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# binary_search

 Category: algorithms Component type: function

### Prototype

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

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

### Description

Binary_search is a version of binary search: it attempts to find the element value in an ordered range [first, last) It returns true if an element that is equivalent to [1] value is present in [first, last) and false if no such element exists. [2] The first version of binary_search uses operator< for comparison, and the second uses the function object comp.

Specifically, the first version returns true if and only if there exists an iterator i in [first, last) such that *i < value and value < *i are both false. The second version returns true if and only if there exists an iterator i in [first, last) such that comp(*i, value) and comp(value, *i) are both false.

### 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 log(last - first) + 2. 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) {
cout << "Searching for " << i << ": "
<< (binary_search(A, A + N, i) ? "present" : "not present") << endl;
}
}
```
The output is:
```Searching for 1: present
Searching for 2: present
Searching for 3: present
Searching for 4: not present
Searching for 5: present
Searching for 6: not present
Searching for 7: not present
Searching for 8: present
Searching for 9: not present
Searching for 10: not present
```

### 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 this is not necessarily the information you are interested in! Usually, if you're testing whether an element is present in a range, you'd like to know where it is (if it's present), or where it should be inserted (if it's not present). The functions lower_bound, upper_bound, and equal_range provide this information.

[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.