std::push_heap - cppreference.com
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    std::push_heap

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    C++
     
    Algorithm library
    Constrained algorithms and algorithms on ranges (C++20)
    Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
    Non-modifying sequence operations    
    Batch operations
    (C++17)
    Search operations
    Modifying sequence operations
    Copy operations
    (C++11)
    (C++11)
    (C++11)
    Swap operations
    Transformation operations
    Generation operations
    Removing operations
    Order-changing operations
    (until C++17)(C++11)
    (C++20)(C++20)
    Sampling operations
    (C++17)

    Sorting and related operations
    Partitioning operations
    (C++11)    
    (C++11)

    Sorting operations
    Binary search operations
    (on partitioned ranges)
    Set operations (on sorted ranges)
    Merge operations (on sorted ranges)
    Heap operations
    Minimum/maximum operations
    (C++11)
    (C++17)
    Lexicographical comparison operations
    (C++20)
    Permutation operations


     
    Defined in header <algorithm> 
    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 the target [first, last).

    1) The heap is with respect to operator<(until C++20)std::less{}(since C++20).
    If [first, last - 1) is not a valid heap with respect to operator<(until C++20)std::less{}(since C++20), the behavior is undefined.
    2) The heap is with respect to comp.
    If [first, last - 1) is not a valid heap with respect to comp, the behavior is undefined.

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

    (until C++11)
    (since C++11)

    Parameters

    first, last - the pair of iterators defining the target range
    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.

    Complexity

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

    1) At most log(N) comparisons using operator<(until C++20)std::less{}(since C++20).
    2) At most log(N) applications of the comparison function comp.

    Example

    Run this code
    #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

    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 target range was not required to be swappable required

    See also