### Linear Search vs Interpolation Search

In this post, we will learn the difference between Linear Search and Interpolation Search in Java. This is a frequently asked question in Java interviews for beginners. Let's dive into it.

## Difference between  Linear Search and Interpolation Search in Java

Feature Linear Search Interpolation Search
Search Algorithm Linear Search is a basic searching algorithm that sequentially checks each element in the list until the target element is found or the end of the list is reached. Interpolation Search is an advanced searching algorithm used for uniformly distributed sorted arrays. It estimates the position of the target element based on the value of the element being searched for.
Sorted Array Linear Search does not require the array to be sorted. It can be used on both sorted and unsorted arrays. Interpolation Search requires the array to be sorted in ascending order for accurate results. It is not suitable for unsorted arrays.
Time Complexity The worst-case time complexity of Linear Search is O(n), where n is the number of elements in the array. The average time complexity of Interpolation Search is O(log(log n)), where n is the number of elements in the array. In practice, it performs close to O(log n) for uniformly distributed arrays.
Performance Linear Search is simple to implement but less efficient for large arrays, especially when the target element is near the end. Interpolation Search is more efficient for large sorted arrays with uniformly distributed data, as it narrows down the search range faster. However, its performance degrades for skewed or non-uniformly distributed data.
Data Distribution Linear Search works well for both uniform and non-uniform data distributions. Interpolation Search performs better for uniformly distributed data, but its performance suffers for non-uniform distributions or when the data is clustered.
Boundary Conditions Linear Search works well even when the elements are not evenly spaced in the array. Interpolation Search assumes that the elements are evenly distributed, so it may produce incorrect results if this assumption is not met. It requires uniform distribution for better performance.
Mathematical Formula Linear Search uses a straightforward comparison (key == array[i]) to find the target element. Interpolation Search uses a mathematical formula to estimate the position of the target element based on the values of the first and last elements of the array.
In summary, Linear Search is a simple algorithm that works for both sorted and unsorted arrays, but its time complexity is linear and may not be efficient for large arrays. On the other hand, Interpolation Search is more efficient for uniformly distributed sorted arrays, but it requires the array to be sorted and may not perform well for non-uniform distributions. Therefore, the choice between Linear Search and Interpolation Search depends on the data distribution and whether the array is sorted.