std::lexicographical_compare() algorithm

since C++20

// (1)
template< class InputIt1, class InputIt2 >
constexpr bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2 );

// (2)
template< class InputIt1, class InputIt2, class Compare >
constexpr bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2, Compare comp );

// (3)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 >
bool lexicographical_compare( ExecutionPolicy&& policy,
                              ForwardIt1 first1, ForwardIt1 last1,
                              ForwardIt2 first2, ForwardIt2 last2 );

// (4)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class Compare >
bool lexicographical_compare( ExecutionPolicy&& policy,
                              ForwardIt1 first1, ForwardIt1 last1,
                              ForwardIt2 first2, ForwardIt2 last2,
                              Compare comp );

since C++17

// (1)
template< class InputIt1, class InputIt2 >
bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2 );

// (2)
template< class InputIt1, class InputIt2, class Compare >
bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2, Compare comp );

// (3)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 >
bool lexicographical_compare( ExecutionPolicy&& policy,
                              ForwardIt1 first1, ForwardIt1 last1,
                              ForwardIt2 first2, ForwardIt2 last2 );

// (4)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class Compare >
bool lexicographical_compare( ExecutionPolicy&& policy,
                              ForwardIt1 first1, ForwardIt1 last1,
                              ForwardIt2 first2, ForwardIt2 last2,
                              Compare comp );

until C++17

// (1)
template< class InputIt1, class InputIt2 >
bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2 );

// (2)
template< class InputIt1, class InputIt2, class Compare >
bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2, Compare comp );

Checks if the first range [first1; last1) is lexicographically less than the second range [first2; last2).

• (1) Elements are compared using operator<.

• (2) Elements are compared using the given binary comparison function comp.

• (2 - 4) Same as (1), but executed according to policy.

  Overload Resolution

  These overloads participate in overload resolution only if std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>  (until C++20) std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>  (since C++20) is true.

Lexicographical comparison is an operation with the following properties:

• Two ranges are compared element by element.
• The first mismatching element defines which range is lexicographically less or greater than the other.
• If one range is a prefix of another, the shorter range is lexicographically less than the other.
• If two ranges have equivalent elements and are of the same length, then the ranges are lexicographically equal.
• An empty range is lexicographically less than any non-empty range.
• Two empty ranges are lexicographically equal.

Parameters

first1 last1	The first range of elements compare.
r1	The first range of elements compare.
first2 last2	The second range of elements compare.
r2	The second range of elements compare.
proj1	Projection to apply to the elements of the first range.
proj2	Projection to apply to the elements of the second range.
comp	Comparison function object (i.e. an object that satisfies the requirements of Compare), which returns true if the first argument is less than second. The signature of the comparison function should be equivalent to the following: bool cmp(const Type1 &a, const Type2 &b); The signature does not need to have const&, but must not modify arguments. Must accept all values of type (possibly const) Type and Type2, regardless of value category (so 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 InputIt1 and InputIt2 can be dereferenced and then implicitly converted to them.

Type requirements

InputIt1 InputIt2	LegacyInputIterator
ForwardIt1 ForwardIt2	LegacyForwardIterator
Compare	Compare

Return value

true if the first range is lexicographically less than the second..

Complexity

Given N1 as ranges::distance(first1, last1) and N2 as ranges::distance(first2, last2)

At most 2 * min(N1, N2) applications of the comparison and corresponding projections.

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.

Possible implementation

lexicographical_compare(1) and lexicographical_compare(2)

struct lexicographical_compare_fn
{
    template<std::input_iterator I1, std::sentinel_for<I1> S1,
             std::input_iterator I2, std::sentinel_for<I2> S2,
             class Proj1 = std::identity, class Proj2 = std::identity,
             std::indirect_strict_weak_order<
                 std::projected<I1, Proj1>,
                 std::projected<I2, Proj2>> Comp = ranges::less>
    constexpr bool operator()(I1 first1, S1 last1, I2 first2, S2 last2,
                              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}) const
    {
        for (; (first1 != last1) && (first2 != last2); ++first1, (void) ++first2)
        {
            if (std::invoke(comp, std::invoke(proj1, *first1), std::invoke(proj2, *first2)))
                return true;

            if (std::invoke(comp, std::invoke(proj2, *first2), std::invoke(proj1, *first1)))
                return false;
        }
        return (first1 == last1) && (first2 != last2);
    }

    template<ranges::input_range R1, ranges::input_range R2,
             class Proj1 = std::identity, class Proj2 = std::identity,
             std::indirect_strict_weak_order<
                 std::projected<ranges::iterator_t<R1>, Proj1>,
                 std::projected<ranges::iterator_t<R2>, Proj2>> Comp = ranges::less>
    constexpr bool operator()(R1&& r1, R2&& r2, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {}) const
    {
        return (*this)(ranges::begin(r1), ranges::end(r1),
                       ranges::begin(r2), ranges::end(r2),
                       std::ref(comp), std::ref(proj1), std::ref(proj2));
    }
};

inline constexpr lexicographical_compare_fn lexicographical_compare;

Examples

Main.cpp

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

int main()
{
    std::vector<char> v1 {'a', 'b', 'c', 'd'};
    std::vector<char> v2 {'a', 'b', 'c', 'd'};

    namespace ranges = std::ranges;
    auto os = std::ostream_iterator<char>(std::cout, " ");

    std::mt19937 g {std::random_device {}()};
    while (not ranges::lexicographical_compare(v1, v2))
    {
        ranges::copy(v1, os);
        std::cout << ">= ";
        ranges::copy(v2, os);
        std::cout << '\n';

        ranges::shuffle(v1, g);
        ranges::shuffle(v2, g);
    }

    ranges::copy(v1, os);
    std::cout << "<  ";
    ranges::copy(v2, os);
    std::cout << '\n';
}

Output

a b c d >= a b c d
d a b c >= c b d a
b d a c >= a d c b
a c d b <  c d a b