std::lexicographical_compare(3)

NAME
std::lexicographical_compare - std::lexicographical_compare

Synopsis
   Defined in header <algorithm>
   template< class InputIt1, class InputIt2 >
   bool lexicographical_compare( InputIt1 first1, (until C++20)
   InputIt1 last1,
   InputIt2 first2, InputIt2 last2 );
   template< class InputIt1, class InputIt2 >
   constexpr bool lexicographical_compare( InputIt1 (since C++20)
   first1, InputIt1 last1,
   InputIt2 first2, InputIt2 last2 );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2 >
   bool lexicographical_compare( ExecutionPolicy&& (2) (since C++17)
   policy, ForwardIt1 first1, ForwardIt1 last1,
   ForwardIt2 first2, ForwardIt2 last2 );
   template< class InputIt1, class InputIt2, class
   Compare >
                        (1)
   bool lexicographical_compare( InputIt1 first1, (until C++20)
   InputIt1 last1,
   InputIt2 first2, InputIt2 last2,
   Compare comp );
   template< class InputIt1, class InputIt2, class
   Compare >
   constexpr bool lexicographical_compare( InputIt1 (3) (since C++20)
   first1, InputIt1 last1,
   InputIt2 first2, InputIt2 last2,
   Compare comp );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2, class Compare >
   bool lexicographical_compare( ExecutionPolicy&& (4) (since C++17)
   policy, ForwardIt1 first1, ForwardIt1 last1,
   ForwardIt2 first2, ForwardIt2 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<.
   3) Elements are compared using the given binary comparison function comp.
   2,4) Same as (1,3), but executed according to policy. These overloads do not
   participate in overload resolution unless
   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 to examine
   first2, last2 - the second range of elements to examine
   policy - the execution policy to use. See execution policy for details.
                   comparison function object (i.e. an object that satisfies the
                   requirements of Compare) which returns true if the first argument
                   is less than the second.
                   The signature of the comparison function should be equivalent to the
                   following:
                   bool cmp(const Type1 &a, const Type2 &b);
   comp -
                   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.

Type requirements
   -
   InputIt1, InputIt2 must meet the requirements of LegacyInputIterator.
   -
   ForwardIt1, ForwardIt2 must meet the requirements of LegacyForwardIterator.

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

Complexity
   At most 2·min(N1, N2) applications of the comparison operation, where N1 =
   std::distance(first1, last1) and N2 = std::distance(first2, last2).

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

First version
   template<class InputIt1, class InputIt2>
   bool lexicographical_compare(InputIt1 first1, InputIt1 last1,
                        InputIt2 first2, InputIt2 last2)
   {
       for ( ; (first1 != last1) && (first2 != last2); ++first1, (void) ++first2 ) {
           if (*first1 < *first2) return true;
           if (*first2 < *first1) return false;
       }
       return (first1 == last1) && (first2 != last2);
   }

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

Example
// Run this code
 #include <algorithm>
 #include <iostream>
 #include <vector>
 #include <random>
 int main()
 {
     std::vector<char> v1 {'a', 'b', 'c', 'd'};
     std::vector<char> v2 {'a', 'b', 'c', 'd'};
     std::mt19937 g{std::random_device{}()};
     while (!std::lexicographical_compare(v1.begin(), v1.end(),
                        v2.begin(), v2.end())) {
         for (auto c : v1) std::cout << c << ' ';
         std::cout << ">= ";
         for (auto c : v2) std::cout << c << ' ';
         std::cout << '\n';
         std::shuffle(v1.begin(), v1.end(), g);
         std::shuffle(v2.begin(), v2.end(), g);
     }
     for (auto c : v1) std::cout << c << ' ';
     std::cout << "< ";
     for (auto c : v2) std::cout << c << ' ';
     std::cout << '\n';
 }

Possible 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

See also
   equal determines if two sets of elements are the same
                        (function template)
   ranges::lexicographical_compare returns true if one range is lexicographically less
   (C++20) than another
                        (niebloid)