This document describes the linear search algorithm. Linear search sequentially checks each element of a data structure one-by-one to find a target item. It works by traversing the list from the first element until either the target is found or all elements are checked. The worst-case complexity is O(n) as it may need to traverse the entire list. An example linear search on an array is provided to demonstrate how it checks each element sequentially until the target item is found or not.

1. DATA STRUCTURE
LINEAR SEARCH
M.RAMYA
III-MCA
HCC
Trichy

2. Searching: Finding the location of item or
printing some message when item is not
found.
SEARCH
LINEAR BINARY

3. • Linear search: Traversing data sequentially to
locate item is called linear search.
• Ex: Searching an item for operation in array.
• Binary search: Data in array which is sorted in
increasing numerical order or alphabetically.
• Ex: Searching name in telephone directory,
searching words in dictionary.

4. LINEAR SEARCH
• It test whether the ITEM in DATA is present or
not.
• It test the data in sequential manner.
• It searches the data one by one fully and
returns the ITEM as the result.
• Otherwise, it returns the value 0.
• We see this by ALGORITHM.

5. Alg:LINEAR(DATA,N,ITEM,LOC)
• Items explanation:
1. DATA --Linear array
2. N --Number of elements
3. ITEM --Elements to find
4. LOC --Location of the item

6. STEPS:
1. [Insert ITEM at the end] Set DATA[N+1]:=ITEM.
2. [Initialize counter] Set LOC:=1.
3. [Search for ITEM]
Repeat while DATA[LOC]= ITEM:
Set LOC:=LOC+1.
[End if loop]
4. [Successful?]If LOC:=N+1, then ;
Set LOC:=0
5. Exit

7. EXECUTION WITH EXAMPLE
PARTICULARS:
1. DATA [6] =
2. ITEM=G
Cell
name
A B C D E F
Loc 1 2 3 4 5 6

8. • To find the item we are first inserting the item
to the end of the list.
• Step 1: DATA[N+1]=ITEM.
Exp:
N=6
DATA[6]=F
DATA[6+1]=G
• So the item is added at LOC[7]
A B C D E F G
1 2 3 4 5 6 7

9. • Step 2:
Initializing the counter to start the search.
Therefore, LOC=1.
It starts the search from LOC=1{i.e. from
DATA[1]=A}
• Step 3:
WHILE loop is executed till DATA[LOC]=ITEM
From the step 2, LOC=1

10. A B C D E F G
A B C D E F G
A B C D E F G
A B C D E F G
S
E
A
R
C
H
I
N
G
DATA[LOC] =ITEM
LOC=LOC+1
DATA[LOC] =ITEM, LOC=LOC+1
DATA[LOC] =ITEM
LOC=LOC+1
LOC=1
LOC=2
LOC=3

11. A B C D E F G
DATA[LOC] =ITEM,
LOC=LOC+1
S
E
A
R
C
H
I
N
G
A B C D E F G
DATA[LOC] =ITEM,
LOC=LOC+1
A B C D E F G
DATA[LOC]
=ITEM,
LOC=LOC+1
LOC=4
LOC=5
LOC=6

12. Here the item is found
The item ‘G’ is located
So the loop executes until this condition
A B C D E F G
DATA[LOC] =ITEM
LOC=7

13. • STEP 4:
Originally the location is 6. We added the
item at the end.
So the item is located in 7.
LOC=N+1
We reached the condition then
LOC=0
• STEP 5:
Searching is finished and the algorithm exits.

14. COMPLEXITY
• Worst Case: The maximum value to search.
• Complexity is measured by f(n).f(n)=n+1
• The average case is measured by probability.
• Here,
• pk – probability that ITEM appears in DATA[K].
• q – probability that ITEM does not appears in
DATA[K].
• Algorithm uses k comparisons when ITEM
appears in DATA[K].

15. • f(n)=1 . p1 + 2 . p2 + … +n . pn + (n+1) . q
• Suppose, q is very small and ITEm appears in
equal probability, then
q=o and pi=1/n
f(n)=1 . 1/n + 2 . 1/n + … +n . 1/n + (n+1).0
=(1+2+…+n) .1/n
=n(n+1)/2.(1/n)
f(n)=(n+1)/2