> For the complete documentation index, see [llms.txt](https://nitinranganath.gitbook.io/data-structures/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://nitinranganath.gitbook.io/data-structures/arrays/binary-search.md).

# Binary Search

Binary search is a searching technique which is considered to be better than linear search as the array size keeps getting smaller and smaller in each iteration or recursive call and the index of found element can be found in fewer steps as compared to linear search.

 **Time Complexity = O(log n)**

### Iterative Method

```c
int binarySearch(int a[], int low, int high, int key) {

    while (low <= high) {
    
       int mid = (low + high)/2; 
       
       if (a[mid] == key) {
           return mid;
        } else if (a[mid] > key) {
            // Key lies in the left sublist
            high = mid - 1;
        } else {
            // Key lies in the right sublist
            low = mid + 1;
        }      
    
    }
    
    return -1;

}
```

### Recursive Method

```c
int binarySearch(int a[], int low, int high, int key) {

    if (low <= high) {
        
        int mid = (low + high)/2;
        
        if (a[mid] == key) {
            return mid;
        } else if (a[mid] > key) {
            // Key lies in left sublist
            return binarySearch(a, low, mid-1, key);
        } else {
            // Key lies in right sublist
            return binarySearch(a, mid+1, high, key);
        }
        
    }
    
    return -1;

}
```

In this case, it is better to use iterative version of binary search as recursion uses internal stack. However, the time complexity remains the same for both the methods.

Contributed by Nitin Ranganath


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://nitinranganath.gitbook.io/data-structures/arrays/binary-search.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.