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| Category: algorithms | | Component type: function |
Prototype
Nth_element is an overloaded name; there are actually two nth_element functions.
template <class RandomAccessIterator>
void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
RandomAccessIterator last);
template <class RandomAccessIterator, class StrictWeakOrdering>
void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
RandomAccessIterator last, StrictWeakOrdering comp);
Description
Nth_element is similar to partial_sort, in that it partially orders a range of elements: it arranges the range [first, last) such that the element pointed to by the iterator nth is the same as the element that would be in that position if the entire range [first, last) had been sorted. Additionally, none of the elements in the range [nth, last) is less than any of the elements in the range [first, nth). [1]
The two versions of nth_element differ in how they define whether one element is less than another. The first version compares objects using operator<, and the second compares objects using a functors comp.
The postcondition for the first version of nth_element is as follows. There exists no iterator i in the range [first, nth) such that *nth < *i, and there exists no iterator j in the range [nth + 1, last) such that *j < *nth.
The postcondition for the second version of nth_element is as follows. There exists no iterator i in the range [first, nth) such that comp(*nth, *i) is true, and there exists no iterator j in the range [nth + 1, last) such that comp(*j, *nth) is true.
Definition
Defined in the standard header algorithm, and in the nonstandard backward-compatibility header algo.h.
Requirements on types
For the first version, the one that takes three arguments:
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RandomAccessIterator is a model of RandomAccessIterator.
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RandomAccessIterator is mutable.
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RandomAccessIterator's value type is LessThanComparable.
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The ordering relation on
RandomAccessIterator's value type is a strict weak ordering, as defined in the LessThanComparable requirements.
For the second version, the one that takes four arguments:
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RandomAccessIterator is a model of RandomAccessIterator.
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RandomAccessIterator is mutable.
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StrictWeakOrdering is a model of StrictWeakOrdering.
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RandomAccessIterator's value type is convertible to StrictWeakOrdering's argument type.
Preconditions
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[first, nth) is a valid range.
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[nth, last) is a valid range.
(It follows from these two conditions that [first, last) is a valid range.)
Complexity
On average, linear in last - first. [2]
Example
int A[] = {7, 2, 6, 11, 9, 3, 12, 10, 8, 4, 1, 5};
const int N = sizeof(A) / sizeof(int);
nth_element(A, A + 6, A + N);
copy(A, A + N, ostream_iterator<int>(cout, " "));
Notes
[1] The way in which this differs from partial_sort is that neither the range [first, nth) nor the range [nth, last) is be sorted: it is simply guaranteed that none of the elements in [nth, last) is less than any of the elements in [first, nth). In that sense, nth_element is more similar to partition than to sort. Nth_element does less work than partial_sort, so, reasonably enough, it is faster. That's the main reason to use nth_element instead of partial_sort.
[2] Note that this is significantly less than the run-time complexity of partial_sort.
See also
partial_sort, partition, sort, StrictWeakOrdering, LessThanComparable
