std::ranges::merge() algorithm

od C++20

Simplified

// (1)
constexpr merge_result<I1, I2, O>
    merge( I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
           Proj1 proj1 = {}, Proj2 proj2 = {} );

// (2)
constexpr merge_result<ranges::borrowed_iterator_t<R1>,
                       ranges::borrowed_iterator_t<R2>, O>
    merge( R1&& r1, R2&& r2, O result, Comp comp = {},
           Proj1 proj1 = {}, Proj2 proj2 = {} );

The type of arguments are generic and have the following constraints:

• I1, I2 - std::forward_iterator
• S1, S2 - std::sentinel_for<I1>, std::sentinel_for<I2>
• R1, R2 - std::ranges::forward_range
• O - std::weakly_incrementable
• Comp - (none)
• Proj1, Proj2 - (none)

The Proj and Comp template arguments have the following default types: std::identity, ranges::less for all overloads.

Additionaly, each overload has the following constraints:

• (1) - mergeable<I1, I2, O, Comp, Proj1, Proj2>
• (2) - mergeable<ranges::iterator_t<R1>, ranges::iterator_t<R2>, O, Comp, Proj1, Proj2>

(The std:: namespace was ommited here for readability)

Detailed

// (1)
template<
  std::input_iterator I1,
  std::sentinel_for<I1> S1,
  std::input_iterator I2
  std::sentinel_for<I2> S2
  std::weakly_incrementable O
  class Comp = ranges::less
  class Proj1 = std::identity
 class Proj2 = std::identity
>
  requires std::mergeable<I1, I2, O, Comp, Proj1, Proj2>
constexpr merge_result<I1, I2, O>
    merge( I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
           Proj1 proj1 = {}, Proj2 proj2 = {} );

// (2)
 template<
  ranges::input_range R1
  ranges::input_range R2
  std::weakly_incrementable O
  class Comp = ranges::less
  class Proj1 = std::identity
  class Proj2 = std::identity
>
  requires std::mergeable<ranges::iterator_t<R1>, ranges::iterator_t<R2>,
                          O, Comp, Proj1, Proj2>
constexpr merge_result<ranges::borrowed_iterator_t<R1>,
                       ranges::borrowed_iterator_t<R2>, O>
    merge( R1&& r1, R2&& r2, O result, Comp comp = {},
           Proj1 proj1 = {}, Proj2 proj2 = {} );

With the helper types defined as follows:

template< class I1, class I2, class O >
using merge_result = ranges::in_in_out_result<I1, I2, O>;

Merges two sorted ranges [first1; last1) and [first2; last2) into one sorted range beginning at result.

A sequence is said to be sorted with respect to the comparator comp if for any iterator it pointing to the sequence and any non-negative integer n such that it + n is a valid iterator pointing to an element of the sequence, std::invoke(comp, std::invoke(proj2, *(it + n)), std::invoke(proj1, *it))) evaluates to false.

• (1) Elements are compared using the given binary comparison function comp.
• (2) Same as (1), but uses r1 as the first range and r2 as the second range, as if using ranges::begin(r1) as first1, ranges::end(r1) as last1, ranges::begin(r2) as first2, and ranges::end(r2) as last2.

This merge function is stable, which means that for equivalent elements in the original two ranges, the elements from the first range precede the elements from the second range, preserving their original order.

Undefined Behaviour

The behavior is undefined

if the destination range overlaps either of the input ranges (the input ranges may overlap each other).

The function-like entities described on this page are niebloids.

Parameters

first1 last1	The first sorted range of elements to merge.
r r1	The first sorted range of elements to merge.
first2 last2	The second sorted range of elements to merge.
r2	The second sorted range of elements to merge.
result	The beginning of the destination range.
proj1	Projection to apply to the elements in the first range.
proj2	Projection to apply to the elements in the second range.

Return value

A value of type ranges::merge_result initialized as follows:

{
  last1,
  last2,
  result_last
}

Where result_last is the end of the constructed range.

Complexity

Given N as ranges::distance(first1, last1) + ranges::distance(first2, last12)

At most N − 1 comparisons and applications of each projection.

Exceptions

(none)

Possible implementation

merge(1) and merge(2)

struct merge_fn
{
  template<std::input_iterator I1, std::sentinel_for<I1> S1,
    std::input_iterator I2, std::sentinel_for<I2> S2,
    std::weakly_incrementable O, class Comp = ranges::less,
    class Proj1 = std::identity, class Proj2 = std::identity>
      requires std::mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr ranges::merge_result<I1, I2, O>
      operator()(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
          Proj1 proj1 = {}, Proj2 proj2 = {}) const
      {
        for (; !(first1 == last1 or first2 == last2); ++result)
        {
          if (std::invoke(comp, std::invoke(proj2, *first2), std::invoke(proj1, *first1)))
            *result = *first2, ++first2;
          else
            *result = *first1, ++first1;
        }
        auto ret1 {ranges::copy(std::move(first1), std::move(last1), std::move(result))};
        auto ret2 {ranges::copy(std::move(first2), std::move(last2), std::move(ret1.out))};
        return {std::move(ret1.in), std::move(ret2.in), std::move(ret2.out)};
      }

  template<ranges::input_range R1, ranges::input_range R2, std::weakly_incrementable O,
    class Comp = ranges::less,
    class Proj1 = std::identity, class Proj2 = std::identity>
      requires std::mergeable<ranges::iterator_t<R1>, ranges::iterator_t<R2>,
    O, Comp, Proj1, Proj2>
      constexpr ranges::merge_result<ranges::borrowed_iterator_t<R1>,
    ranges::borrowed_iterator_t<R2>, O>
      operator()(R1&& r1, R2&& r2, O result, Comp comp = {},
          Proj1 proj1 = {}, Proj2 proj2 = {}) const
      {
        return (*this)(ranges::begin(r1), ranges::end(r1),
            ranges::begin(r2), ranges::end(r2),
            std::move(result), std::move(comp),
            std::move(proj1), std::move(proj2));
      }
};

inline constexpr merge_fn merge {};

Notes

This algorithm performs a similar task as ranges::set_union does. Both consume two sorted input ranges and produce a sorted output with elements from both inputs.

The difference between these two algorithms is with handling values from both input ranges which compare equivalent (see notes on LessThanComparable.

If any equivalent values appeared n times in the first range and m times in the second, ranges::merge would output all n + m occurrences whereas ranges::set_union would output ranges::max(n, m) ones only.

So std::merge outputs exactly std::distance(first1, last1) + std::distance(first2, last2) values and std::set_union may produce fewer.

Examples

The following code uses ranges::merge to convert a string in place to uppercase using the std::toupper function and then merges each char to its ordinal value.

Then ranges::merge with a projection is used to merge elements of std::vector<Foo> into chars to fill a std::string.

Main.cpp

#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>

void print(const auto& in1, const auto& in2, auto first, auto last)
{
    std::cout << "{ ";
    for (const auto& e : in1) { std::cout << e << ' '; }
    std::cout << "} +\n{ ";
    for (const auto& e : in2) { std::cout << e << ' '; }
    std::cout << "} =\n{ ";
    while (!(first == last)) { std::cout << *first++ << ' '; }
    std::cout << "}\n\n";
}

int main()
{
    std::vector<int> in1, in2, out;

    in1 = {1, 2, 3, 4, 5};
    in2 = {      3, 4, 5, 6, 7};
    out.resize(in1.size() + in2.size());
    const auto ret = std::ranges::merge(in1, in2, out.begin());
    print(in1, in2, out.begin(), ret.out);

    in1 = {1, 2, 3, 4, 5, 5, 5};
    in2 = {      3, 4, 5, 6, 7};
    out.clear();
    out.reserve(in1.size() + in2.size());
    std::ranges::merge(in1, in2, std::back_inserter(out));
    print(in1, in2, out.cbegin(), out.cend());
}

Output

{ 1 2 3 4 5 } +
{ 3 4 5 6 7 } =
{ 1 2 3 3 4 4 5 5 6 7 }

{ 1 2 3 4 5 5 5 } +
{ 3 4 5 6 7 } =
{ 1 2 3 3 4 4 5 5 5 5 6 7 }