What Is a Binary Search in Data Structure?

A binary search is a popular algorithm used to search for an element in a sorted array or list. It follows the divide and conquer approach and is highly efficient compared to other searching algorithms like linear search.

## How Does Binary Search Work?

The binary search algorithm works by repeatedly dividing the search interval in half. It starts by comparing the Target element with the middle element of the sorted array.

If they match, the search is successful. Otherwise, depending on whether the Target is greater or smaller than the middle element, the algorithm eliminates half of the remaining elements and continues searching in the remaining half.

This process of dividing the array in half and narrowing down the search range continues until either the Target element is found, or there are no more elements left to search.

## Binary Search Implementation

To implement a binary search, you can follow these steps:

- Set two pointers,
**low**and**high**, pointing to the first and last index of the array or sublist. - Calculate
**mid**, which is equal to (**low + high**) / 2. - If the middle element equals the Target element, return its index as it has been found.
- If the middle element is greater than the Target element, update
**high**to be (**mid – 1**) and go back to step 2. - If the middle element is smaller than the Target element, update
**low**to be (**mid + 1**) and go back to step 2. - If the search interval becomes empty (i.e.,
**low > high**), the Target element is not present in the array.

## Time Complexity and Space Complexity

The time complexity of binary search is O(log n), where n is the number of elements in the array. This means that as the size of the array increases, the time taken to perform a binary search grows logarithmically.

The space complexity of binary search is O(1) since it does not require any extra space apart from a few variables to store indices and temporary values.

## Advantages of Binary Search

__Efficiency:__Binary search is highly efficient due to its logarithmic time complexity.__Applicability:__It can be applied to both sorted arrays and sorted lists.__Versatility:__Binary search can be easily implemented iteratively or recursively.

## Conclusion

A binary search algorithm is an efficient way to find an element in a sorted array or list. It follows a divide and conquer strategy, making it faster than linear search.

By dividing the search interval in half repeatedly, it quickly narrows down the possibilities until either finding the Target element or determining its absence. With its efficiency and versatility, binary search proves to be an essential algorithm in data structures.