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Showing content from https://en.cppreference.com/w/cpp/language/../error/error_code/../../algorithm/push_heap.html below:

std::push_heap - cppreference.com

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

(1) (constexpr since C++20)

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

(2) (constexpr since C++20)

Inserts the element at the position last - 1 into the heap [first, last - 1). The heap after the insertion will be [first, last).

1)

The heap is with respect to

operator<(until C++20)std::less{}(since C++20)

2) The heap is with respect to comp.

If any of the following conditions is satisfied, the behavior is undefined:

[first, last - 1) is not a heap with respect to the corresponding comparator.

[edit] Parameters first, last - the pair of iterators defining the range of elements that form the binary heap after insertion 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. -Compare must meet the requirements of Compare. [edit] Complexity

Given \(\scriptsize N\)N as std::distance(first, last):

1)

At most

\(\scriptsize \log(N)\)log(N)

comparisons using

operator<(until C++20)std::less{}(since C++20)

2) At most \(\scriptsize \log(N)\)log(N) applications of the comparison function comp.

[edit] Example

#include <algorithm>
#include <iostream>
#include <string_view>
#include <vector>
 
void println(std::string_view rem, const std::vector<int>& 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

[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior LWG 3032 C++98 the elements of [first, last) was not required to be swappable required [edit] See also checks if the given range is a max heap
(function template) [edit] finds the largest subrange that is a max heap
(function template) [edit] creates a max heap out of a range of elements
(function template) [edit] removes the largest element from a max heap
(function template) [edit] turns a max heap into a range of elements sorted in ascending order
(function template) [edit] adds an element to a max heap
(algorithm function object)[edit]

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