Data structure

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

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

• 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.

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.

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

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

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

• 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

• 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

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

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

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

• 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.

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].

• 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

Data structure

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