What are the time complexity and applicability differences between binary and ternary search in Java?

Binary Search and Ternary Search are both divide-and-conquer algorithms used to find elements in a sorted array or to optimize functions. While they share similar goals, they differ significantly in their approach, time complexity, and practical applicability. This explanation will detail these differences with Java code examples, focusing on their theoretical and practical aspects.

Binary Search Overview

Binary Search is a well-known algorithm that divides a sorted array into two halves at each step, eliminating one half based on the comparison between the target value and the middle element.

Java Implementation of Binary Search

public class BinarySearch {
    public static int binarySearch(int[] arr, int target) {
        int left = 0;
        int right = arr.length - 1;
        
        while (left <= right) {
            int mid = left + (right - left) / 2; // Avoids integer overflow
            
            if (arr[mid] == target) {
                return mid;
            } else if (arr[mid] < target) {
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }
        return -1; // Target not found
    }…