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std::ranges::is_heap

From cppreference.com
< cpp‎ | algorithm‎ | ranges
 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. 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
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
Operations on uninitialized storage
(C++17)
(C++17)
(C++17)
C library
 
Constrained algorithms
Non-modifying sequence operations
Modifying sequence operations
Partitioning operations
Sorting operations
Binary search operations
Set operations (on sorted ranges)
Heap operations
ranges::is_heap
Minimum/maximum operations
Permutations
Operations on uninitialized storage
Return types
 
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 bool is_heap( 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 bool is_heap( R&& r, Comp comp = {}, Proj proj = {} );
(2) (since C++20)

Checks if the elements in range [first, last) are 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

true if the range is max heap, false otherwise.

[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[(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 π“ž(log N) time.
  • the first element can be removed using ranges::pop_heap(), in π“ž(log N) time.

[edit] Possible implementation

struct is_heap_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 bool operator()( I first, S last, Comp comp = {}, Proj proj = {} ) const {
        return (last == ranges::is_heap_until(first, last, std::move(comp), std::move(proj)));
    }
 
    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 bool 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_fn is_heap{};

[edit] Example

#include <algorithm>
#include <bit>
#include <cmath>
#include <iostream>
#include <vector>
 
void out(const auto& what, int n = 1) { while (n-- > 0) std::cout << what; }
 
void draw_heap(auto const& v);
 
int main()
{
    std::vector<int> v { 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8 };
 
    out("initially, v:\n");
    for (auto i : v) std::cout << i << ' ';
    out('\n');
 
    if (!std::ranges::is_heap(v)) {
        out("making heap...\n");
        std::ranges::make_heap(v);
    }
 
    out("after make_heap, v:\n");
    for (auto t{1U}; auto i : v) {
        std::cout << i << (std::has_single_bit(++t) ? " β”‚ " : " ");
    }
 
    out("\n" "corresponding binary tree is:\n");
    draw_heap(v);
}
 
void draw_heap(auto const& v)
{
    auto bails = [](int n, int w) {
        auto b = [](int w) { out("β”Œ"), out("─", w), out("β”΄"), 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 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()); }
}

Output:

initially, v:
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8
making heap...
after make_heap, v:
9 β”‚ 8 9 β”‚ 6 5 8 9 β”‚ 3 5 3 5 3 4 7 2 β”‚ 1 2 3 1
corresponding binary tree is:
               9
       β”Œβ”€β”€β”€β”€β”€β”€β”€β”΄β”€β”€β”€β”€β”€β”€β”€β”
       8               9
   β”Œβ”€β”€β”€β”΄β”€β”€β”€β”       β”Œβ”€β”€β”€β”΄β”€β”€β”€β”
   6       5       8       9
 β”Œβ”€β”΄β”€β”   β”Œβ”€β”΄β”€β”   β”Œβ”€β”΄β”€β”   β”Œβ”€β”΄β”€β”
 3   5   3   5   3   4   7   2
β”Œβ”΄β” β”Œβ”΄β” β”Œβ”΄β” β”Œβ”΄β” β”Œβ”΄β” β”Œβ”΄β” β”Œβ”΄β” β”Œβ”΄β”
1 2 3 1

[edit] See also

finds the largest subrange that 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]
(C++11)
checks if the given range is a max heap
(function template) [edit]