# binary_search

Returns whether the range contains an element

### Key Facts

**Gyroscopic Couple**: The rate of change of angular momentum () = (In the limit).

- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.

**Blaise Pascal**(1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.

**Leonhard Euler**(1707-1783) was a pioneering Swiss mathematician and physicist.

## Definition

The**binary_search()**algorithm is defined in the standard header

**<algorithm>**and in the nonstandard backward-compatibility header

**<algo.h>**.

## Interface

#include <algorithm> template < class ForwardIterator, class Type > bool binary_search( ForwardIterator first, ForwardIterator last, const Type& val ); template < class ForwardIterator, class Type, class BinaryPredicate > bool binary_search( ForwardIterator first, ForwardIterator last, const Type& val, BinaryPredicate comp );

**Parameters:**

Parameter | Description |
---|---|

first | A forward iterator addressing the position of the first element in the range to be searched |

last | A forward iterator addressing the position one past the final element in the range to be searched |

val | The value required to be matched by the value of the element or that must satisfy the condition with the element value specified by the binary predicate |

comp | User-defined predicate function object that defines sense in which one element is less than another. A binary predicate takes two arguments and returns `true` when satisfied and `false` when not satisfied |

## Description

**Binary_search**tests if there is an element in a sorted range that is equal to a specified value or that is equivalent to it in a sense specified by a binary predicate. The first version uses

`operator<`

for comparison, and the second uses the function object `comp`

.Example:

##### Example - binary_search algorithm

Problem

This program illustrates the use of the STL

**binary_search()**algorithm (default version) to determine whether a given integer is one of the values in a vector of integers that are sorted in ascending order.Workings

#include <iostream> #include <vector> #include <algorithm> using namespace std; int main() { int a[] = {1, 2, 3, 4, 5, 6, 7, 9, 10}; vector<int> v(a, a+9); cout <<"\nHere are the values in the vector:\n"; for (vector<int>::size_type i=0; i<v.size(); i++) cout <<v.at(i)<<" "; if (binary_search(v.begin(), v.end(), 3)) cout <<"\nThe value 3 was found."; else cout <<"\nThe value 3 was not found."; if (binary_search(v.begin(), v.end(), 8)) cout <<"\nThe value 8 was found."; else cout <<"\nThe value 8 was not found."; return 0; }

Solution

**Output:**Here are the values in the vector:

1 2 3 4 5 6 7 9 10 The value 3 was found. The value 8 was not found.

References