap default (1)

template <class RandomAccessIterator>  void push_heap (RandomAccessIterator first, RandomAccessIterator last);

custom (2)

template <class RandomAccessIterator, class Compare>  void push_heap (RandomAccessIterator first, RandomAccessIterator last,                   Compare comp);

Push element into heap range

Given a heap in the range [first,last-1), this function extends the range considered a heap to [first,last) by placing the value in (last-1) into its corresponding location within it.

A range can be organized into a heap by calling make_heap. After that, its heap properties are preserved if elements are added and removed from it using push_heap and pop_heap, respectively.

Parameters

first, last: Random-access iterators to the initial and final positions of the new heap range, including the pushed element. The range used is [first,last), which contains all the elements between first and last, including the element pointed by first but not the element pointed by last.
comp: Binary function that accepts two elements in the range as arguments, and returns a value convertible to bool. The value returned indicates whether the element passed as first argument is considered to be less than the second in the specific strict weak ordering it defines.
Unless [first,last) is an empty or one-element heap, this argument shall be the same as used to construct the heap.
The function shall not modify any of its arguments.
This can either be a function pointer or a function object.

Return value none

Example

// range heap example
#include <iostream>     // std::cout
#include <algorithm>    // std::make_heap, std::pop_heap, std::push_heap, std::sort_heap
#include <vector>       // std::vector

int main () {
  int myints[] = {10,20,30,5,15};
  std::vector<int> v(myints,myints+5);

  std::make_heap (v.begin(),v.end());
  std::cout << "initial max heap   : " << v.front() << '\n';

  std::pop_heap (v.begin(),v.end()); v.pop_back();
  std::cout << "max heap after pop : " << v.front() << '\n';

  v.push_back(99); std::push_heap (v.begin(),v.end());
  std::cout << "max heap after push: " << v.front() << '\n';

  std::sort_heap (v.begin(),v.end());

  std::cout << "final sorted range :";
  for (unsigned i=0; i<v.size(); i++)
    std::cout << ' ' << v[i];

  std::cout << '\n';

  return 0;
}

Output:

initial max heap   : 30
max heap after pop : 20
max heap after push: 99
final sorted range : 5 10 15 20 99

Complexity Up to logarithmic in the distance between first and last: Compares elements and potentially swaps (or moves) them until rearranged as a longer heap.

Data races Some (or all) of the objects in the range [first,last) are modified.

Exceptions Throws if any of the element comparisons, the element swaps (or moves) or the operations on iterators throws.
Note that invalid arguments cause undefined behavior.

See also

make_heap: Make heap from range (function template)

pop_heap: Pop element from heap range (function template)

sort_heap: Sort elements of heap (function template)

reverse: Reverse range (function template)

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