equal_range


Category: algorithms	Component type: function

Prototype

Equal_range is an overloaded name; there are actually two equal_range functions.

template <class ForwardIterator, class LessThanComparable>
pair<ForwardIterator, ForwardIterator>
equal_range(ForwardIterator first, ForwardIterator last,
            const LessThanComparable& value);

template <class ForwardIterator, class T, class StrictWeakOrdering>
pair<ForwardIterator, ForwardIterator>
equal_range(ForwardIterator first, ForwardIterator last, const T& value,
            StrictWeakOrdering comp);

Description

Equal_range is a version of binary search: it attempts to find the element value in an ordered range [first, last) [1]. The value returned by equal_range is essentially a combination of the values returned by lower_bound and upper_bound: it returns a pair of iterators i and j such that i is the first position where value could be inserted without violating the ordering and j is the last position where value could be inserted without violating the ordering. It follows that every element in the range [i, j) is equivalent to [1] value, and that [i, j) is the largest subrange of [first, last) that has this property. The first version of equal_range uses operator< for comparison, and the second uses the function object comp.

The first version of equal_range returns a pair of iterators [i, j). i is the furthermost iterator in [first, last) such that, for every iterator k in [first, i), *k < value. j is the furthermost iterator in [first, last) such that, for every iterator k in [first, j), value < *k is false. For every iterator k in [i, j), neither value < *k nor *k < value is true. [2]

The second version of equal_range returns a pair of iterators [i, j). i is the furthermost iterator in [first, last) such that, for every iterator k in [first, i), comp(*k, value) is true. j is the furthermost iterator in [first, last) such that, for every iterator k in [first, j), comp(value, *k) is false. For every iterator k in [i, j), neither comp(value, *k) nor comp(*k, value) is true. [2]

Definition

Defined in the standard header algorithm, and in the nonstandard backward-compatibility header algo.h.

Requirements on types

For the first version:

ForwardIterator is a model of Forward Iterator.
LessThanComparable is a model of LessThan Comparable.
The ordering on objects of type LessThanComparable is a strict weak ordering, as defined in the LessThan Comparable requirements.
ForwardIterator's value type is the same type as LessThanComparable.

For the second version:

ForwardIterator is a model of Forward Iterator.
StrictWeakOrdering is a model of Strict Weak Ordering.
ForwardIterator's value type is the same type as T.
ForwardIterator's value type is convertible to StrictWeakOrdering's argument type.

Preconditions

For the first version:

[first, last) is a valid range.
[first, last) is ordered in ascending order according to operator<. That is, for every pair of iterators i and j in [first, last) such that i precedes j, *j < *i is false.

For the second version:

[first, last) is a valid range.
[first, last) is ordered in ascending order according to the function object comp. That is, for every pair of iterators i and j in [first, last) such that i precedes j, comp(*j, *i) is false.

Complexity

The number of comparisons is logarithmic: at most 2 * log(last - first) + 1. If ForwardIterator is a Random Access Iterator then the number of steps through the range is also logarithmic; otherwise, the number of steps is proportional to last - first. [3]

Example

int main()
{
  int A[] = { 1, 2, 3, 3, 3, 5, 8 };
  const int N = sizeof(A) / sizeof(int);

  for (int i = 2; i <= 4; ++i) {
    pair<int*, int*> result = equal_range(A, A + N, i);

    cout << endl;
    cout << "Searching for " << i << endl;
    cout << "  First position where " << i << " could be inserted: "
         << result.first - A << endl;
    cout << "  Last position where " << i << " could be inserted: "
         << result.second - A << endl;
    if (result.first < A + N)
      cout << "  *result.first = " << *result.first << endl;
    if (result.second < A + N)
      cout << "  *result.second = " << *result.second << endl;
  }
}

The output is:

Searching for 2
  First position where 2 could be inserted: 1
  Last position where 2 could be inserted: 2
  *result.first = 2
  *result.second = 3

Searching for 3
  First position where 3 could be inserted: 2
  Last position where 3 could be inserted: 5
  *result.first = 3
  *result.second = 5

Searching for 4
  First position where 4 could be inserted: 5
  Last position where 4 could be inserted: 5
  *result.first = 5
  *result.second = 5

Notes

[1] Note that you may use an ordering that is a strict weak ordering but not a total ordering; that is, there might be values x and y such that x < y, x > y, and x == y are all false. (See the LessThan Comparable requirements for a more complete discussion.) Finding value in the range [first, last), then, doesn't mean finding an element that is equal to value but rather one that is equivalent to value: one that is neither greater than nor less than value. If you're using a total ordering, however (if you're using strcmp, for example, or if you're using ordinary arithmetic comparison on integers), then you can ignore this technical distinction: for a total ordering, equality and equivalence are the same.

[2] Note that equal_range may return an empty range; that is, it may return a pair both of whose elements are the same iterator. Equal_range returns an empty range if and only if the range [first, last) contains no elements equivalent to value. In this case it follows that there is only one position where value could be inserted without violating the range's ordering, so the return value is a pair both of whose elements are iterators that point to that position.

[3] This difference between Random Access Iterators and Forward Iterators is simply because advance is constant time for Random Access Iterators and linear time for Forward Iterators.