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upper_bound

Category: algorithms Component type: function

Prototype

Upper_bound is an overloaded name; there are actually two upper_bound functions.
template <class ForwardIterator, class LessThanComparable>
ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last,
                            const LessThanComparable& value);

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

Description

Upper_bound is a version of binary search: it attempts to find the element value in an ordered range [first, last) [1]. Specifically, it returns the last position where value could be inserted without violating the ordering. [2] The first version of upper_bound uses operator< for comparison, and the second uses the function object comp.

The first version of upper_bound returns the furthermost iterator i in [first, last) such that, for every iterator j in [first, i), value < *j is false.

The second version of upper_bound returns the furthermost iterator i in [first, last) such that, for every iterator j in [first, i), comp(value, *j) is false.

Definition

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

Requirements on types

For the first version: For the second version:

Preconditions

For the first version: For the second version:

Complexity

The number of comparisons is logarithmic: at most 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 = 1; i <= 10; ++i) {
    int* p = upper_bound(A, A + N, i);
    cout << "Searching for " << i << ".  ";
    cout << "Result: index = " << p - A << ", ";
    if (p != A + N)
      cout << "A[" << p - A << "] == " << *p << endl;
    else
      cout << "which is off-the-end." << endl;
  }
}
The output is:
Searching for 1.  Result: index = 1, A[1] == 2
Searching for 2.  Result: index = 2, A[2] == 3
Searching for 3.  Result: index = 5, A[5] == 5
Searching for 4.  Result: index = 5, A[5] == 5
Searching for 5.  Result: index = 6, A[6] == 8
Searching for 6.  Result: index = 6, A[6] == 8
Searching for 7.  Result: index = 6, A[6] == 8
Searching for 8.  Result: index = 7, which is off-the-end.
Searching for 9.  Result: index = 7, which is off-the-end.
Searching for 10.  Result: index = 7, which is off-the-end.

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 even if an element that is equivalent to [1] value is already present in the range [first, last), the return value of upper_bound will not point to that element. The return value is either last or else an iterator i such that value < *i. If i is not equal to first, however, then *(i - 1) is less than or equivalent to value.

[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.

See also

lower_bound, equal_range, binary_search


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