Implement Exponential Search Algorithm (fixes #54)

[saurabh12nxf]

This pull request addresses issue #54 by implementing the Exponential Search Algorithm. I have a solid understanding of searching algorithms and am confident in delivering an efficient solution.

High-Level Approach
Exponential Search Function:

Created a function exponentialSearch to locate the range in which the target element might be present.

Performed a binary search within that interval to find the target element.

Binary Search Function:

Created a helper function binarySearch to conduct the search within the identified range from the Exponential Search Function.

Testing the Implementation:

Built test sorted arrays and thoroughly tested the functions to ensure proper working.

Detailed Implementation
Exponential Search Function

java
public static int exponentialSearch(int[] arr, int target) {
int n = arr.length;
if (arr[0] == target) {
return 0;
}
int i = 1;
while (i < n && arr[i] <= target) {
i = i * 2;
}
return binarySearch(arr, target, i / 2, Math.min(i, n - 1));
}
Binary Search Function

java
public static int binarySearch(int[] arr, int target, int left, int right) {
while (left <= right) {
int mid = left + (right - left) / 2;
if (arr[mid] == target) {
return mid;
}
if (arr[mid] < target) {
left = mid + 1;
} else {
right = mid - 1;
}
}
return -1; // target not found
}
Main Method for Testing

java
public static void main(String[] args) {
int[] arr = {2, 3, 4, 10, 40, 50, 60, 70, 80, 90};
int target = 10;
int result = exponentialSearch(arr, target);
if (result != -1) {
System.out.println("Element found at index: " + result);
} else {
System.out.println("Element not found in array.");
}
}
Testing
Created test arrays with different target values to verify the implementation.

Ensured that both edge cases and typical scenarios are handled correctly.

Verified that the solution works efficiently on large arrays.