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std::ranges::is_heap_until

From cppreference.com
< cpp‎ | algorithm‎ | ranges
 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms: std::ranges::copy, std::ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
(C++11)(C++11)(C++11)
(C++17)
Modifying sequence operations
Operations on uninitialized storage
Partitioning operations
Sorting operations
(C++11)
Binary search operations
Set operations (on sorted ranges)
Heap operations
(C++11)
Minimum/maximum operations
(C++11)
(C++17)

Permutations
Numeric operations
C library
 
Constrained algorithms
Non-modifying sequence operations
Modifying sequence operations
Operations on uninitialized storage
Partitioning operations
Sorting operations
Binary search operations
Set operations (on sorted ranges)
Heap operations
ranges::is_heap_until
Minimum/maximum operations
Permutations
 
Defined in header <algorithm>
Call signature
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

ranges::is_heap_until( I first, S last, Comp comp = {}, Proj proj = {} );
(1) (since C++20)
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>

ranges::is_heap_until( R&& r, Comp comp = {}, Proj proj = {} );
(2) (since C++20)

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 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:

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

Contents

[edit] 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 - projection to apply to the elements.

[edit] 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.

[edit] Complexity

Linear in the distance between first and last.

[edit] Notes

The 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, for all 0 < i < N, p = f[floor(
    i-1
    2
    )], and q = f[i], 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 𝓞(log N) time.
  • the first element can be removed using ranges::pop_heap(), in 𝓞(log N) time.

[edit] Possible implementation

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{};

[edit] Example

The example renders a given vector as a (balanced) binary tree.

#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); }
}

Output:

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

[edit] See also

checks if the given range is a max heap
(niebloid) [edit]
creates a max heap out of a range of elements
(niebloid) [edit]
adds an element to a max heap
(niebloid) [edit]
removes the largest element from a max heap
(niebloid) [edit]
turns a max heap into a range of elements sorted in ascending order
(niebloid) [edit]
finds the largest subrange that is a max heap
(function template) [edit]