# Binary search algorithm in C

A quick method for locating a particular element in a sorted array is a binary search. The initial task of this algorithm is to compare the target value to the array's middle element. The search is deemed successful if the target value is contained in the middle element. The algorithm will look in the left half of the array if the goal value is less than the centre element. The programme will scan the right half of the array if the goal value is greater than the centre element. This method is repeated until either the goal value or the search range is exhausted.

### Usage:

Databases, search engines, and data processing are just a few of the applications that use the binary search strategy.

### Characteristics:

• The array of input values must be sorted.
• With each iteration, the method shrinks the search range by half, making it particularly efficient for huge datasets.
• The algorithm has an O (log n) worst-case time complexity.
• Finding the desired value is done by the programme using a divide-and-conquer strategy.

Here is a straightforward example of the binary search algorithm written in C:

Output:

```Target found at index 2
```
• The binary_search function accepts four arguments: the array to search, the left and right search range boundaries, and the target value to look for. The function returns its index if the desired value can be found; else, it returns -1.
• The main function creates an array arr and a value target. The binary_search function is then used to search the array for the desired value. The function returns the index where the target value was located if it was, the function returns the index at which it was found. Otherwise, the message "Target not found" is displayed.
• The binary search algorithm's implementation is basic. We begin by setting the left border to the array's initial index and the right boundary to the array's last index. Once the left boundary is less than or equal to the right border, the array is looped through one more time. We use the formula (left + right) / 2 within the loop to calculate the middle index of the search range. This formula computes the integer value of the middle index's floor.
• The centre member of the array is contrasted with the target value. We return the index of the middle element if they are equal. We change the right boundary to be one less than the middle index if the desired value is less than the middle element. If not, we adjust the left border so that it is one more than the centre index. We continue doing this until the goal value is obtained or the search space is filled.
• The temporal complexity of the binary search algorithm, where n is the array size, is O(log n). This is far more efficient than linear search, which has a temporal complexity of O(n), where n is the size of the array.
• Finally, the binary search technique offers a useful way to locate a particular member in a sorted array. It is easy to build and has an O(log n) time complexity, making it an efficient approach for large datasets.

• For large datasets, the binary search algorithm is exceptionally efficient, and it is capable of handling a wide range of input sizes.
• The algorithm is simple to implement in almost all programming languages.

• Before using the binary search technique, the input array must be sorted, which takes more time and memory.
• The algorithm cannot be applied to unsorted arrays.
• The algorithm may yield inaccurate results if the input array is not sorted.
• The binary search algorithm is not appropriate for tiny datasets since the technique's overhead may outweigh its benefits.

## Conclusion:

A sorted array can be quickly searched for a specific element using the binary search technique. It employs a divide-and-conquer strategy to cut the search range in half with each iteration, allowing it to be highly efficient for large datasets. However, before using the binary search technique, the input array must be sorted, which takes extra time and memory. The binary search algorithm is a sophisticated data processing tool that is widely utilised in various sectors.