SEARCHING TECHNIQUES IN DATA STRUCTURE

1. Submitted To :- Submitted By :-
Miss Jaspreet Kaur
(Assistant Prof.)
Parteek Girdhar
(B130020031)

2. Searching Technique :-
It refers to the operation of finding the location LOC of
ITEM in DATA, or printing some message that ITEM
does not appear there. The search is said to be
successful if ITEM does not appear in DATA and
unsuccessful otherwise.

3. Types of Searching :-
Linear Search
 Binary Search

4. Linear Search :-
 It is a technique for finding a particular element in a
list that checks each element in sequence until the
desired element is found or the list is finished. The list
need not be ordered.
For example:- We have an array of 6 elements.
A={1,2,3,4,5,6}
suppose we want to find 5.
for this we have to traverse the array by comparing
each element of array A one by one.

5. How Long Does Linear Search Take?
Best Case :- In this case, the target value is in the first
element of the array. So it is denoted with O(1).
Worst Case :- In this case, the target value is in the
last element of the array. So it is denoted with O(n).
Average Case :- In this case, the target value is
somewhere in the array. So this search takes an
amount of time proportional to half the length of the
array – also proportional to the length of the array –
O(n).

6. Algorithm for Linear Search
LINEAR(DATA,N,ITEM,LOC)
Here DATA is a linear array with N elements, and ITEM is given item of
information. This algorithm finds the location LOC of ITEM in DATA,
or sets LOC:= 0 if the search is unsuccessful.
1. [Insert ITEM at the end of DATA.] 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 of loop.]
4. [Successful?] If LOC =N+1,then: Set LOC:=0.
5. Exit.

7. Binary Search
 In binary search we first access the middle element
of given array.
 If the element to be searched is same as middle
element of array then our search is successful.
 If not then look weather the element is in left or
right half of sub-arrays.
After this apply binary search on sub-arrays.
Given array should be ordered.

8. How a Binary Search Works
Always look at the
center value. Each time
you get to discard half of
the remaining list.
Is this fast ?

9. For example:-
Suppose we have to find the location of a name in a
telephone directory.
For this we will apply Binary Search.
We will find the middle elements first.If it matches
our search element then we will stop here.
If not then we will determine which half contains the
element and we will access the middle elements of that
half.
If middle element is not same then repeat the same
procedure as we did above for each quarter and so on.

10. Algorithm:-
BINARY(DATA,LB,UB,ITEM,LOC)
1. [Initialize = segment variables.]
Set BEG:=LB,END:=UB and MID=INT((BEG+END)2)
2. Repeat step 3 and 4 while BEG<=END and DATA[MID]!=ITEM.
3. If ITEM <DATA[Mid],then:
Set END:=MID-1.
Else:
Set BEG:=MID+1.
[END of If structure.]
4. Set MID:=INT((BEG+END)/2)
[End of step 2 Loop.]
5. If DATA[MID]= ITEM, then:
Set LOC:=MID.
Else:
Set LOC:=NULL.
[End of if structure.]
6. Exit.

11. THANKS ;)