std::set_sy...c_difference(3)

💖 NAME 💖

std::set_symmetric_difference — std::set_symmetric_difference (yes, the NAME line said it twice, and honestly? iconic 😭👑).

Okay bestie, this is the std::set_sy...c_difference(3) page from the C++ Standard Libary manual — and yes, “Libary” is literally what the header says, we keep the lore 💀. It’s the standard-library algorithm that takes two sorted ranges and gives you the “in one but not both” girlies. Let’s get into it ✨

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✨ Synopsis ✨

Defined in header <algorithm>.

Overload (1) — constexpr since C++20:

template< class InputIt1, class InputIt2, class OutputIt >
OutputIt set_symmetric_difference
    ( InputIt1 first1, InputIt1 last1,
      InputIt2 first2, InputIt2 last2,
      OutputIt d_first );

Overload (2) — since C++17:

template< class ExecutionPolicy,
          class ForwardIt1, class ForwardIt2, class ForwardIt3 >
ForwardIt3 set_symmetric_difference
    ( ExecutionPolicy&& policy,
      ForwardIt1 first1, ForwardIt1 last1,
      ForwardIt2 first2, ForwardIt2 last2,
      ForwardIt3 d_first );

Overload (3) — constexpr since C++20:

template< class InputIt1, class InputIt2,
          class OutputIt, class Compare >
OutputIt set_symmetric_difference
    ( InputIt1 first1, InputIt1 last1,
      InputIt2 first2, InputIt2 last2,
      OutputIt d_first, Compare comp );

Overload (4) — since C++17:

template< class ExecutionPolicy,
          class ForwardIt1, class ForwardIt2,
          class ForwardIt3, class Compare >
ForwardIt3 set_symmetric_difference
    ( ExecutionPolicy&& policy,
      ForwardIt1 first1, ForwardIt1 last1,
      ForwardIt2 first2, ForwardIt2 last2,
      ForwardIt3 d_first, Compare comp );

So what does it actually do? It computes the symmetric difference of two sorted ranges: the elements that are found in either of the ranges, but not in both of them, get copied to the range beginning at d_first. The output range is also sorted. Slay, sorted, no notes 💅✨

If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, then std::abs(m - n) of those elements will be copied to the output range, preserving order:

• if m > n, the final m - n of these elements from [first1, last1).
• if m < n, the final n - m of these elements from [first2, last2).

Warning bestie: 1) If [first1, last1) or [first2, last2) is not sorted with respect to operator< (until C++20) or std::less{} (since C++20), the behavior is undefined. Not “undefined-ish”, not “we’ll figure it out” — undefined, periodt 💀

3) If [first1, last1) or [first2, last2) is not sorted with respect to comp, the behavior is undefined.

2,4) Same as (1,3), but executed according to policy. These overloads participate in overload resolution only if:

• std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true. (until C++20)
• std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. (since C++20)

Also important: if the output range overlaps with [first1, last1) or [first2, last2), the behavior is undefined. Keep your ranges out of each other’s business, bestie 🙈

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🫶 Parameters 🫶

• first1, last1 — the first sorted range of elements.
• first2, last2 — the second sorted range of elements.
• d_first — the beginning of the output range.
• policy — the execution policy to use. See execution policy for details.
• comp — comparison function object (i.e. an object that satisfies the requirements of Compare) which returns true if the first argument is less than (i.e. is ordered before) the second.

The signature of the comparison function should be equivalent to the following:

bool cmp(const Type1& a, const Type2& b);

While the signature does not need to have const&, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) Type1 and Type2 regardless of value category (thus, Type1& is not allowed, nor is Type1 unless for Type1 a move is equivalent to a copy (since C++11)). The types Type1 and Type2 must be such that objects of types InputIt1 and InputIt2 can be dereferenced and then implicitly converted to both Type1 and Type2.

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🧚 Type requirements 🧚

• InputIt1, InputIt2 must meet the requirements of LegacyInputIterator.
• OutputIt must meet the requirements of LegacyOutputIterator.
• ForwardIt1, ForwardIt2, ForwardIt3 must meet the requirements of LegacyForwardIterator.
• Compare must meet the requirements of Compare.

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🎀 Return value 🎀

Iterator past the end of the constructed range. That’s the whole vibe: point to where the new range stops, bestie 🫶

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⭐ Complexity ⭐

Given N_1 as std::distance(first1, last1) and N_2 as std::distance(first2, last2):

• 1,2) At most 2 \cdot (N_1+N_2)-1 — aka 2⋅(N_1+N_2)-1 — comparisons using operator< (until C++20) or std::less{} (since C++20).
• 3,4) At most 2 \cdot (N_1+N_2)-1 — aka 2⋅(N_1+N_2)-1 — applications of the comparison function comp.

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💀 Exceptions 💀

The overloads with a template parameter named ExecutionPolicy report errors as follows:

• If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the standard policies, std::terminate is called. For any other ExecutionPolicy, the behavior is implementation-defined. 😭
• If the algorithm fails to allocate memory, std::bad_alloc is thrown.

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👑 Possible implementation 👑

Here’s the possible implementation of set_symmetric_difference (1):

template<class InputIt1, class InputIt2, class OutputIt>
OutputIt set_symmetric_difference(InputIt1 first1, InputIt1 last1,
                                  InputIt2 first2, InputIt2 last2,
                                  OutputIt d_first)
{
    while (first1 != last1)
    {
        if (first2 == last2)
            return std::copy(first1, last1, d_first);

        if (*first1 < *first2)
            *d_first++ = *first1++;
        else
        {
            if (*first2 < *first1)
                *d_first++ = *first2;
            else
                ++first1;
            ++first2;
        }
    }
    return std::copy(first2, last2, d_first);
}

And here’s the possible implementation of set_symmetric_difference (3):

template<class InputIt1, class InputIt2, class OutputIt, class Compare>
OutputIt set_symmetric_difference(InputIt1 first1, InputIt1 last1,
                                  InputIt2 first2, InputIt2 last2,
                                  OutputIt d_first, Compare comp)
{
    while (first1 != last1)
    {
        if (first2 == last2)
            return std::copy(first1, last1, d_first);

        if (comp(*first1, *first2))
            *d_first++ = *first1++;
        else
        {
            if (comp(*first2, *first1))
                *d_first++ = *first2;
            else
                ++first1;
            ++first2;
        }
    }
    return std::copy(first2, last2, d_first);
}

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🌈 Example 🌈

// Run this code

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

int main()
{
    std::vector<int> v1{1, 2, 3, 4, 5, 6, 7, 8};
    std::vector<int> v2{5, 7, 9, 10};
    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());

    std::vector<int> v_symDifference;

    std::set_symmetric_difference(v1.begin(), v1.end(), v2.begin(),
                                  v2.end(),
                                  std::back_inserter(v_symDifference));

    for (int n : v_symDifference)
        std::cout << n << ' ';
    std::cout << '\n';
}

Output:

1 2 3 4 6 8 9 10

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🦋 Defect reports 🦋

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

• DR: LWG 291
• Applied to: C++98
• Behavior as published: it was unspecified how to handle equivalent elements in the input ranges
• Correct behavior: specified

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🔥 See also 🔥

• includes — returns true if one sequence is a subsequence of another (function template).
• set_difference — computes the difference between two sets (function template).
• set_union — computes the union of two sets (function template).
• set_intersection — computes the intersection of two sets (function template).
• ranges::set_symmetric_difference (C++20) — computes the symmetric difference between two sets (niebloid).

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Cute sign-off bestie: shoutout to http://cppreference.com, dated 2024.06.10, for this std::set_symmetric_difference(3) page — footer truncates it as std::set_sy...c_difference(3), and honestly? love that for us 😭💖✨