The communication network is expanding, and so the people are using the internet! Businesses are going digital for efficient management. The data generated on the internet is rising, and thus datasets are becoming complex. It is essential to organise, manage, access and analyse the data carefully and efficiently, a data structure is the most helpful technique, and the article focuses on the same!

Data Structure

In computer science, data structures are the basis for abstract data types (ADT), where ADT are the logical form of the data type. The physical layout of the data type is implemented using the data structure. Different data structure types are used for different kinds of applications; some are specialised in particular tasks. 

The data structure is a collection of data values and relationships among them, operations and functions applicable to the data.  It assists in organising, managing and storing data in a particular format. Thus, users can have easy access and modify the data efficiently. 

Data structures help to manage large amounts of data, such as massive databases. Efficient algorithms are built based on efficient data structures. Besides efficient storage, data structures are also responsible for the efficient retrieval of information from stored memory. It includes an array, Linked List, Pointer, Searching, Stack, Graph, Queue, Structure, Programs, Sorting and so forth.

The article covers the concept of Searching in Data Structure with example and its methods. Two examples of algorithms are explained in detail to understand the concept clearly. To gain further knowledge, skills and expertise, online courses on data structure are available, mentioned at the end of the article. 

What is Searching in Data Structure?

The process of finding the desired information from the set of items stored in the form of elements in the computer memory is referred to as ‘searching in data structure’. These sets of items are in various forms, such as an array, tree, graph, or linked list. Another way of defining searching in the data structure is by locating the desired element of specific characteristics in a collection of items. 

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Searching Methods in Data Structures

Searching in the data structure can be done by implementing searching algorithms to check for or retrieve an element from any form of stored data structure. These algorithms are categorised based on their type of search operation, such as:

• Sequential search

The array or list of elements is traversed sequentially while checking every component of the set.

For example, Linear Search.

• Interval Search

Algorithms designed explicitly for searching in sorted data structures are included in the interval search. The efficiency of these algorithms is far better than linear search algorithms.

For example, Binary Search, Logarithmic Search.

These methods are examined based on the time taken by an algorithm to search an element matching the search item in the data collections and are given by,

• The best possible time
• The average time
• The worst-case time

The primary concerns are regarding worst-case times that lead to guaranteed predictions of the algorithm’s performance and are also easy to calculate compared to average times. 
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To illustrate examples and concepts in this article, ‘n’ items in the data collection in any data format are considered. Dominant operations are used to simplify analysis and algorithm comparison. For searching in a data structure, a comparison is a dominant operation, which is denoted by O() and pronounced as “big-Oh” or “Oh”.   

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There are numerous searching algorithms in a data structure such as linear search, binary search, interpolation search, jump search, exponential search, Fibonacci search, sublist search, the ubiquitous binary search, unbounded binary search, recursive function for substring search, and recursive program to search an element linearly in the given array. The article is restricted to linear and binary search algorithms and their working principles.

Let’s get detailed insight into the linear search and binary search in the data structure.

Linear Search

The linear search algorithm searches all elements in the array sequentially. Its best execution time is one, whereas the worst execution time is n, where n is the total number of items in the search array.

It is the most simple search algorithm in data structure and checks each item in the set of elements until it matches the search element until the end of data collection. When data is unsorted, a linear search algorithm is preferred.

Linear search has some complexities as given below:

• Space Complexity

Space complexity for linear search is O(n) as it does not use any extra space where n is the number of elements in an array.

• Time Complexity

*Best- case complexity = O(1) occurs when the search element is present at the first element in the search array.

*Worst- case complexity = O(n) occurs when the search element is not present in the set of elements or array.

*Average complexity = O(n) is referred to when the element is present somewhere in the search array.

Example,

Let’s take an array of elements as given below:

45, 78, 12, 67, 08, 51, 39, 26

To find ‘51’ in an array of 8 elements given above, a linear search algorithm will check each element sequentially till its pointer points to 51 in the memory space. It takes O(6) time to find 51 in an array. To find 12, in the above array, it takes O(3), whereas, for 26, it requires O(8) time.  

Binary Search

This algorithm finds specific items by comparing the middlemost items in the data collection. When a match occurs, it returns the index of the item. When the middle item is greater than the item, it searches for a central item of the left sub-array. In contrast, if the middle item is smaller than the search item, it explores the middle of the item in the right sub-array. It continues searching for an item until it finds it or until the sub-arrays size becomes zero.

Binary search needs sorted order of items. It is faster than a linear search algorithm. It works on the divide and conquers principle.

Run-time complexity = O(log n) 

The binary search algorithm has complexities as given below:

• Worst-case complexity = O (n log n)
• Average complexity = O (n log n)
• Best case complexity = O (1)

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Example,

Let’s take a sorted algorithm of 08 elements:

08, 12, 26, 39, 45, 51, 67, 78

To find 51 in an array of the above elements,

The algorithm will divide an array into two arrays, 08, 12, 26, 39 and 45, 51, 67, 78

As 51 is greater than 39, it will start searching for elements on the array’s right side.

It will further divide the into two such as 45, 51 and 67, 78

As 51 is smaller than 67, it will start searching left of that sub-array.

That subarray is again divided into two as 45 and 51.

As 51 is the number matching to the search element, it will return its index number of that element in the array.

It will conclude that the search element 51 is located at the 6th position in an array.

Binary search reduces the time to half as the comparison count is reduced significantly than the linear search algorithm. 

Read: Types of Data Structures in Python

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Interpolation Search

It is an improved variant of the binary search algorithm and works on the search element’s probing position. Similar to binary search algorithms, it works efficiently only on sorted data collection. 

Worst execution time = O(n)

When the target element’s location is known in the data collection, an interpolation search is used. To find a number in the telephone directory, if one wants to search Monica’s telephone number, instead of using linear or binary search, one can directly probe to memory space storage where names start from ‘M’. 

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Hashing

One of the most widely used searching techniques in data structure, the underlying method of hashing transforms how we access and retrieve data. Fundamental to hashing are hash functions, which convert input data into fixed-size values called hashes. Hashing allows constant access, providing a direct path to the element of interest.

To explain searching in data structure, let’s examine the intricacies of creating hash functions and overcoming potential obstacles like collisions as we go into the principles of hashing.

Understanding Hashing

Hashing is essentially the same as a secret code for data. An input (or key) is passed to a hash function, which converts it into a fixed-length string of characters—typically a combination of integers and letters. The generated hash is then used to search data structures, usually an array, as an index or address to find the corresponding data.

Compromises in hashing

Hashing has trade-offs, even if it has constant-time access appeal. The quality of the hash function determines how efficient hashing is; poorly constructed methods can increase collisions and reduce performance. Furthermore, overly complicated hash functions could introduce computational costs.

Selecting the best hash function and collision resolution plan requires considering the dataset’s unique properties and anticipated usage patterns. One must strike a balance between simplicity, efficiency, and uniform distribution.

Depth-First Search (DFS)

When we move from what is searching in data structure in linear structures to the more complex domain of trees, Depth-First Search (DFS) becomes a key method to investigate tree branch searching in DS. 

The structural diversity of trees and graphs is easily accommodated by DFS in algorithms for searching. The implementation is elegant because of its recursive nature, which mimics the innate recursive structure of trees. The traversal’s depth-first design is advantageous when focusing on taking a path and working your way to the end rather than examining other options.

Let’s examine the versatility and effectiveness of DFS for searching operation in data structure by exploring its uses in various tree-based structures, such as binary trees and graphs. 

How Depth-First Search Works

DFS investigates as thoroughly as possible along one branch, starting with the root of a tree or a selected node in a graph, and then turns around to examine other branches. The process continues till every node has been visited.

Applications of DFS in binary trees

DFS fits in well with the structure of binary trees. It performs well when the objective is to search for a specific element or navigate the whole depth of the tree. Pre-order, in-order, and post-order DFS variations provide flexibility in capturing various facets of the tree’s contents and structure.

• Preorder DFS: Visits the live node before any offspring. To create a sorted list for binary search trees, in-order DFS visits the left child first, then the current node, and lastly, the right child.
• Post-order DFS: Frequently employed to remove nodes from a tree, it visits the children before the current node.

Breadth-First Search (BFS)

Breadth-First Search (BFS) is a logical and systematic way to explore a tree’s levels. In contrast to Depth-First Search (DFS), BFS chooses a different approach by focusing on the shallowest levels before going deeper. 

Let’s examine the complexities of BFS, how to use it for search in data structure, its benefits, and applications.

How Breadth-First Search Works

BFS goes through a tree or graph level by level, methodically investigating every node at each level before going on to the next. The method ensures a thorough examination of the entire structure by gradually covering each level, starting from the root (or a selected node). BFS uses a queue data structure to keep track of the node processing order, which promotes a systematic and well-organized traversal.

Applications of BFS

• Shortest Path Finding: BFS works exceptionally well when determining the shortest path is essential. BFS determines the shortest path from the root to any reachable node by methodically investigating levels. Because of this feature, BFS is an excellent option for applications such as navigation systems and network routing.
• Least Spanning Trees: BFS helps determine a graph’s least spanning trees. By methodically examining the graph, BFS finds the edges that make up the minimum spanning tree—a tree that spans all nodes with the lowest feasible total edge weight.
• Connected Components: BFS is skilled at locating connected components while working with undirected graphs. BFS assists in classifying nodes into discrete connected components by beginning at a node and investigating every reachable node.

Benefits of BFS

• Optimal Path Finding: BFS ensures that the shortest path will always be used to reach a target node first. Because of its optimality, it is recommended in situations where accuracy and efficiency are crucial.
• Whole Investigation: BFS ensures that every level in a tree or graph is thoroughly and methodically investigated. When processing or analyzing every node in an organized way is the objective, this feature is helpful.
• Easily Implemented: Compared to more intricate traversal algorithms, BFS is comparatively simple to build due to its simplicity. Its popularity across various applications can be attributed in part to its simplicity.

Future Trends in Data Structure

Emerging technologies are changing the way we define searching in data structure in response to our increasingly digitally complex environment, which has seen an increase in demands driven by data. Future trends are set to transform data generation, organization, and consumption, as demonstrated by a 45% increase in AI integration. 

Data structures have several uses in the rapidly changing technological scene, ranging from decentralized methods to quantum-inspired systems. Let’s explore some of these trends:

• Quantum Realm Navigation via Quantum Data Structures

Designing quantum data structures becomes important as quantum computing gets closer to being a reality. Quantum algorithms may prove challenging for use in conventional data structures.

Quantum data structures are expected to rise, using the concepts of superposition and entanglement. These structures will transform the effectiveness of quantum algorithms for information processing by optimizing data representation and manipulation in quantum computing environments.

• Decentralized Information Structures

Decentralized data structures are now possible thanks to blockchain technology, which puts the traditional centralized methods of the types of searching in data structure to the test. 

Decentralized data structures provide improved ownership, security, and transparency. They are frequently built on distributed ledger technology. Users now have more control over the data they own, and the immutability of blockchain guarantees data integrity. Decentralized data structures might play a key role in applications in the future, such as transparent supply chain tracking and safe identity management.

• Self-Correcting Data Structures

Modern data is dynamic, necessitating any type of searching in data structures to be flexible. Self-adjusting data structures are modeled after self-healing systems and can optimize and rearrange their configurations in response to environmental changes, usage patterns, or data properties. 

By increasing system flexibility and efficiency, these structures should lessen the requirement for human involvement in data structure management.

• Adaptive Memory Allocation Frameworks

It is frequently difficult for traditional memory allocation architectures to handle dynamic workloads effectively. The creation of dynamic memory allocation structures capable of deallocating and allocating memory intelligently in response to real-time demand will likely be a trend in the future for searching in DSA. 

These architectures are designed to minimize memory fragmentation, maximize resource utilization, and enhance overall system performance, especially in workload-varying applications.

• Data Structures for Privacy

The development of data structures that put data safety and protection first is driven by privacy concerns. Private-preserving algorithms for searching, homomorphic encryption methods, and cryptographic data structures are becoming essential for protecting confidential data. 

Privacy preservation will be given top priority in the future for search in data structure, enabling people to keep control over their data while also taking advantage of cutting-edge computational capabilities.

Conclusion

Searching in data structures refers to finding a given element in the array of ‘n’ elements. There are two categories, viz. Sequential search and interval search in searching. Almost all searching algorithms are based on one of these two categories. Linear and binary searches are the two simple and easy-to-implementing algorithms in which binary works faster than linear algorithms.

Though linear search is most straightforward, it checks each element until it finds a match to the search element, thus efficient when data collection is not sorted correctly. But, if the data collection is sorted and the length of an array is considerable, then binary search is faster.

The data structure is an essential part of computer programming while dealing with datasets. Programmers and developers need to keep updating and upskilling themselves with basics and updates in computer programming techniques. Programmers dealing with data structure should opt for courses often.  

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