# What Is Fibonacci Search in Data Structure?

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Angela Bailey

What Is Fibonacci Search in Data Structure?

Data structures play a crucial role in organizing and storing data effectively. Various search algorithms are used to efficiently retrieve data from these structures.

One such algorithm is the Fibonacci Search algorithm. In this article, we will explore what the Fibonacci Search algorithm is and how it works.

## Fibonacci Search Algorithm

The Fibonacci Search algorithm is an efficient searching technique that operates on sorted arrays. It is based on the famous Fibonacci sequence, which starts with 0 and 1, and each subsequent number is the sum of the previous two numbers (0, 1, 1, 2, 3, 5, 8, ..).

How does it work?
The Fibonacci Search algorithm follows a divide-and-conquer approach to find an element’s position in a sorted array. Let’s understand its working through the following steps:

### Step 1: Generate the Fibonacci series

Firstly, generate a Fibonacci series that has numbers greater than or equal to the size of the array you want to search within. For example:

• Array size: N
• Fibonacci series: F, F, F, ., F[k]
• The last number (F[k]) should be greater than or equal to N.

### Step 2: Calculate the offset and compare elements

Next, calculate an offset value by finding the largest fibonacci number smaller than or equal to N. This offset value helps in dividing the array into subarrays for comparison.

• If N is less than F[k], set the offset as F[k-1] and continue.
• If N is equal to or greater than F[k], set the offset as F[k] and continue.

### Step 3: Perform comparison operations

Now, perform comparison operations on elements within the array using the calculated offset value.

• If the current element is equal to the element being searched, return its position.
• If the current element is smaller than the element being searched, ignore the left subarray (before offset) and update offset accordingly for the right subarray (after offset).
• If the current element is larger than the element being searched, ignore the right subarray (after offset) and update offset accordingly for the left subarray (before offset).

Repeat these steps until either you find a match or exhaust all elements in the array.

## Advantages of Fibonacci Search Algorithm

The Fibonacci Search algorithm offers several advantages over other searching algorithms:

• Efficiency: The algorithm has a time complexity of O(log N), making it highly efficient.
• Better than Binary Search: In certain scenarios where there are many repeated elements in an array, Fibonacci Search performs better than Binary Search.
• Works well with large arrays: The algorithm works well even with large arrays due to its logarithmic time complexity.

## Conclusion

The Fibonacci Search algorithm is a powerful searching technique that efficiently finds an element within a sorted array. By leveraging properties of Fibonacci numbers, it divides and conquers to quickly locate elements.

Its efficiency and ability to handle large arrays make it a valuable addition to any programmer’s toolkit.