Question

The _________ search algorithm requires that the array's contents be sorted.

Short answer

Answer: Binary Search

Step-by-step solution

List common search algorithms

There are two common search algorithms - Linear Search and Binary Search.

Determine which algorithm requires a sorted array

Linear search works with both sorted and unsorted arrays, as it iterates through each element, checking if it matches the target value. On the other hand, Binary search specifically requires the input array to be sorted, as it repeatedly divides the array into two halves and searches for the target value in the more likely half based on the value's comparison with the middle element.

Answer the question

The search algorithm that requires the array's contents to be sorted is the Binary Search algorithm.

Key concepts

Binary Search

Binary Search is a highly efficient search algorithm that is particularly useful when dealing with sorted arrays. Unlike its counterpart, the Linear Search, Binary Search takes advantage of the sorted nature of the data by targeting the middle element of the array to determine where the target value might be.

Here’s how it works:

• First, identify the middle element of the array.
• If this middle element is the target value, the search is complete.
• If the target value is smaller, focus on the left sub-array. Conversely, if larger, focus on the right sub-array.
• Repeat the process with the new subset of the array until the target is found or the search space is exhausted.

The beauty of Binary Search is its logarithmic time complexity, denoted as O(log n), which means that even in large arrays, the number of comparisons needed grows very slowly compared to the number of elements.

Linear Search

Linear Search is the simplest and most straightforward search algorithm. It is versatile as it does not require the array to be sorted. When you implement a Linear Search, you start at one end of the list and check each element in sequence until the target value is found or the end of the array is reached.

The steps involved in a Linear Search are invariably consistent:

• Begin at the first element of the array.
• Compare each element with the target value.
• If a match is found, return the index of the element.
• If no match is found and the end of the array is reached, conclude that the target is not present.

While Linear Search has a time complexity of O(n), indicating that it checks each element once, its simplicity makes it a reliable choice for smaller datasets or unsorted arrays where sorting costs could be prohibitive.

Sorted Arrays

A sorted array is an arrangement where the elements are in a specific order, often numerical or lexicographical. Sorting is crucial for Binary Search because it relies on the order of elements to reduce the potential search space efficiently.

There are various algorithms used to sort arrays, including but not limited to:

• Quick Sort
• Merge Sort
• Bubble Sort
• Insertion Sort

Each sorting algorithm has its own strengths and best use cases, but the primary goal remains the same: to enable efficient searches and data access.

Having sorted data can significantly enhance performance in multiple applications, from databases to real-time data processing, making it a fundamental aspect of many computational tasks.