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Difference between revisions of "cpp/algorithm/ranges/is heap"

From cppreference.com
< cpp‎ | algorithm‎ | ranges
(created a page for ranges::is_heap + example)
 
(Wording update.)
 
(10 intermediate revisions by 3 users not shown)
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{{cpp/algorithm/ranges/navbar}}
 
{{cpp/algorithm/ranges/navbar}}
 
{{dcl begin}}
 
{{dcl begin}}
{{dcl header | algorithm}}
+
{{dcl header|algorithm}}
 
{{dcl h|Call signature}}
 
{{dcl h|Call signature}}
{{dcl | num=1 | since=c++20 |1=
+
{{dcl|num=1|since=c++20|1=
 
template< std::random_access_iterator I, std::sentinel_for<I> S,
 
template< std::random_access_iterator I, std::sentinel_for<I> S,
           class Proj = std::identity, std::indirect_strict_weak_order<
+
           class Proj = std::identity,
          std::projected<I, Proj>> Comp = ranges::less >
+
          std::indirect_strict_weak_order
constexpr bool ranges::is_heap( I first, S last, Comp comp = {}, Proj proj = {} );
+
              <std::projected<I, Proj>> Comp = ranges::less >
 +
constexpr bool is_heap( I first, S last, Comp comp = {}, Proj proj = {} );
 
}}
 
}}
{{dcl | num=2 | since=c++20 |1=
+
{{dcl|num=2|since=c++20|1=
 
template< ranges::random_access_range R, class Proj = std::identity,
 
template< ranges::random_access_range R, class Proj = std::identity,
           std::indirect_strict_weak_order<projected<ranges::iterator_t<R>, Proj>>
+
           std::indirect_strict_weak_order
          Comp = ranges::less >
+
              <std::projected
constexpr bool ranges::is_heap( R&& r, Comp comp = {}, Proj proj = {} );
+
                  <ranges::iterator_t<R>, Proj>> Comp = ranges::less >
 +
constexpr bool is_heap( R&& r, Comp comp = {}, Proj proj = {} );
 
}}
 
}}
 
{{dcl end}}
 
{{dcl end}}
  
Checks if the elements in range {{tt|[first, last)}} are a [[enwiki:Binary_heap|''max heap'']].
+
Checks whether the specified range represents a [[cpp/algorithm#Heap operations|heap]] with respect to {{c|comp}} and {{c|proj}}.
  
@1@ Elements are compared using the given binary comparison function {{tt|comp}} and projection object {{tt|proj}}.
+
@1@ The specified range is {{range|first|last}}.
  
@2@ Same as {{v|1}}, but uses {{tt|r}} as the range, as if using {{c|ranges::begin(r)}} as {{tt|first}} and {{c|ranges::end(r)}} as {{tt|last}}.
+
@2@ The specified range is {{c|r}}.
  
 
{{cpp/ranges/niebloid}}
 
{{cpp/ranges/niebloid}}
Line 28: Line 30:
 
===Parameters===
 
===Parameters===
 
{{par begin}}
 
{{par begin}}
{{par | first, last | the range of elements to examine}}
+
{{par|first, last|the iterator and sentinel designating the range of elements to examine}}
{{par | r           | the range of elements to examine}}
+
{{par|r|the range of elements to examine}}
{{par | pred        | predicate to apply to the projected elements}}
+
{{par|comp|comparator to apply to the projected elements}}
{{par | proj       | projection to apply to the elements.}}
+
{{par|proj|projection to apply to the elements}}
 
{{par end}}
 
{{par end}}
  
 
===Return value===
 
===Return value===
{{c|true}} if the range is ''max heap'', {{c|false}} otherwise.
+
@1@ {{c|1=ranges::is_heap_until(first, last, comp, proj) == last}}
 +
@2@ {{c|1=ranges::is_heap_until(r, comp, proj) == ranges::end(r)}}
  
 
===Complexity===
 
===Complexity===
Linear in the distance between {{tt|first}} and {{tt|last}}.
+
{{mathjax-or|\(\scriptsize O(N) \)|O(N)}} applications of {{c|comp}} and {{c|proj}}, where {{mathjax-or|\(\scriptsize N \)|N}} is:
 
+
@1@ {{c|ranges::distance(first, last)}}
===Notes===
+
@2@ {{c|ranges::distance(r)}}
<!-- TODO: create a separate template for these notes -- it will be used in 6 pages. -->
+
The ''max heap'' is a range of elements {{tt|[f, l)}}, arranged with respect to comparator {{tt|comp}} and projection {{tt|proj}}, that has the following properties:
+
:* With {{c|1=N = l - f}}, for all {{tt|0 < i < N}}, p = f[floor({{mfrac||i-1|2}})], and q = f[i], the expression {{c|1=std::invoke(comp, std::invoke(proj, p), std::invoke(proj, q))}} evaluates to {{tt|false}}.
+
:* a new element can be added using {{c|ranges::push_heap()}}, in {{math|𝓞(log N)}} time.
+
:* the first element can be removed using {{c|ranges::pop_heap()}}, in {{math|𝓞(log N)}} time.
+
  
 
===Possible implementation===
 
===Possible implementation===
{{eq fun | 1=
+
{{eq fun|1=
struct is_heap_fn {
+
struct is_heap_fn
     template< std::random_access_iterator I, std::sentinel_for<I> S,
+
{
              class Proj = std::identity, std::indirect_strict_weak_order<
+
     template<std::random_access_iterator I, std::sentinel_for<I> S,
              std::projected<I, Proj>> Comp = ranges::less >
+
            class Proj = std::identity,
     constexpr bool operator()( I first, S last, Comp comp = {}, Proj proj = {} ) const {
+
            std::indirect_strict_weak_order
         return (last == ranges::is_heap_until(first, last, std::move(comp), std::move(proj)));
+
                <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,
+
     template<ranges::random_access_range R, class Proj = std::identity,
              std::indirect_strict_weak_order<projected<ranges::iterator_t<R>, Proj>>
+
            std::indirect_strict_weak_order
              Comp = ranges::less >
+
                <std::projected<ranges::iterator_t<R>, Proj>> Comp = ranges::less>
     constexpr bool operator()( R&& r, Comp comp = {}, Proj proj = {} ) const {
+
     constexpr bool operator()(R&& r, Comp comp = {}, Proj proj = {}) const
         return (*this)(ranges::begin(r), ranges::end(r), std::move(comp), std::move(proj));
+
    {
 +
         return (*this)(ranges::begin(r), ranges::end(r),
 +
                      std::move(comp), std::move(proj));
 
     }
 
     }
 
};
 
};
Line 69: Line 73:
  
 
===Example===
 
===Example===
{{example|code=
+
{{example
 +
|code=
 
#include <algorithm>
 
#include <algorithm>
 
#include <bit>
 
#include <bit>
Line 76: Line 81:
 
#include <vector>
 
#include <vector>
  
void out(const auto& what, int n = 1) { while (n-- > 0) std::cout << what; }
+
void out(const auto& what, int n = 1)
 +
{
 +
    while (n-- > 0)
 +
        std::cout << what;
 +
}
  
void draw_heap(auto const& v);
+
void draw_heap(const auto& v)
 +
{
 +
    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 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()
 
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 };
+
     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");
 
     out("initially, v:\n");
     for (auto i : v) std::cout << i << ' ';
+
     for (auto i : v)
 +
        std::cout << i << ' ';
 
     out('\n');
 
     out('\n');
 
+
   
     if (!std::ranges::is_heap(v)) {
+
     if (!std::ranges::is_heap(v))
 +
    {
 
         out("making heap...\n");
 
         out("making heap...\n");
 
         std::ranges::make_heap(v);
 
         std::ranges::make_heap(v);
 
     }
 
     }
 
+
   
 
     out("after make_heap, v:\n");
 
     out("after make_heap, v:\n");
 
     for (auto t{1U}; auto i : v)
 
     for (auto t{1U}; auto i : v)
 
         std::cout << i << (std::has_single_bit(++t) ? " │ " : " ");
 
         std::cout << i << (std::has_single_bit(++t) ? " │ " : " ");
 +
   
 
     out("\n" "corresponding binary tree is:\n");
 
     out("\n" "corresponding binary tree is:\n");
 
    for (auto& e : v) { e += '0'; }
 
 
     draw_heap(v);
 
     draw_heap(v);
 
}
 
}
 
+
|output=<nowiki/>
void draw_heap(auto const& v)
+
{
+
    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(char(*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=<nowiki/>
+
 
initially, v:
 
initially, v:
 
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8
 
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8
Line 145: Line 162:
 
===See also===
 
===See also===
 
{{dsc begin}}
 
{{dsc begin}}
{{dsc inc | cpp/algorithm/ranges/dsc is_heap_until}}
+
{{dsc inc|cpp/algorithm/ranges/dsc is_heap_until}}
{{dsc inc | cpp/algorithm/ranges/dsc make_heap}}
+
{{dsc inc|cpp/algorithm/ranges/dsc make_heap}}
{{dsc inc | cpp/algorithm/ranges/dsc push_heap}}
+
{{dsc inc|cpp/algorithm/ranges/dsc push_heap}}
{{dsc inc | cpp/algorithm/ranges/dsc pop_heap}}
+
{{dsc inc|cpp/algorithm/ranges/dsc pop_heap}}
{{dsc inc | cpp/algorithm/ranges/dsc sort_heap}}
+
{{dsc inc|cpp/algorithm/ranges/dsc sort_heap}}
{{dsc inc | cpp/algorithm/dsc is_heap}}
+
{{dsc inc|cpp/algorithm/dsc is_heap}}
 
{{dsc end}}
 
{{dsc end}}
  
 
{{langlinks|de|es|fr|it|ja|pt|ru|zh}}
 
{{langlinks|de|es|fr|it|ja|pt|ru|zh}}

Latest revision as of 18:37, 15 October 2024

 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
Batch operations
(C++17)
Search operations
(C++11)                (C++11)(C++11)

Modifying sequence operations
Copy operations
(C++11)
(C++11)
Swap operations
Transformation operations
Generation operations
Removing operations
Order-changing operations
(until C++17)(C++11)
(C++20)(C++20)
Sampling operations
(C++17)

Sorting and related operations
Partitioning operations
Sorting operations
Binary search operations
(on partitioned ranges)
Set operations (on sorted ranges)
Merge operations (on sorted ranges)
Heap operations
Minimum/maximum operations
(C++11)
(C++17)
Lexicographical comparison operations
Permutation operations
C library
Numeric operations
Operations on uninitialized memory
 
Constrained algorithms
All names in this menu belong to namespace std::ranges
Non-modifying sequence operations
Modifying sequence operations
Partitioning operations
Sorting operations
Binary search operations (on sorted ranges)
       
       
Set operations (on sorted ranges)
Heap operations
is_heap
     
         
Minimum/maximum operations
       
       
Permutation operations
Fold operations
Numeric operations
(C++23)            
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 whether the specified range represents a heap with respect to comp and proj.

1) The specified range is [firstlast).
2) The specified range is r.

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 iterator and sentinel designating the range of elements to examine
r - the range of elements to examine
comp - comparator to apply to the projected elements
proj - projection to apply to the elements

[edit] Return value

1) ranges::is_heap_until(first, last, comp, proj) == last
2) ranges::is_heap_until(r, comp, proj) == ranges::end(r)

[edit] Complexity

O(N) applications of comp and proj, where N is:

1) ranges::distance(first, last)

[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(const auto& v)
{
    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 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{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) ? " │ " : " ");
 
    out("\n" "corresponding binary tree is:\n");
    draw_heap(v);
}

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 │ 8 9 │ 6 5 8 9 │ 3 5 3 5 3 4 7 2 │ 1 2 3 1
corresponding binary tree is:
               9
       ┌───────┴───────┐
       8               9
   ┌───┴───┐       ┌───┴───┐
   6       5       8       9
 ┌─┴─┐   ┌─┴─┐   ┌─┴─┐   ┌─┴─┐
 3   5   3   5   3   4   7   2
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
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]