# Binary Search Program, Algorithm & their Time Complexity

Binary Search Program, Algorithm & their Time Complexity. In this tutorial, You’ll learn about binary search algorithm, how it’s useful in searching and the time complexity of a binary search.

## Binary Search

A Binary Search is used to search an element in a sorted array.  Binary search is also known as half-interval search or logarithmic search. It works by comparing a value (value needs to search) to the middle element an array. If a value matches with the middle element then the position is returned otherwise the algorithm repeats if the value is less than or greater than the middle element.

A Binary search algorithm is efficient than the linear search algorithm. The time complexity of binary search is O(log(n)).

Important Points

i) A Binary search  algorithm is applicable only for sorted values. An array should be sorted  either in ascending or descending order.

ii) Binary search average and worst-case time complexity is O(log(n)).

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Binary search implementation using Recursion

## Binary Search Algorithm

Let’s check the algorithm of binary search.

i) Initialize two indexes low and high. Initialize the value of low to zero and high is n – 1 where n is the length of an array.

low = 0
high = N – 1

ii)
Run a loop while low is less than equal to high.

## Binary Search Program in C

We have learned about binary search, let’s implement them in C.

## Reference Books for Data Structure

For reference, you can read these good books for a data structure.

Data Structure Books on Amazon India

Data Structure Books on Flipkart