Standard Template Library Programmer's Guide

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]

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 = lower_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 = 0, A[0] == 1

Searching for 2. Result: index = 1, A[1] == 2

Searching for 3. Result: index = 2, A[2] == 3

Searching for 4. Result: index = 5, A[5] == 5

Searching for 5. Result: index = 5, A[5] == 5

Searching for 6. Result: index = 6, A[6] == 8

Searching for 7. Result: index = 6, A[6] == 8

Searching for 8. Result: index = 6, A[6] == 8

Searching for 9. Result: index = 7, which is off-the-end.

Searching for 10. Result: index = 7, which is off-the-end.

[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] If an element that is equivalent to [1] value is already present in the range [first, last) , then the return value of lower_bound will be an iterator that points to that element.

[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.

upper_bound , equal_range , binary_search

Category: algorithms

Component type: function

Upper_bound is an overloaded name; there are actually two upper_bound functions.

template

ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last, const LessThanComparable& value);

template

ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last, const T& value, StrictWeakOrdering comp);

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 .

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

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.

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 .

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]

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