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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../algorithm/includes.html below:

std::includes - cppreference.com

Returns true if the sorted range [first2, last2) is a subsequence of the sorted range [first1, last1) (a subsequence need not be contiguous).

If

or

is not

with respect to

, the behavior is undefined.

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 all following conditions are satisfied:

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 an object of type InputIt can be dereferenced and then implicitly converted to both of them. ​

true if [first2, last2) is a subsequence of [first1, last1); otherwise false.

An empty sequence is a subsequence of any sequence, so true is returned if [first2, last2) is empty.

Given \(\scriptsize N_1\)N1 as std::distance(first1, last1) and \(\scriptsize N_2\)N2 as std::distance(first2, last2):

At most

comparisons using

.

3,4) At most \(\scriptsize 2 \cdot (N_1+N_2)-1\)2⋅(N1+N2)-1 applications of the comparison function comp.

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.

template<class InputIt1, class InputIt2>
bool includes(InputIt1 first1, InputIt1 last1,
              InputIt2 first2, InputIt2 last2)
{
    for (; first2 != last2; ++first1)
    {
        if (first1 == last1 || *first2 < *first1)
            return false;
        if (!(*first1 < *first2))
            ++first2;
    }
    return true;
}

template<class InputIt1, class InputIt2, class Compare>
bool includes(InputIt1 first1, InputIt1 last1,
              InputIt2 first2, InputIt2 last2, Compare comp)
{
    for (; first2 != last2; ++first1)
    {
        if (first1 == last1 || comp(*first2, *first1))
            return false;
        if (!comp(*first1, *first2))
            ++first2;
    }
    return true;
}

#include <algorithm>
#include <cctype>
#include <iostream>
 
template<class Os, class Co>
Os& operator<<(Os& os, const Co& v)
{
    for (const auto& i : v)
        os << i << ' ';
    return os << '\t';
}
 
int main()
{
    const auto
        v1 = {'a', 'b', 'c', 'f', 'h', 'x'},
        v2 = {'a', 'b', 'c'},
        v3 = {'a', 'c'},
        v4 = {'a', 'a', 'b'},
        v5 = {'g'},
        v6 = {'a', 'c', 'g'},
        v7 = {'A', 'B', 'C'};
 
    auto no_case = [](char a, char b) { return std::tolower(a) < std::tolower(b); };
 
    std::cout
    << v1 << "\nincludes:\n" << std::boolalpha
    << v2 << ": " << std::includes(v1.begin(), v1.end(), v2.begin(), v2.end()) << '\n'
    << v3 << ": " << std::includes(v1.begin(), v1.end(), v3.begin(), v3.end()) << '\n'
    << v4 << ": " << std::includes(v1.begin(), v1.end(), v4.begin(), v4.end()) << '\n'
    << v5 << ": " << std::includes(v1.begin(), v1.end(), v5.begin(), v5.end()) << '\n'
    << v6 << ": " << std::includes(v1.begin(), v1.end(), v6.begin(), v6.end()) << '\n'
    << v7 << ": " << std::includes(v1.begin(), v1.end(), v7.begin(), v7.end(), no_case)
          << " (case-insensitive)\n";
}

Output:

a b c f h x
includes:
a b c   : true
a c     : true
a a b   : false
g       : false
a c g   : false
A B C   : true (case-insensitive)

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