Question

A binary search will find the value it is looking for with just one comparison if that value is stored in the ____________ array element.

Short answer

Answer: A binary search will find the value it is looking for with just one comparison if the target value is present at the middle element's position in the sorted array.

Step-by-step solution

Understanding the Binary Search Algorithm

In a binary search algorithm, one needs to search for a target element in a sorted array. The algorithm starts by comparing the target value with the middle element of the array. If the target value is found, then the search is successful, and if it is not found, then the search will reduce the search space by half, either focusing on elements to the right or left of the middle element, depending on whether the target value is larger or smaller than the middle element. The process continues until the value is found or the search space becomes empty.

Array Element in One Comparison

For a binary search algorithm to find the value it is looking for with just one comparison, the target value should be placed at the middle element's position. This is because the binary search algorithm begins its search by comparing the target value with the middle element of the array. If the target value is at the middle element's position, then it will be found in the first comparison, fulfilling the desired condition.

The Answer

So, the value that will be found with just one comparison will be stored in the middle array element.

Key concepts

Sorted Array

A sorted array is a fundamental requirement for the binary search algorithm. A sorted array means that the elements in the array are arranged in a specific, orderly sequence. This sequence could be in ascending order, where each element is greater than or equal to its predecessor, or in descending order, where each element is less than or equal to its predecessor.

Understanding the importance of a sorted array is crucial for a binary search because the sorting allows the algorithm to predict the location of the target element effectively. If the array wasn't sorted, the algorithm wouldn't be able to determine which half of the array contains the target after each comparison, thereby negating the efficiency of halving the search space with each step.

• Ascending order: 1, 2, 3, 4, 5
• Descending order: 5, 4, 3, 2, 1

When performing a binary search on a computer array, always start by confirming that the array is sorted; otherwise, sort it first before starting the search.

Search Space

The term search space in the context of binary search refers to the subset of elements within the array that could potentially include the target element. Initially, the search space is the entire array. After the binary search algorithm compares the middle element with the target element, the search space is reduced by half.

The reduction of the search space is based on the comparison's outcome:

• If the target is greater than the middle element, the search space is reduced to the elements on the right side of the middle.
• If the target is less than the middle element, the search space is reduced to the elements on the left side of the middle.

This process of halving the search space continues recursively or iteratively until the target element is found or until the search space is empty, which would mean that the target element is not present in the array. This systematic reduction is what makes binary search a fast and efficient searching technique, especially suited for large datasets.

Target Element

The target element is the value that the binary search algorithm is tasked with finding within the array. In the case of the exercise, the target element is that singular value which would be found with just one comparison if it's positioned at the middle of a sorted array. This is because binary search always starts by examining the middle element in the search space.

Therefore, if the target element coincides with the middle element, the search concludes immediately, making it the best-case scenario for binary search. In practical scenarios, the chances of this happening are generally not high, and as a result, the process involves progressively narrowing down the search space until the target is located or determined to be absent.

The efficiency of the binary search comes from its nature of discarding half of the remaining elements from consideration if they do not match the target element with each comparison. This highlights the algorithm's strengths in quickly narrowing down the possible location of the target element within the array.