public class BinarySearch { // Main binary search function that matches the required signature public int binarySearch(int[] arr, int k) { // Call the recursive helper function with initial bounds return binarySearchHelper(arr, 0, arr.length - 1, k); } // Recursive helper function private int binarySearchHelper(int[] arr, int left, int right, int target) { // Base case: if bounds cross, element not found if (left > right) { return -1; } // Calculate middle index int mid = left + (right - left) / 2; // If element found at mid, return its index if (arr[mid] == target) { return mid; } // If target is less than middle element, search left half if (target < arr[mid]) { return binarySearchHelper(arr, left, mid - 1, target); } // If target is greater than middle element, search right half return binarySearchHelper(arr, mid + 1, right, target); } // Main method for testing public static void main(String[] args) { BinarySearch bs = new BinarySearch(); // Test case from assignment int[] arr = {12, 45, 67, 89}; // Test cases System.out.println("Searching for 67: " + bs.binarySearch(arr, 67)); // Should print 2 System.out.println("Searching for 31: " + bs.binarySearch(arr, 31)); // Should print -1 } }