# std::lexicographical_compare

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< cpp‎ | algorithm

Defined in header `<algorithm>` |  |
| (1) |
template< class InputIt1, class InputIt2 > bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2 ); |  | (until C++20)
template< class InputIt1, class InputIt2 > constexpr bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2 ); |  | (since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > bool lexicographical_compare( ExecutionPolicy&& policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2 ); | (2) | (since C++17)
| (3) |
template< class InputIt1, class InputIt2, class Compare > bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2, Compare comp ); |  | (until C++20)
template< class InputIt1, class InputIt2, class Compare > constexpr bool lexicographical_compare( InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2, Compare comp ); |  | (since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class Compare > bool lexicographical_compare( ExecutionPolicy&& policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2, Compare comp ); | (4) | (since C++17)

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`. This overload only participates in overload resolution if std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true

Lexicographical comparison is a 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.

comp

-

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);

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)

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