# std::push_heap

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< cpp‎ | algorithm

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 heap `[`first`,` last - 1`)`. The heap after the insertion will be `[`first`,` last`)`.

1) The heap is with respect to operator<.
2) The heap is with respect to comp.

If `[`first`,` last - 1`)` is not a heap, the behavior is undefined.

### Parameters

first, last | - | the range indicating the heap after the 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.
- The type of dereferenced `RandomIt` must meet the requirements of MoveAssignable and MoveConstructible.
- `Compare` must meet the requirements of Compare.

### Return value

(none)

### Complexity

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

1) At most \(\scriptsize log(N)\)log(N) comparisons using operator<.
2) At most \(\scriptsize log(N)\)log(N) applications of the comparison function comp.

### Notes

A heap with respect to comp (max heap) is a random access range `[`first`,` last`)` that has the following properties:

- Given \(\scriptsize N\)N as last - first, for all integer i where \(\scriptsize 0 < i < N\)0 < i < N, bool(comp(first[(i - 1) / 2], first[i])) is false.
- A new element can be added using std::push_heap, in \(\scriptsize \mathcal{O}(\log N)\)𝓞(log N) time.
- *first can be removed using std::pop_heap, in \(\scriptsize \mathcal{O}(\log N)\)𝓞(log N) time.

### Example

Run this code

    #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

### 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 193 | C++98 | heap required *first to be the largest element | there can be elements equal to *first
LWG 2166 | C++98 | the heap reqirement did not match the definition of max heap closely enough | requirement imporved

### See also

is_heap (C++11) | checks if the given range is a max heap (function template)
is_heap_until (C++11) | finds the largest subrange that is a max heap (function template)
make_heap | creates a max heap out of a range of elements (function template)
pop_heap | removes the largest element from a max heap (function template)
sort_heap | turns a max heap into a range of elements sorted in ascending order (function template)
ranges::push_heap (C++20) | adds an element to a max heap (niebloid)

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