Searching techniques in Data Structure And Algorithm

SEARCHING TECHNIQUES
DATA STRUCTURE AND
ANALYSIS
Instructor
Pir Syed M Ayaz Farid Shah

What is searching?
 Searching is an operation or a technique that
helps finds the place of a given element or
value in the list. Any search is said to be
successful or unsuccessful depending upon
whether the element that is being searched is
found or not.

Searching Techniques
There are tow types of searching in data
structure and analysis
 Linear Search
 Binary Search
 Interpolation Search

Linear Search
Linear search is a very simple search algorithm.
In this type of search, a sequential search
is made over all items one by one. Every item is
checked and if a match is found then that
particular item is returned, otherwise the search
continues till the end of the data
collection.

Linear Search Algorithm
 Linear Search ( Array A, Value x)
 Step 1: Set i to 1
 Step 2: if i > n then go to step 7
 Step 3: if A[i] = x then go to step 6
 Step 4: Set i to i + 1
 Step 5: Go to Step 2
 Step 6: Print Element x Found at index i and go to
step 8
 Step 7: Print element not found
 Step 8: Exit

Binary search
Binary search is a fast search algorithm with run-time complexity of Ο(log n).
This search
algorithm works on the principle of divide and conquer. For this algorithm to
work properly,
the data collection should be in the sorted form.
Binary search looks for a particular item by comparing the middle most item of
the
collection. If a match occurs, then the index of item is returned. If the middle
item is
greater than the item, then the item is searched in the sub-array to the right of
the middle
item. Otherwise, the item is searched for in the sub-array to the left of the
middle item.
This process continues on the sub-array as well until the size of the subarray
reduces to
zero.

Binary Search Algorithm
 Compare x with the middle element.
 If x matches with middle element, we return
the mid index.
 Else If x is greater than the mid element, then
x can only lie in right half subarray after the
mid element. So we recur for right half.
 Else (x is smaller) recur for the left half.

Binary vs. Linear Search
•Input data needs to be sorted in Binary Search and not in Linear Search
•Linear search does the sequential access whereas Binary search access
data randomly.
•Time complexity of linear search -O(n) , Binary search has time complexity
O(log n).
• Linear search performs equality comparisons and Binary search performs
ordering comparisons

Interpolation Search
Interpolation search is an improved variant of binary
search. This search algorithm works on the probing
position of the required value. For this algorithm to work
properly, the data collection should be in a sorted form
and equally distributed.
Binary search has a huge advantage of time complexity
over linear search. Linear search has worst-case
complexity of Ο(n) whereas binary search has Ο(log n).
There are cases where the location of target data may
be known in advance. For example, in case of a
telephone directory, if we want to search the telephone
number of Morphius. Here, linear search and even
binary search will seem slow as we can directly jump to
memory space where the names start from 'M' are
stored.

Interpolation Search Algorithm
Step 1 − Start searching data from middle of the list.
Step 2 − If it is a match, return the index of the item, and exit.
Step 3 − If it is not a match, probe position.
Step 4 − Divide the list using probing formula and find the new midle.
Step 5 − If data is greater than middle, search in higher sub-list.
Step 6 − If data is smaller than middle, search in lower sub-list.
Step 7 − Repeat until match.

Binary vs. Interpolation Search
 Positioning in Binary Search
 Position Probing in Interpolation Search

Searching techniques in Data Structure And Algorithm

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