Searching is an essential operation performed everywhere. Searching is vital whether it’s finding a chapter in a book, locating a specific file in a computer file storage, or anything else. Searching, in data structures, is the process through which the target element is found within a given dataset. Based on the structure of data and desired outcomes, many different search algorithms can be implemented. The rate at which data is being created over the internet is rising, and data sets have begun to become exceptionally complex. The efficient, careful organisation and easy access and manipulation of data require it to rely on some data structure.

In this article, we will cover searching in data structures and various searching techniques & algorithms, pseudo-codes, characteristic features, and applications. It also discusses the general significance of searching, the problems that it resolves, and the impact that it has on other aspects of computing.

What is Searching in Data Structure?

Searching involves finding a specific item or a piece of information within a collection of items. The main objective of searching is to determine whether the target element exists within the data, and if so, then find its precise position or location. Searching algorithms are implemented to check for an element or retrieve an element from any data structure where it is stored. Searching is crucial in applications right from databases to operating systems where information has to be retrieved quickly and effectively. An efficient searching algorithm tries to minimise the number of comparisons or operations necessary to obtain an element being searched for.

Searching in data structure means finding the required information from a collection of items stored as elements in computer memory. Most of the time, the searching complexity determines the optimality of the algorithm for a given problem.

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Characteristics of Searching Algorithms

Designing effective algorithms and choosing the best searching technique requires an understanding of searching algorithm characteristics. Here are the key characteristics of the search algorithm:

Completeness: A search algorithm is said to be complete if it is ensured to find a solution (or the target element at hand) whenever one exists. For instance, these will always be able to locate a certain element or a certain path if it exists. An example would be breadth-first search (BFS) in graphs which ensures that, if a solution exists, it shall be obtained at some instant during the search process.

Stability: Stability addresses how an algorithm treats elements that are equal concerning the search criterion. A stable algorithm maintains the relative order of the elements.

Time Complexity: Time complexity analyses the number of steps taken by any search algorithm about the input size n and hence the speed iterating times of the algorithm is understood. Various arrangements e.g. arrays, trees, and hash tables increase the number of operations necessary to conduct a search and vice versa.

Space Complexity: Space complexity refers to the amount of storage that an algorithm requires other than that used to contain the input. Auxiliary space denotes the extra space the algorithm requires when solving a problem besides the input data.

Optimality: An algorithm could also be said to be optimal if it can obtain the most optimised solution such as the shortest distance between two points.

Deterministic vs Non-deterministic: Binary search is one example of a deterministic search algorithm, which takes a methodical and transparent approach. Others, like linear search, are non-deterministic as, in the worst situation, they might have to look across the whole search space.

Adaptability: Adaptability measures how well an algorithm can handle different input structures and characteristics. Some algorithms are adaptive, meaning they adjust their strategy based on the properties of the input.

Iterative vs Recursive: Compared to recursive methods, iterative algorithms usually consume less space (O(1) space complexity) by repeating processes over loops. Recursive algorithms, on the other hand, divide the problem into smaller subproblems by using function calls.

Types of Searching Algorithms

Searching plays an important role in finding the target element but doing this efficiently requires an understanding of different types of algorithms. Here are the different types of search algorithms:

Linear Search

Linear search, or sequential search, is one of the most simplest and basic search algorithms. It checks all the elements of the data structure one by one in a sequence until it finds the target element or reaches the last element.

Linear Search compares the search element with each array element, beginning with the first element and working its way through the remaining elements Until a match is found or the array’s end is reached.

Pseudo Code

function linearSearch(array, target):
for i = 0 to size of array:
if array[i] == target:
return i // Target is found
return -1 // Target not found

Time Complexity

Best Case: O(1), target found at the first position

Worst Case: O(n), target is at the end or not present

Average Case: O(n/2), assumes the target is equally likely to be at any position or simply O(n).

Space Complexity

O(1) (Constant space)

Binary Search

Binary search is an advanced version of linear search. However, it requires the data to be sorted. It consists of successively dividing the search interval by half and searching the left or the right depending on whether the target is less or greater than the mid element.

Simply, the first step in a binary search is to compare the target value with the array’s middle element. The search is finished if the target equals the middle element. The search proceeds in the lower half of the array if the target is smaller, and in the upper half if it is larger. Until the target is located or the search space is depleted, this halving keeps happening.

Pseudo Code

function binarySearch(array, target):
left = 0
right = size of array - 1
while left <= right:
middle = (left + right) / 2
if array[middle] == target:
return middle
else if array[middle] < target:
left = middle + 1
else:
right = middle - 1
return -1 // Target not found

Time Complexity

Best Case: O(1), target found in the middle

Worst Case: O(log n), dividing search space until size 1

Interpolation search is an improvement over binary search for uniformly distributed data. Rather than splitting the interval into half, this algorithm predicts the target location based on the proportional distribution of the array’s elements.

Pseudo Code

function interpolationSearch(array, target):
low = 0
high = size of array - 1
while low <= high and target >= array[low] and target <= array[high]:
position = low + ((target - array[low]) * (high - low)) / (array[high] - array[low])
if array[position] == target:
return position
if array[position] < target:
low = position + 1
else:
high = position - 1
return -1 // not found

Time Complexity

Best Case: O(1), ideal uniform distribution

Worst Case: O(n), poor distribution, target near the end

Average Case: O(log log n), uniform distribution

Space Complexity

O(1), as it operates in constant space

Exponential Search

Exponential search deals with unbounded (infinite) lists. It functions by first determining an interval within which the target element lies and thereafter, it performs binary search within the defined range.

Pseudo Code

function exponentialSearch(array, target):
if array[0] == target:
return 0
i = 1
while i < length of array and array[i] <= target:
i *= 2
return binarySearch(array, target, i/2, min(i, length of array - 1))

Time Complexity

Best Case: O(1), the target found in the first comparison

Worst Case: O(log n), Doubling indices, then binary search

Average Case: O(log n)

Space Complexity

O(1), as it operates in constant space

Jump Search

Jump search moves forward a certain number of steps at a time in the sorted array to get near the target and switches to linear search within this target interval. This algorithm involves moving forward by a fixed step and then executing a linear search backward from the current place until the target is discovered. The step is typically sqrt(n) where n is the array size, which is critical for maximising search performance.

Pseudo Code

function jumpSearch(array, target):
n = length of array
step = sqrt(n)
prev = 0
while array[min(step, n) - 1] < target:
prev = step
step += sqrt(n)
if prev >= n:
return -1
for i = prev to min(step, n):
if array[i] == target:
return i
return -1

Time Complexity

Best Case: O(1), target found at the first jump

Worst Case: O(√n), Searching within sub-blocks

Average Case: O(√n)

Space Complexity

O(1), as it operates in constant space

Fibonacci Search

The Fibonacci search is yet another variation of the binary search that makes use of Fibonacci numbers to segment the array into various subarrays. For certain types of data distributions, it is more effective as compared to binary search.

A sorted array can be searched using the Fibonacci search method by splitting it up into portions of a certain proportion. It starts by comparing the element at a position defined by a Fibonacci number with the target value, progressively narrowing down the search space based on Fibonacci values. This process continues until the target is found or the search space is empty.

Pseudo Code

function fibonacciSearch(array, target):
fibMMm2 = 0 // m-2th no
fibMMm1 = 1 // m-1th no
fibM = fibMMm2 + fibMMm1 // mth no
while fibM < n:
fibMMm2 = fibMMm1
fibMMm1 = fibM
fibM = fibMMm2 + fibMMm1
offset = -1
while fibM > 1:
i = min(offset + fibMMm2, n-1)
if array[i] < target:
fibM = fibMMm1
fibMMm1 = fibMMm2
fibMMm2 = fibM - fibMMm1
offset = i
else if array[i] > target:
fibM = fibMMm2
fibMMm1 = fibMMm1 - fibMMm2
fibMMm2 = fibM - fibMMm1
else:
return i
return -1 // Target not found

Time Complexity

Best Case: O(1), when the target is found at the initial position

Worst Case: O(log n)

Average Case: O(log n), due to the efficient partitioning of the search space

Space Complexity

O(1), as it operates in constant space

Ternary Search

The ternary search algorithm divides the array into three parts and then decides whether the element is in the first, second, or last third of the array. It is a more generalised form and is used for specific types of arrays, for which it can outperform binary search.

The process begins by finding the two midpoints to divide the array into three equal segments. Whichever position is chosen as equal in between decides which segment to follow and the other two-thirds are discarded for every step of the process. The process continues until either the target element is found or the search boundary is exhausted.

Pseudo Code

function ternarySearch(array, left, right, target):
if right >= left:
mid1 = left + (right - left) / 3
mid2 = right - (right - left) / 3
if array[mid1] == target:
return mid1
if array[mid2] == target:
return mid2
if target < array[mid1]:
return ternarySearch(array, left, mid1 - 1, target)
else if target > array[mid2]:
return ternarySearch(array, mid2 + 1, right, target)
else:
return ternarySearch(array, mid1 + 1, mid2 - 1, target)
return -1 // Target not found

Time Complexity

Best Case: O(1), If the element is found at the first middle.

Worst Case: O(log3 n), better than Binary Search.

Average Case: O(log3 n), divides the search space into three parts.

Space Complexity

O(1), as it operates in constant space in the case of an iterative approach.

Searching in Non-linear Data Structures

Non-linear data structures also use the searching to search for an element efficiently. There are various non-linear data structures such as trees, graphs, etc.

Searching in Trees

Trees are hierarchical data structures that consist of nodes and connecting nodes with various levels. Searching in a tree involves various algorithms depending on the type of tree (binary, AVL, BST, etc.).

Binary Search Tree (BST): The BST algorithm goes on to traverse the tree from the root node, continuously moving to the left if the target value is smaller than the current node and to the right if it is larger.

function searchBST(root, target):
if root == null or root.value == target:
return root
if target < root.value:
return searchBST(root.left, target)
else:
return searchBST(root.right, target)

Time Complexity

Best Case: O(1), the target is at the root node

Worst Case: O(n), unbalanced tree, like a linked list

Average Case: O(log n), balanced tree

Space Complexity

O(n), for a balanced tree, due to storage of nodes.

Searching in Graphs

Graph search involves traversing nodes connected by edges. Graphs also utilise the searching algorithms to search for a node using two different techniques: DFS and BFS.

Depth-First Search (DFS)

DFS explores as far as possible along each branch before backtracking. DFS is a traversal technique, starting from the root node and moving through the nodes as far as it can till it reaches the node that has no unvisited neighbouring nodes.

Pseudo Code

function DFS(graph, node, visited):
if node not in visited:
visited.add(node)
for neighbour in graph[node]:
DFS(graph, neighbour, visited)

Time Complexity

Best Case: O(V), all vertices explored once

Worst Case: O(V + E), exploring all vertices and edges

Average Case: O(V + E)

Space Complexity

O(V), due to the recursion stack or explicit stack and visited array.

Breadth-First Search (BFS)

BFS explores all neighbours at the present depth before moving on to nodes at the next depth level. In other words, before going on to the next level, we first traverse every node on the current level using the BFS traversal technique.

Pseudo Code

function BFS(graph, start):
queue = [start]
visited = set([start])
while queue is not empty:
node = queue.pop(0)
for neighbour in graph[node]:
if neighbour not in visited:
visited.add(neighbour)
queue.append(neighbour)

Time Complexity

Best Case: O(V), as all vertices explored once

Worst Case: O(V + E), for exploring all vertices and edges

Average Case: O(V + E)

Space Complexity

O(V), due to the queue and visited array

Applications of Searching Algorithms

Below are some of the real-world applications and the most popular use cases of searching algorithms:

Database Management: Algorithms developed for searching databases are crucial elements in databases for search-based retrieval of information. To illustrate, Binary Search Trees (BSTs), Hashing, and B-trees improve searching speeds of record access within database management systems.

File Systems: Searching algorithms are used when working with deep hierarchical file systems in operating systems to find files. For instance, when you search for a file on your computer, you utilise algorithms like DFS or BFS to shred any inefficiencies in locating where the file or directory resides.

Web Search Engines: Search engines have developed the skill to index and fetch information with the help of algorithmic measures on the web data. Binary search trees, Hashing, and many other advanced mechanisms work together to produce a ranking order for numerous pages and present the most useful information that matches the user’s search request.

Cybersecurity: Searching algorithms find their applications too in cybersecurity where potential threats can be located and monitored. Pattern-matching algorithms try to find known malware signatures or even any abnormal behaviour in the data to assess possible security threats.

E-commerce: E-commerce platforms tend to operate big product businesses and some algorithms need to be in place to make sure that consumers can be able to find the items that they want on the websites without going through the entire catalogue. Those who write efficient searching algorithms help users to sell more by making sure that the users get pertinent search results.

Network Routing: Searching algorithms contribute significantly to the area of network routing and network pathfinding in graph-based networks. In routing applications, A* search would be used to seek the shortest path, while Dijkstra’s algorithm can be utilised when needed to maximise network flow.

Data Analytics: Searching algorithms like Linear Search and Binary Search, can be employed in data analysis as aids in searching for particular and well-defined records in large datasets.

Artificial Intelligence (AI): Searching algorithms continue to be a major dependency in a wide range of AI use cases with most of them being game-related and robotics. A* heuristic search, Depth-First and Breadth-First Search are also used in AI.

Searching vs Sorting Algorithms

Searching and Sorting both are different terms in computer science. Searching involves finding an element in a given data in the most efficient manner whereas sorting involves arranging the elements in either ascending or descending order in an efficient order.

Here are the key differences between Searching and Sorting algorithms:

Goal: Searching allows identifying certain data and sorting allows getting the data in the sort and order that would ease any subsequent operations.

Dependency: Sorting comes first almost in all cases. For example, in the case of binary search, the argument is that data requires a sorted order to search for an element.

Use Cases: Sorting expects data to be in the form that the researchers require while searching allocates the information. Together, they allow performance improvement of operations in databases, file management, and finally data science providing great resources for processing data.

Types: Searching includes linear search, binary search, interpolation search, etc., whereas sorting includes bubble sort, merge sort, quick sort, etc.

Conclusion

Searching in the data structure is the fundamental operations that help in efficient data retrieval. Searching involves finding an element in the best possible and efficient way with the help of different searching algorithms. With each algorithm tailored to specific needs—whether sequential, binary, or graph-based—choosing the right search method can significantly optimise performance and system responsiveness.

We have covered everything in detail about searching, including types such as linear, binary search, exponential search, interpolation search, etc., and also discussed the binary search tree and DFS and BFS searching algorithms. The time and space complexities of all these algorithms and various applications of searching algorithms have also been discussed in this article.

In today’s data-driven world, knowing the advantages, disadvantages, and complexity of these algorithms helps developers choose the optimal search strategy for their data structures, guaranteeing quicker and more effective processing. Are you an aspiring data scientist? Consider pursuing the Hero Vired Integrated Program in Data Science, Artificial Intelligence, & Machine Learning to advance your career.

FAQs

What is binary search in data structures?

Binary search is an efficient searching algorithm in computer science. Binary search is used for finding the position of a target element in a sorted array and is better than other search algorithms. Binary search has a time complexity of O(log n), which is less compared to linear search on larger datasets.

What is the difference between DFS and BFS in data structures?

Depth-First Search (DFS) and Breadth-First Search (BFS) are two general methods for traversing a graph. In its classic recursive approach, DFS visits a node, then explores the first of its unvisited children, going as deep as possible along that branch until the node contains no more children, at which point it backtracks in the opposite order.
On the other hand, the BFS strategy visits all nodes at the same tree depth before going to the next node, and this level-order traversal uses a queue.

What are the different types of search algorithms?

In data structures, there are various types of search algorithms including linear search, binary search, ternary search, exponential search, Fibonacci search, interpolation search, etc.

What is a search structure?

A search structure is a basic data structure that organises elements in such a way that search operations may be facilitated. Arrays, hash tables, binary search trees (BST), and graph structures are some of the examples of search structures. Each one of these data structures is designed to allow its associated algorithms to function, such as binary search on a sorted array, DFS and BFS on a graph, etc.

What is the algorithm for binary search in data structure?

The algorithm for binary search is as follows:

Initialize two pointers, low and high, at the start and end of the array.

Calculate the middle element index using mid = (low + high) / 2.

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