Question:

Consider the following binary search method in Java:

public static int binarySearch(int[] arr, int target) {
    int left = 0;
    int right = arr.length - 1;
    
    while (left <= right) {
        int middle = (left + right) / 2;
        
        if (arr[middle] == target) {
            return middle;
        }
        else if (arr[middle] < target) {
            left = middle + 1;
        }
        else {
            right = middle - 1;
        }
    }
    
    return -1;
}

Given the sorted array int[] arr = {1, 4, 7, 10, 14, 19, 21, 27, 30} and the target value target = 14, apply the binary search method and determine the index at which the target value is found. If the target value is not found in the array, return -1.

Answer with Step-by-Step Explanation:

To apply the binary search method to find the target value 14 in the given sorted array, int[] arr = {1, 4, 7, 10, 14, 19, 21, 27, 30}, we follow these steps:

Step 1: Initialize the variables left and right. Set left = 0 and right = arr.length - 1. In this case, left = 0 and right = 8.

Step 2: Calculate the middle index as middle = (left + right) / 2. The middle index is (0 + 8) / 2 = 4.

Step 3: Check if the value at the middle index (arr[middle]) is equal to the target value 14. In this case, arr[4] = 14, which is equal to the target value. Therefore, return the middle index 4.

The target value 14 is found at index 4.

Answer:

The index at which the target value 14 is found in the given array is 4.