# 27 Algorithms library [algorithms]

## 27.8 Sorting and related operations [alg.sorting]

### 27.8.11 Lexicographical comparison [alg.lex.comparison]

```template<class InputIterator1, class InputIterator2> constexpr bool lexicographical_compare(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> bool lexicographical_compare(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class InputIterator1, class InputIterator2, class Compare> constexpr bool lexicographical_compare(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class Compare> bool lexicographical_compare(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, Compare comp); template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2, class Proj1 = identity, class Proj2 = identity, indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp = ranges::less> constexpr bool ranges::lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_range R1, input_range R2, class Proj1 = identity, class Proj2 = identity, indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>> Comp = ranges::less> constexpr bool ranges::lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); ```
Returns: true if and only if the sequence of elements defined by the range [first1, last1) is lexicographically less than the sequence of elements defined by the range [first2, last2).
Complexity: At most 2 min(last1 - first1,  last2 - first2) applications of the corresponding comparison and each projection, if any.
Remarks: If two sequences have the same number of elements and their corresponding elements (if any) are equivalent, then neither sequence is lexicographically less than the other.
If one sequence is a proper prefix of the other, then the shorter sequence is lexicographically less than the longer sequence.
Otherwise, the lexicographical comparison of the sequences yields the same result as the comparison of the first corresponding pair of elements that are not equivalent.
[Example 1:
ranges​::​lexicographical_compare(I1, S1, I2, S2, Comp, Proj1, Proj2) can be implemented as: for ( ; first1 != last1 && first2 != last2 ; ++first1, (void) ++first2) { if (invoke(comp, invoke(proj1, *first1), invoke(proj2, *first2))) return true; if (invoke(comp, invoke(proj2, *first2), invoke(proj1, *first1))) return false; } return first1 == last1 && first2 != last2;
â€” end example]
[Note 1:
An empty sequence is lexicographically less than any non-empty sequence, but not less than any empty sequence.
â€” end note]