Question

The _________ search algorithm repeatedly divides the portion of an array being searched in half.

Short answer

#Question# Using the Binary Search algorithm, find the index of the target value 7 in the given sorted array: [1, 5, 7, 10, 12, 15, 20].

Step-by-step solution

1. Understand the problem

For the Binary Search algorithm, we will be searching for a specific element in a sorted array. It adopts a divide and conquer strategy by repeatedly dividing the search interval in half. If the target value matches the middle element of the interval, we found the desired element. If the target value is less or greater than the middle element, the left or right half of the interval will be searched again, respectively.

2. Identify the Input and Output

The input for the Binary Search algorithm is a sorted array and a target value to search. The output is the index of the target element if found in the array, or -1 otherwise.

3. Perform a binary search on an example

Let's apply the Binary Search algorithm on the following example: Sorted array: [1, 5, 7, 10, 12, 15, 20] Target value: 10 Step by step solution: Step 1: Find the middle element of the array. Middle index = (0 + 6) / 2 = 3 (start index = 0, end index = 6) Middle element = Array[3] = 10 Step 2: Check if the middle element is equal to the target value. Middle element (10) == Target value (10) Step 3: The middle element is equal to the target value, so the index of the target element is the middle index. Index of target element = 3

4. Conclude the process

By following the Binary Search algorithm steps, we found that the target value (10) is located at index 3 in the sorted array. If the target value was not found in the array, we would return -1.