NAME¶

std::ranges::push_heap - std::ranges::push_heap

Synopsis¶

Defined in header <algorithm>
Call signature
template< std::random_access_iterator I, std::sentinel_for<I> S,

class Comp = ranges::less, class Proj = std::identity >
requires std::sortable<I, Comp, Proj> (1) (since C++20)
constexpr I

push_heap( I first, S last, Comp comp = {}, Proj proj = {} );
template< ranges::random_access_range R, class Comp =
ranges::less,

class Proj = std::identity > (2) (since C++20)
requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
constexpr ranges::borrowed_iterator_t<R>

push_heap( R&& r, Comp comp = {}, Proj proj = {} );

Inserts the element at the position last - 1 into the max heap defined by the range
[first, last - 1).

1) Elements are compared using the given binary comparison function comp and
projection object proj.
2) Same as (1), but uses r as the range, as if using ranges::begin(r) as first and
ranges::end(r) as last.

The function-like entities described on this page are niebloids, that is:

* Explicit template argument lists cannot be specified when calling any of them.
* None of them are visible to argument-dependent lookup.
* When any of them are found by normal unqualified lookup as the name to the left
of the function-call operator, argument-dependent lookup is inhibited.

In practice, they may be implemented as function objects, or with special compiler
extensions.

Parameters¶

first, last - the range of elements defining the heap to modify
r - the range of elements defining the heap to modify
pred - predicate to apply to the projected elements
proj - projection to apply to the elements

Return value¶

An iterator equal to last.

Complexity¶

Given N = ranges::distance(first, last), at most \(\scriptsize \log{(N)}\)log(N)
comparisons and \(\scriptsize 2\log{(N)}\)2log(N) projections.

Notes¶

A max heap is a range of elements [f, l), arranged with respect to comparator comp
and projection proj, that has the following properties:

* With N = l - f, p = f[(i - 1) / 2], and q = f[i], for all 0 < i < N, the
expression std::invoke(comp, std::invoke(proj, p), std::invoke(proj, q))
evaluates to false.
* A new element can be added using ranges::push_heap, in \(\scriptsize
\mathcal{O}(\log N)\)𝓞(log N) time.
* The first element can be removed using ranges::pop_heap, in \(\scriptsize
\mathcal{O}(\log N)\)𝓞(log N) time.

Possible implementation¶

struct push_heap_fn {
template<std::random_access_iterator I, std::sentinel_for<I> S,
class Comp = ranges::less, class Proj = std::identity>
requires std::sortable<I, Comp, Proj>
constexpr I
operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
{
const auto n{ranges::distance(first, last)};
const auto length{n};
if (n > 1)
{
I last{first + n};
n = (n - 2) / 2;
I i{first + n};
if (std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, *--last)))
{
std::iter_value_t<I> v {ranges::iter_move(last)};
do
{
*last = ranges::iter_move(i);
last = i;
if (n == 0)
break;
n = (n - 1) / 2;
i = first + n;
}
while (std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, v)));
*last = std::move(v);
}
}
return first + length;
}

template<ranges::random_access_range R, class Comp = ranges::less,
class Proj = std::identity>
requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
constexpr ranges::borrowed_iterator_t<R>
operator()(R&& r, Comp comp = {}, Proj proj = {}) const
{
return (*this)(ranges::begin(r), ranges::end(r), std::move(comp), std::move(proj));
} };

inline constexpr push_heap_fn push_heap {};

Example¶

// Run this code

#include <algorithm>
#include <cmath>
#include <iostream>
#include <vector>

void out(const auto& what, int n = 1)
{
while (n-- > 0)
std::cout << what;
}

void print(auto rem, auto const& v)
{
out(rem);
for (auto e : v)
out(e), out(' ');
out('\n');
}

void draw_heap(auto const& v)
{
auto bails = [](int n, int w)
{
auto b = [](int w) { out("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
if (!(n /= 2))
return;
for (out(' ', w); n-- > 0;)
b(w), out(' ', w + w + 1);
out('\n');
};
auto data = [](int n, int w, auto& first, auto last)
{
for (out(' ', w); n-- > 0 && first != last; ++first)
out(*first), out(' ', w + w + 1);
out('\n');
};
auto tier = [&](int t, int m, auto& first, auto last)
{
const int n{1 << t};
const int w{(1 << (m - t - 1)) - 1};
bails(n, w), data(n, w, first, last);
};
const int m{static_cast<int>(std::ceil(std::log2(1 + v.size())))};
auto first{v.cbegin()};
for (int i{}; i != m; ++i)
tier(i, m, first, v.cend());
}

int main()
{
std::vector<int> v{1, 6, 1, 8, 0, 3,};
print("source vector v: ", v);

std::ranges::make_heap(v);
print("after make_heap: ", v);
draw_heap(v);

v.push_back(9);

print("before push_heap: ", v);
draw_heap(v);

std::ranges::push_heap(v);
print("after push_heap: ", v);
draw_heap(v);
}

Output:¶

source vector v: 1 6 1 8 0 3
after make_heap: 8 6 3 1 0 1
8
┌─┴─┐
6 3
┌┴┐ ┌┴┐
1 0 1
before push_heap: 8 6 3 1 0 1 9
8
┌─┴─┐
6 3
┌┴┐ ┌┴┐
1 0 1 9
after push_heap: 9 6 8 1 0 1 3
9
┌─┴─┐
6 8
┌┴┐ ┌┴┐
1 0 1 3

See also¶

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