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std::push_heap

Defined in header `<algorithm>`
	(1)
template< class RandomIt > void push_heap( RandomIt first, RandomIt last );		(until C++20)
template< class RandomIt > constexpr void push_heap( RandomIt first, RandomIt last );		(since C++20)
	(2)
template< class RandomIt, class Compare > void push_heap( RandomIt first, RandomIt last, Compare comp );		(until C++20)
template< class RandomIt, class Compare > constexpr void push_heap( RandomIt first, RandomIt last, Compare comp );		(since C++20)

Inserts the element at the position last - 1 into the max heap defined by the range [first, last - 1). The first version of the function uses operator< to compare the elements, the second uses the given comparison function comp.

Parameters

first, last	-	the range of elements defining the heap to modify
comp	-	comparison function object (i.e. an object that satisfies the requirements of Compare) which returns `true` if the first argument is less than the second. The signature of the comparison function should be equivalent to the following: `bool cmp(const Type1 &a, const Type2 &b);` While the signature does not need to have `const &`, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) `Type1` and `Type2` regardless of value category (thus, `Type1 &` is not allowed, nor is `Type1` unless for `Type1` a move is equivalent to a copy (since C++11)). The types Type1 and Type2 must be such that an object of type RandomIt can be dereferenced and then implicitly converted to both of them.
Type requirements
-`RandomIt` must meet the requirements of LegacyRandomAccessIterator.
-The type of dereferenced `RandomIt` must meet the requirements of MoveAssignable and MoveConstructible.

Return value

(none).

Complexity

At most log(N) comparisons where N = std::distance(first, last).

Notes

A max heap is a range of elements [f, l) that has the following properties:

With N = l - f, for all 0 < i < N, f[(i - 1) / 2] does not compare less than f[i].
A new element can be added using std::push_heap, in \(\scriptsize \mathcal{O}(\log N)\)𝓞(log N) time.
The first element can be removed using std::pop_heap, in \(\scriptsize \mathcal{O}(\log N)\)𝓞(log N) time.

Example

#include <algorithm>
#include <iostream>
#include <string_view>
#include <vector>
 
void println(std::string_view rem, std::vector<int> const& v)
{
    std::cout << rem;
    for (int e : v)
        std::cout << e << ' ';
    std::cout << '\n';
}
 
int main()
{
    std::vector<int> v {3, 1, 4, 1, 5, 9};
 
    std::make_heap(v.begin(), v.end());
    println("after make_heap: ", v);
 
    v.push_back(6);
    println("after push_back: ", v);
 
    std::push_heap(v.begin(), v.end());
    println("after push_heap: ", v);
}

Output:

after make_heap: 9 5 4 1 1 3
after push_back: 9 5 4 1 1 3 6
after push_heap: 9 5 6 1 1 3 4