Searching Linear & Binary Search.....subject data structure

1. LINEAR SEARCH
Presented By
Nikunj Patel
Parth Patel
DATA
STRUCTURE

2. Searching: Finding the location of
item or printing some message when
item is not found.
SEARC
H
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

11. A B C D E F G
S
E
A
R
C
H
I
N
G
A B C D E F G
A B C D E F G

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

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. Binary Search
• If the array is sorted, then we can apply the binary
search technique.
number
• The basic idea is straightforward. First search the
value in the middle position. If X is less than this
value, then search the middle of the left half next. If
X is greater than this value, then search the middle
of the right half next. Continue in this manner.
5 12 17 23 38 44 77
0 1 2 3 4 5 6 7 8
84 90

15. Sequence of Successful Search - 1
5 12 17 23 38 44 77
0 1 2 3 4 5 6 7 8
84 90
search( 44 )low high mid
0 8#1
highlow



 

2
highlow
mid
38 < 44 low = mid+1 = 5
mid
4

16. Sequence of Successful Search - 2
5 12 17 23 38 44 77
0 1 2 3 4 5 6 7 8
84 90
search( 44 )low high mid
0 8#1



 

2
highlow
mid
44 < 77high = mid-1=5
4
mid
6
highlow
5 8#2

17. Sequence of Successful Search - 3
5 12 17 23 38 44 77
0 1 2 3 4 5 6 7 8
84 90
search( 44 )low high mid
0 8#1



 

2
highlow
mid
44 == 44
4
5 8#2 6
highlow
5 5#3
mid
5
Successful Search!!

18. Sequence of Unsuccessful Search
- 4
5 12 17 23 38 44 77
0 1 2 3 4 5 6 7 8
84 90
search( 45 )low high mid
0 8#1



 

2
highlow
mid
4
5 8#2 6
5 5#3 5
high low
6 5#4
Unsuccessful Search
low > highno more elements to search

19. Binary Search Routine
public int binarySearch (int[] number, int searchValue) {
int low = 0,
high = number.length - 1,
mid = (low + high) / 2;
while (low <= high && number[mid] != searchValue) {
if (number[mid] < searchValue) {
low = mid + 1;
} else { //number[mid] > searchValue
high = mid - 1;
}
mid = (low + high) / 2; //integer division will
truncate
}
if (low > high) {
mid = NOT_FOUND;
}
return mid;
}