6 Types of Search Algorithms & How They Work

You can imagine search algorithms as digital detectives, finding what you need in vast data collections, such as websites or databases, with the fewest steps possible.

From Google and Amazon to Facebook and Netflix, search algorithms play a vital role in digital interactions in everyday life.

In this article, you’ll learn about the most common types of search algorithms, their time complexities, how their search processes work, and real-life applications in computer science.

Lower average case complexity is better for faster performance, especially with large inputs. Algorithms like binary search O(log n) are highly efficient.

On the other hand, higher complexities, such as O(n), may become impractical for large datasets due to linear or worse runtime growth. However, efficiency also depends on factors like data structures, problem context, resources, and application requirements.

1. Linear search algorithm

Linear search, also known as sequential search, iterates through each array element in a dataset sequentially, comparing it with the target element until it finds an exact match. If the search function reaches the end of the array without a match, it signals that the target element is not present in the dataset.

The target element you’re looking for might be numbers, strings, objects, or any other data type that can be stored in an array. This flexibility makes linear search a versatile algorithm that can be applied to a wide range of data types.

To better illustrate this search process, let’s look at a real-life example.

Let’s say you have an unsorted list of integers representing the ages of people in a group. You’re asked to find out if a specific age, let’s say 25, is present in the array. You would start at the beginning of the array and check each element, one by one until you either find the age 25 or reach the end of the array.

The execution time of a linear search algorithm is proportional to the array size. The computational complexity for linear search is O(n), where n is the number of elements in the array.

Applications of linear search

• Simple search tasks: Linear search is often used for a broad spectrum of basic search tasks where the dataset is small or where the additional complexity of other algorithms isn’t warranted. For example, searching a small list of names or numbers.
• Linear data structures: Linear search is fundamental to many linear data structures like arrays, lists, and stacks. It’s typically used for scanning these structures to locate specific elements or perform operations.
• Unordered arrays: Since linear search checks each element sequentially, it can locate items regardless of their positions in the array.

2. Binary search algorithm

Binary search is an efficient algorithm used for finding a target value within a sorted list. It repeatedly divides the search interval in half using the binary search method. Then it checks the target value against the middle element and proceeds to a right or left part of the array. This process continues until the target value is found. Alternatively, the search interval turns up empty when the target is not present in the array.

Let’s look at an example of using binary search to find a specific numerical value.

Imagine you have an array of numbers: [2,5,8,12,16,23,38,56,72,91], and you want to find the number 23.

You start by looking at the middle element (root node), which is 16. Since 23 is bigger than 16, you only look at the numbers to the right of 16. Next, you look at the middle element of this part, which is 56. Since 23 is smaller than 56, you only look at the numbers to the left of 56. Now you look at the middle element again, which is 23. You found the search key!

The execution time of a binary search algorithm is O (log n), where n is the number of elements in the array.

Applications of binary search

• Searching in databases: This is an effective algorithm for database search to quickly locate records based on indexed fields, such as IDs or keys.
• Finding elements in sorted arrays: Binary search efficiently locates elements in sorted arrays, which is useful in index-based data structures and applications like searching for a word in a dictionary or finding an item in a sorted list.
• Algorithmic foundation: It serves as a fundamental component in developing sophisticated machine learning algorithms. Binary search helps in training neural networks and optimizing model hyperparameters.
• Optimizing algorithms: Binary search is used in algorithms, including divide and conquer strategies, to efficiently solve problems like finding square roots or locating peak elements in arrays.
• Searching in trees: Binary search trees (BSTs) use this algorithm to efficiently search, insert, and delete elements while maintaining the sorted order of the tree.

3. Interpolation search

When values in a sorted array are evenly distributed, interpolation search offers an advantage over binary search. Interpolation involves creating new data points within the range of known search space.

While binary search always focuses on the middle element, interpolation search adjusts its search position based on the target value being sought. For instance, if the search key is closer to the end, the interpolation search tends to start searching for data from that end.

To put this into perspective, let’s imagine you’re searching for a particular price among a list of item prices in a store. These prices are arranged from the lowest to the highest. Instead of always checking halfway through the list (like in binary search), interpolation search estimates where the price might fall based on its value compared to the lowest and highest prices. Then, you repeat this process until you find the price.

The execution time of an interpolation search algorithm is O(log log n), where n is the number of elements in the array.

Applications of interpolation search

• Searching in databases: Interpolation search is commonly used in databases for searching records based on some key element.
• Searching in large arrays: This search algorithm facilitates more efficient searching in large sorted arrays, especially when the distribution of values is uniform. It can be applied in various fields such as scientific computing, where large datasets need to be searched efficiently.
• Retrieving data from symbol tables: Interpolation search can be used in symbol tables, where keys are associated with values. For instance, in programming languages, symbol tables are used to store variables, functions, and other identifiers. Interpolation search can quickly locate the information associated with a specific identifier.
• Time-sensitive applications: Due to its ability to quickly retrieve data, interpolation search is suitable for time-sensitive applications.
• Hash tables: Efficient for finding data when combined with a hash function.

4. Jump search

Jump search, otherwise known as block search, is specifically designed for sorted arrays. Unlike linear search, which examines each element sequentially, jump search leaps in fixed-size increments, bypassing multiple elements for quicker searches.

If the target element is within a specified range, the algorithm employs a linear search within that block. This approach substantially cuts down on operations, enhancing search efficiency.

Let’s look at an example of the jump search algorithm.

Imagine you’re trying to find a specific number in a long list of numbers, and want to do it faster than checking each number one by one.

1. Decide how many numbers to skip each time you look: Let’s say you’ll skip 3 numbers at a time.
2. Start looking through the list, skipping ahead by the chosen amount each time, until you find a number equal to or greater than the one you’re looking for.
3. Once you’ve found a range where the number might be, perform a linear search until you find the target one.

The execution time of a jump search algorithm is O(√n), where n is the number of elements in the sorted array.

Applications of jump search

• JavaScript applications: Jump search optimizes the search process in JavaScript applications, improving efficiency and responsiveness.
• Searching in database systems: This algorithm searches for records based on some key element in large databases.
• Retrieving data from visual media: Jump search efficiently locates a specific frame within a large video file by advancing a fixed number of frames at a time.

5. Exponential search

The exponential search algorithm, also known as doubling or galloping search, differs from jump search in how it divides the array and the type of search employed within these divisions. While jump search divides the array into blocks and uses linear search, exponential search divides the array using exponential powers of 2 and applies binary search.

Essentially, the search function exponentially traverses the entire array, from the left, segmenting it into smaller blocks using powers of 2. The algorithm conducts a binary search within each of these blocks until the target is found.

Since this search algorithm can be a bit complex, let’s illustrate its functionality by applying it to a real-life scenario.

Imagine you have a bookshelf filled with books sorted alphabetically by title. You’re looking for a specific book, let’s say “Harry Potter and the Philosopher’s Stone.” Instead of searching through each book one by one, you decide to use exponential search.

Here’s how it works:

1. Starting point: You begin with the first book on the left side of your bookshelf. If this is not the book, you are looking for, proceed.
2. Move to the right, doubling your search window: If you find “Harry Potter and the Philosopher’s Stone” in one of these positions, you’ve found your book.
3. Repeat the process: You keep repeating the process, doubling the range each time, until you find the book.

While not the exact application of exponential search, this example helps demonstrate how you can quickly locate the book without the need to go through each book one by one.

The execution time of an exponential search algorithm is O(log n), where n is the number of elements in the sorted array.

Applications of exponential search

• Finding data in large sorted arrays: Exponential search quickly finds elements in large sorted arrays, such as product listings, by exponentially extending the search range, ideal for situations where the linear search is too slow.
• Searching file systems: This algorithm improves file system searches by quickly finding files or directories within directory structures through exponential expansion of the search range.

6. Ternary search

Ternary search is a search algorithm designed to determine the position of a target value within a sorted array. Unlike binary search, which divides the array into two parts, ternary search divides it into three. By comparing the target value with elements at two points and dividing the array into three parts, the search function efficiently narrows down the search space.

To illustrate an example, let’s apply ternary search to find the number 6 in the array [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].

• Split the search area:
  • Divide your search area into three parts by finding two split points: One point is at around one-third of the way from the left (let’s say 4), and the other is at around two-thirds from the left (let’s say 8).
  • This splits the area into [1, 4], (5, 8), and [9, 10].
• Compare with the target:
  • Check if the number we’re looking for (6) is equal to either 4 or 8.
  • It’s not equal to 4 or 8, so you adjust your pointers based on where 6 might be located:
    • Since 6 is greater than 4 but less than 8, we move the left pointer to 5 and the right pointer to 7.
• Repeat or conclude:
  • Keep repeating this process with the reduced search space until you find the number 6 or have no more area left to search.
  • Eventually, you narrow down the search area to [6, 6], and you find the number you were looking for!

The execution time of a ternary search algorithm is O(log3 n), where n is the number of elements in the sorted array.

Applications of ternary search

• Unimodal functions: Ternary search is applied in unimodal functions to identify their maximum or minimum values. Unimodal functions are those that have a single highest value.

Conclusion

Applications of different types of search algorithms are vast and diverse, spanning from searching large databases, and helping optimize applications, to serving as foundation blocks for developing advanced machine learning algorithms for searching.

By keeping in mind the time and space complexities, capabilities, combined with the advantages and disadvantages of each of the mentioned algorithms, you can make informed decisions. Whether it is on your computer science class assignment, or when you are developing the next breakthrough app, mastering techniques like binary search, DFS, BFS, and divide-and-conquer, you can unlock the full potential of data structures and enhance your system performance.

If you’re building or evaluating search for an online store specifically, the mechanics work a bit differently in practice. See how e-commerce search works under the hood.

Frequently asked questions