This document summarizes the linear search algorithm. It begins with an introduction describing the problem of searching for an element x in an array. It then provides an example with figures and outlines the algorithm which is to start from the leftmost element and compare each element to x. Implementation in various languages is shown. Runtime is analyzed as theta(n) in best, average and worst cases. An example execution is provided to search for the element 2 in a sample array. Other notes classify it as a linear approach and stable algorithm but note it is rarely used practically due to faster alternatives like binary search.

1. Algorithms
Linear Search
Abdelrahman M. Saleh

2. List of contents
● Introduction
● Example w/ illustrating figures
● Algorithm
● implementation (Java, C++, Python)
● Performance Runtime
○ Best, Average and worst cases.
● Execution
● Other Notes

3. Introduction
● Problem : Given an array arr[] of n elements, write a function to search a given element
x in arr[] .
● Linear search is the simplest but most timfull algorithm to find an element .

4. Example w/ illustrating figures

5. Algorithm .
● Start from the leftmost element of arr[] and one by one compare x with each element of
arr[]
● If “x” matches with an element, return the index.
● If “x” doesn’t match with any of elements, return -1.

6. Implementation .
int linearSearch(int arr[], int n, int x)
{
for (int i=0; i<n; i++)
if (arr[i] == x)
return i ;
return -1;
}
//for java add static .
C++ / JAVA
def linearSearch(arr, x):
for i in range(len(arr)):
if arr[i] == x:
return i
return -1
PYTHON

7. Performance Runtime
● Time complexity Θ(n) .
● Best case : when the element is at first index .
● Average case : if it exists between first to last .
● Worst case : if the element doesn’t exist .

8. Execution .
Input array : [4, 6, 3, 2, 1, 9, 7]
Find 2 .
if(4 == 2) no
if(6 == 2) no
if(3 == 2) no
if(2 == 2) return 3
Element exists at index 3.

9. Other Notes .
● Algorithmic Paradigm: Linear Approach
● Stable: Yes
● Linear search is rarely used practically because other search algorithms such as the binary
search algorithm and hash tables allow significantly faster searching comparison to Linear
search.