Searching in Data Structure: Different Search Methods Explained

In today’s rapidly expanding communication network, businesses are going digital to enhance management efficiency searching in DSA. With the increasing amount of data generated on the internet, datasets are becoming more complex. To carefully and efficiently organize, manage, access, and analyze data, utilizing a data structure is crucial. This article focuses on the significance of data structures, exploring the fundamental concept of searching. It delves into various search techniques, including linear and binary search, evaluating their complexities, strengths, and weaknesses.

This article was published as a part of the Data Science Blogathon.

What is a Data Structure?

In computer science, data structures(searching in DSA) serve as the foundation for abstract data types (ADT), where ADT is the logical form of data types. The physical design of data types is implemented using data structures. various types of data structures are used for different types of applications; some are specialized in specific tasks.

Data structures are referred to as a collection of data values and relationships between them, functions, and operations applicable to the data. so that, users can easily access and modify the data efficiently.

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

The concepts of searching in a data structure, as well as its methods, are covered in this article.

What is Searching in Data Structure?

Searching in data structure refers to the process of finding the required information from a collection of items stored as elements in the computer memory. These sets of items are in different forms, such as an array, linked list, graph, or tree. Another way to define searching in the data structures is by locating the desired element of specific characteristics in a collection of items.

Different Searching Metods

Searching in DSA can be done by applying searching algorithms to check for or extract an element from any form of stored data structure.

These algorithms are classified according to the type of search operation they perform, such as:

• Sequential search
  The list or array of elements is traversed sequentially while checking every component of the set. For example – Linear Search.
• Interval Search
  The interval search includes algorithms that are explicitly designed for searching in sorted data structures. In terms of efficiency, these algorithms are far better than linear search algorithms. Example- Logarithmic Search, Binary search.

These methods are evaluated 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 with worst-case times, which provide guaranteed predictions of the algorithm’s performance and are also easier to calculate than average times.

To illustrate concepts and examples in this article, we are assuming ‘n’ items in the data collection in any data format. To make analysis and algorithm comparison easier, dominant operations are used. A comparison is a dominant operation for searching in a data structure, denoted by O() and pronounced as “big-Oh” or “Oh.”

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

Let’s take a closer look at the linear and binary searches in the data structure.

What is Linear Search?

The linear searching in DSA iteratively searches all elements of the array. It has the best execution time of one and the worst execution time of n, where n is the total number of items in the search array.

It is the simplest searching in DSA and checks each item in the set of elements until it matches the searched element till the end of data collection. When the given data is unsorted, a linear search algorithm is preferred over other search algorithms.

Complexities in linear search are given below:

Space Complexity

Since linear searching in DSA uses no extra space, its space complexity is O(n), where n is the number of elements in an array.

Time Complexity

• Best-case complexity = O(1) occurs when the searched item is present at the first element in the search array.
• Worst-case complexity = O(n) occurs when the required element is at the tail of the array or not present at all.
• Average- case complexity = average case occurs when the item to be searched is in somewhere middle of the Array.

Pseudocode for Linear Search Algorithm

procedure linear_search (list, value)

   for each item in the list
      if match item == value
         return the item's location
      end if
   end for

end procedure

Let’s take the following array of elements:

45, 78, 15, 67, 08, 29, 39, 40, 12, 99

To find ‘29’ in an array of 10 elements given above, as we know linear search algorithm will check each element sequentially till its pointer points to 29 in the memory space. It takes O(6) time to find 29 in an array. To find 15, in the above array, it takes O(3), whereas, for 39, it requires O(7) time.

What is Binary Search?

This algorithm locates specific items by comparing the middlemost items in the data collection. When a match is found, it returns the index of the item. When the middle item is greater than the search item, it looks for a central item of the left sub-array. If, on the other hand, the middle item is smaller than the search item, it explores for the middle item in the right sub-array. It keeps looking for an item until it finds it or the size of the sub-arrays reaches zero.

Binary search needs sorted order of items of the array. It works faster than a linear search algorithm. The binary search uses the divide and conquers principle.

Run-time complexity = O(log n)

Complexities in binary search are given below:

• The worst-case complexity in binary search is O(n log n).
• The average case complexity in binary search is O(n log n)
• Best case complexity = O (1)

Pseudocode for Binary Search Algorithm

Procedure binary_search
   A ← sorted array
   n ← size of array
   x ← value to be searched

   Set lowerBound = 1
   Set upperBound = n 

   while x not found
      if upperBound < lowerBound 
         EXIT: x does not exists.
   
      set midPoint = lowerBound + ( upperBound - lowerBound ) / 2
      
      if A[midPoint]  x
         set upperBound = midPoint - 1 

      if A[midPoint] = x 
         EXIT: x found at location midPoint
   end while
   
end procedure

Example,

Let’s take a sorted array of 08 elements:
09, 12, 26, 39, 45, 61, 67, 78

• To find 61 in an array of the above elements,
• The algorithm will divide an array into two arrays, 09, 12, 26, 39 and 45, 61, 67, 78
• As 61 is greater than 39, it will start searching for elements on the right side of the array.
• It will further divide the into two such as 45, 61 and 67, 78
• As 61 is smaller than 67, it will start searching on the left of that sub-array.
• That subarray is again divided into two as 45 and 61.
• As 61 is the number matching to the search element, it will return the index number of that element in the array.
• It will conclude that the search element 61 is located at the 6th position in an array.

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

Also Read: String Data Structure in Python | Complete Case Study

What is Interpolation Search?

It’s a better version of the binary searching in DSA that focuses on the probing position of the search element. It only works on sorted data collection, similar to binary search algorithms.

Complexities in interpolation search are given below:

• When the middle (our approximation) is the desired key, Interpolation Search works best. As a result, the best case time complexity is O(1).
• If the data set is sorted and distributed uniformly, the interpolation search’s average time complexity is O(log2(log2n)), where n denotes the total of elements in an array.
• In the worst-case scenario, we’ll have to traverse the entire array, which will take O(n) time.

An interpolation search is used when the location of the target element is known in the data collection. If you want to find Rahul’s phone number in the phone book, instead of using a linear or binary search, you can directly probe to memory space storage where names begin with ‘R’.

Pseudocode for Interpolation Search Algorithm

A → Array list
N → Size of A
X → Target Value

Procedure Interpolation_Search()

   Set Lo  →  0
   Set Mid → -1
   Set Hi  →  N-1

   While X does not match
   
      if Lo equals to Hi OR A[Lo] equals to A[Hi]
         EXIT: Failure, Target not found
      end if
      
      Set Mid = Lo + ((Hi - Lo) / (A[Hi] - A[Lo])) * (X - A[Lo]) 

      if A[Mid] = X
         EXIT: Success, Target found at Mid
      else 
         if A[Mid]  X
            Set Hi to Mid-1
         end if
      end if
   End While

End Procedure

Master All Searching Techniques

Mastering the art of searching in DSA is essential in today’s data-driven world. By understanding and implementing efficient search algorithms, you can unlock valuable insights and make informed decisions. As you delve into data structures, consider taking your skills to the next level with our Blackbelt program. With its comprehensive curriculum and hands-on projects, the program equips you with the expertise to become a data structure expert. Join the Blackbelt program and embark on a transformative journey towards becoming a proficient data scientist capable of harnessing the power of data structures to drive meaningful impact and innovation.

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Prashant Sharma 15 Feb 2024

Currently, I Am pursuing my Bachelors of Technology( B.Tech) from Vellore Institute of Technology. I am very enthusiastic about programming and its real applications including software development, machine learning and data science.