Advanced Searching Algorithms

In addition to linear search and binary search, there are several advanced searching algorithms that are more specialized and optimized for specific scenarios. Two examples of such algorithms are Interpolation Search and Exponential Search.

Interpolation Search

Interpolation Search is an algorithm used to search for a target value in a sorted array with uniformly distributed values. Unlike linear search and binary search, Interpolation Search makes an educated guess of the target value's position based on the values of the first and last elements of the array.

The basic idea of Interpolation Search is to probe the array position at a value corresponding to the position of the target value in a linear ascending order. This probing is done by using interpolation formula to find the probable position of the target value.

Here's an example implementation of Interpolation Search in Java:

1{{code}}

In the example code above, we have an array arr with values [2, 4, 6, 8, 10], and we want to find the index of the target value x = 6. The interpolationSearch function uses the interpolation formula to calculate the probable position of x in the array. It continuously adjusts the range of the search until it finds the target value, or determines that it's not present in the array.

Exponential Search

Exponential Search is another algorithm used for searching in sorted and uniformly distributed arrays. It works by finding the range in which the target value may be present and then performing a binary search within that range.

The basic idea of Exponential Search is to exponentially increase the range by powers of 2 until an element greater than or equal to the target value is found. Once the range is determined, a binary search is performed within that range to find the exact index of the target value.

Here's an example implementation of Exponential Search in Java:

1{{code}}

In the example code above, we have an array arr with values [2, 4, 6, 8, 10], and we want to find the index of the target value x = 6. The exponentialSearch function starts with a range of size 1 and doubles the size of the range until it finds a value greater than or equal to the target value. The range is then passed to the binarySearch function to perform a binary search and find the exact index of the target value.

These advanced searching algorithms provide alternative approaches to searching in arrays. Depending on the distribution of data and other factors, they can sometimes outperform linear search and binary search. It's important to consider the characteristics of the data and the specific requirements of the problem when choosing the most suitable searching algorithm.

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}

class Main {

  public static void main(String[] args) {

    // Replace with your Java logic here

    int[] arr = {2, 4, 6, 8, 10};

    int x = 6;

    int result = interpolationSearch(arr, x);

    if (result != -1) {

      System.out.println("Element found at index " + result);

    } else {

      System.out.println("Element not found in the array");

    }

  }

​

  public static int interpolationSearch(int[] arr, int x) {

    int left = 0;

    int right = arr.length - 1;

​

    while (left <= right && x >= arr[left] && x <= arr[right]) {

      if (left == right) {

        if (arr[left] == x) {

          return left;

        }

        return -1;

      }

​

      int position = left + ((x - arr[left]) * (right - left)) / (arr[right] - arr[left]);

​

      if (arr[position] == x) {

        return position;