Linear Search Algorithm | Example | Time Complexity

Searching-

 

  • Searching is a process of finding a particular element among several given elements.
  • The search is successful if the required element is found.
  • Otherwise, the search is unsuccessful.

 

Searching Algorithms-

 

Searching Algorithms are a family of algorithms used for the purpose of searching.

The searching of an element in the given array may be carried out in the following two ways-

 

 

  1. Linear Search
  2. Binary Search

 

In this article, we will discuss about Linear Search Algorithm.

 

Linear Search-

 

  • Linear Search is the simplest searching algorithm.
  • It traverses the array sequentially to locate the required element.
  • It searches for an element by comparing it with each element of the array one by one.
  • So, it is also called as Sequential Search.

 

Linear Search Algorithm is applied when-

  • No information is given about the array.
  • The given array is unsorted or the elements are unordered.
  • The list of data items is smaller.

 

Linear Search Algorithm-

 

Consider-

  • There is a linear array ‘a’ of size ‘n’.
  • Linear search algorithm is being used to search an element ‘item’ in this linear array.
  • If search ends in success, it sets loc to the index of the element otherwise it sets loc to -1.

 

Then, Linear Search Algorithm is as follows-

 

Linear_Search (a , n , item , loc)

 

Begin

for i = 0 to (n - 1) by 1 do

    if (a[i] = item) then

        set loc = i

        Exit

    endif

endfor

set loc = -1

End

 

Time Complexity Analysis-

 

Linear Search time complexity analysis is done below-

 

Best case-

 

In the best possible case,

  • The element being searched may be found at the first position.
  • In this case, the search terminates in success with just one comparison.
  • Thus in best case, linear search algorithm takes O(1) operations.

 

Worst Case-

 

In the worst possible case,

  • The element being searched may be present at the last position or not present in the array at all.
  • In the former case, the search terminates in success with n comparisons.
  • In the later case, the search terminates in failure with n comparisons.
  • Thus in worst case, linear search algorithm takes O(n) operations.

 

Thus, we have-

 

Time Complexity of Linear Search Algorithm is O(n).

Here, n is the number of elements in the linear array.

 

Linear Search Efficiency-

 

  • Linear Search is less efficient when compared with other algorithms like Binary Search & Hash tables.
  • The other algorithms allow significantly faster searching.

 

Linear Search Example-

 

Consider-

  • We are given the following linear array.
  • Element 15 has to be searched in it using Linear Search Algorithm.

 

 

Now,

  • Linear Search algorithm compares element 15 with all the elements of the array one by one.
  • It continues searching until either the element 15 is found or all the elements are searched.

 

Linear Search Algorithm works in the following steps-

 

Step-01:

 

  • It compares element 15 with the 1st element 92.
  • Since 15 ≠ 92, so required element is not found.
  • So, it moves to the next element.

 

Step-02:

 

  • It compares element 15 with the 2nd element 87.
  • Since 15 ≠ 87, so required element is not found.
  • So, it moves to the next element.

 

Step-03:

 

  • It compares element 15 with the 3rd element 53.
  • Since 15 ≠ 53, so required element is not found.
  • So, it moves to the next element.

 

Step-04:

 

  • It compares element 15 with the 4th element 10.
  • Since 15 ≠ 10, so required element is not found.
  • So, it moves to the next element.

 

Step-05:

 

  • It compares element 15 with the 5th element 15.
  • Since 15 = 15, so required element is found.
  • Now, it stops the comparison and returns index 4 at which element 15 is present.

 

To gain better understanding about Linear Search Algorithm,

Watch this Video Lecture

 

Next Article- Binary Search

 

Get more notes and other study material of Design and Analysis of Algorithms.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Summary
Linear Search Algorithm | Example | Time Complexity
Article Name
Linear Search Algorithm | Example | Time Complexity
Description
Linear Search Algorithm is the simplest searching algorithm. Linear Search Algorithm Example & Time Complexity. Linear Search Algorithm searches for an element by comparing it with each element of the array.
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Gate Vidyalay
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