std::ranges::is_heap_until() algorithm
- od C++20
- Simplified
- Detailed
// (1)
constexpr I is_heap_until( I first, S last, Comp comp = {}, Proj proj = {} );
// (2)
constexpr ranges::borrowed_iterator_t<R>
is_heap_until( R&& r, Comp comp = {}, Proj proj = {} );
The type of arguments are generic and have the following constraints:
I
-std::random_access_iterator
S
-std::sentinel_for<I>
R
-std::ranges::random_access_range
Comp
:- (1) -
std::indirect_strict_weak_order<std::projected<I, Proj>>
- (2) -
std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>, Proj>>
- (1) -
Proj
- (none)
The Proj
and Comp
template arguments have the following default types: std::identity
, ranges::less
for all overloads.
// (1)
template<
std::random_access_iterator I,
std::sentinel_for<I> S,
class Proj = std::identity,
std::indirect_strict_weak_order<std::projected<I, Proj>> Comp = ranges::less
>
constexpr I is_heap_until( I first, S last, Comp comp = {}, Proj proj = {} );
// (2)
template<
ranges::random_access_range R,
class Proj = std::identity,
std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>, Proj>> Comp = ranges::less
>
constexpr ranges::borrowed_iterator_t<R>
is_heap_until( R&& r, Comp comp = {}, Proj proj = {} );
Examines the range [first
; last
) and finds the largest range beginning at first
which is a max heap.
-
(1) Elements are compared using the given binary comparison function
comp
and projection objectproj
. -
(2) Same as (1), but uses
r
as the source range, as if usingranges::begin(r)
asfirst
andranges::end(r)
aslast
.
The function-like entities described on this page are niebloids.
Parameters
first last | The range of elements to examine. |
r | The range of elements to examine. |
pred | Predicate to apply to the projected elements. |
proj | The projection to apply to the elements. |
Return value
The upper bound of the largest range beginning at first
which is a max heap.
That is, the last iterator it for which range [first
; it
) is a max heap with respect to comp
and proj
.
Complexity
Linear in the distance between first
and last
.
Exceptions
(none)
Possible implementation
is_heap_until(1) and is_heap(2)
struct is_heap_until_fn
{
template<std::random_access_iterator I, std::sentinel_for<I> S,
class Proj = std::identity, std::indirect_strict_weak_order<
std::projected<I, Proj>> Comp = ranges::less>
constexpr I
operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
{
std::iter_difference_t<I> n {ranges::distance(first, last)}, dad {0}, son {1};
for (; son != n; ++son)
{
if (std::invoke(comp, std::invoke(proj, *(first + dad)),
std::invoke(proj, *(first + son))))
return first + son;
else if ((son % 2) == 0)
++dad;
}
return first + n;
}
template<ranges::random_access_range R, class Proj = std::identity,
std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>, Proj>>
Comp = ranges::less>
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 is_heap_until_fn is_heap_until {};
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:
- Given
N
asl - f
,p = f[(i - 1) / 2]
, andq = f[i]
, for all0 < i < N
, the expressionstd::invoke(comp, std::invoke(proj, p), std::invoke(proj, q))
evaluates tofalse
. - A new element can be added using
ranges::push_heap
, in O(log(N)) time. - The first element can be removed using
ranges::pop_heap
, in O(log(N)) time.
Examples
#include <algorithm>
#include <cmath>
#include <iostream>
#include <iterator>
#include <vector>
void out(const auto& what, int n = 1)
{
while (n-- > 0)
std::cout << what;
}
void draw_bin_tree(auto first, auto last);
int main()
{
std::vector<int> v {3, 1, 4, 1, 5, 9};
std::ranges::make_heap(v);
// probably mess up the heap
v.push_back(2);
v.push_back(6);
out("v after make_heap and push_back: \n");
draw_bin_tree(v.begin(), v.end());
out("the max-heap prefix of v: \n");
const auto heap_end = std::ranges::is_heap_until(v);
draw_bin_tree(v.begin(), heap_end);
}
void draw_bin_tree(auto first, auto last)
{
auto bails = [](int n, int w)
{
auto b = [](int w) { out("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
n /= 2;
if (!n)
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 auto size {std::ranges::distance(first, last)};
const int m {static_cast<int>(std::ceil(std::log2(1 + size)))};
for (int i {}; i != m; ++i)
tier(i, m, first, last);
}
v after make_heap and push_back:
9
┌───┴───┐
5 4
┌─┴─┐ ┌─┴─┐
1 1 3 2
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
6
the max-heap prefix of v:
9
┌─┴─┐
5 4
┌┴┐ ┌┴┐
1 1 3 2
Hover to see the original license.