The document discusses various searching algorithms and their time complexities. It describes linear search, binary search, jump search, interpolation search, exponential search, sublist search, Fibonacci search. Linear search has a time complexity of O(n) while binary search has O(log n) time complexity. Binary search uses a divide and conquer approach to search sorted data more efficiently. Exponential and Fibonacci searches also have O(log n) time complexity for bounded arrays.

2. CS702
ADVANCED
ALGORITHMS ANALYSIS
AND DESIGN
MUHAMMAD JIBREEL SAMMAR
ID:(MS210400019)

3. MY TOPIC
SEARCHING
ALGORITHMS AND
THEIR EFFICIENCY,
CONSIDERING TIME
COMPLEXITY

4. SEARCHING ALGORITHMS AND THEIR
EFFICIENCY
•Searching algorithms is a basic, fundamental
step in computing done via step-by-step method
to locate a specific data among a collection of
data.
•any algorithm which solves the search problem,
namely, to retrieve information stored within
some data structure, or calculated in the search
space of a problem domain, either with discrete
or continuous values.
•Searching Algorithms are designed to check
or retrieve an element from any data
structure where it is being stored.
Define: Searching
algorithms?

5. algorithms are mainly classified in 2 categories according to
their type of search operations
. sequential search in this, the list or array is traversed
sequentially and every element is checked.
• interval search these algorithms are specifically designed for
searching in sorted data-structures. these type of searching algorithms
are more efficient than linear search method.
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

6. • LINEAR SEARCH
• BINARY SEARCH
• JUMP SEARCH
• INTERPOLATION SEARCH
• EXPONENTIAL SEARCH
• SUBLIST SEARCH (SEARCH A LINKED LIST IN
ANOTHER LIST)
• FIBONACCI SEARCH
• THE UBIQUITOUS BINARY SEARCH
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY
Types of Searching Algorithms

7. Linear Search:
•A linear search or sequential search is a method
for finding an element within a list. This type
of searching algorithms sequentially checks
each element of the list until a match is found or
the whole list has been searched.
•The time complexity
algorithm is O(n)
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

8. Binary Search:
•This type of searching algorithms is used to
find the position of a specific value contained
in a sorted array.
•Binary search algorithm works on the
principle of divide & conquer and it is
considered the best searching algorithms
because of its faster speed to search (
Provided the data is in sorted form).
•A binary search is also known as a half-
interval search or logarithmic search.
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

9. •Binary Search:
•Binary Search Tree, is a node-based binary tree
data structure which has the following properties.
•The left subtree of a node contains only nodes
with keys lesser than the node’s key.
•The right subtree of a node contains only nodes
with keys greater than the node’s key.
•The left and right subtree each must also be a
binary search tree. There must be no duplicate
nodes.
•The time complexity of the binary search
algorithm is O(log n)
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

10. Jump Search:
•just like Binary Search, Jump Search is one
of the searching algorithms for sorted
arrays.
•The basic idea is to check fewer elements
(than linear search) by jumping ahead by fixed
steps or skipping some elements in place of
searching all elements.
•Time Complexity : O(√n)
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

11. INTERPOLATION SEARCH:
• interpolation search is that type of searching algorithms, used for
searching for a key in an array that has been ordered by numerical
values assigned to the keys ( key ,values ).
• algorithm to work properly, the data collection should be in a sorted
form and equally distributed
interpolation algorithm the same except the above partition logic.
step1: in a loop step3: if the item is less than arr[pos]
step2: if it is a match step4: repeat until a match
• time complexity: if elements are uniformly distributed, then O (log
log n)). in worst case it can take upto o(n).
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

12. • EXPONENTIAL SEARCH:
• exponential search is also known as doubling or
galloping search. this mechanism is used to find the
range where the search key may present.
• if l and u are the upper and lower bound of the list,
then l and u both are the power of 2. for the last
section, the u is the last position of the list. for that
reason, it is known as exponential.
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

13. EXPONENTIAL SEARCH INVOLVES 2 BASIC STEPS:
• find range where element is present
• do binary search in above found range.
• TIME COMPLEXITY : O(log N)
applications of exponential search:
• exponential binary search is particularly useful for
unbounded searches, where size of array is infinite.
• it works better than binary search for bounded arrays,
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

14. Sublist Search:
sublist search is used to detect a presence
of one list in another list. suppose we have
a single-node list (let’s say the first list),
and we want to ensure that the list is
present in another list (let’s say the second
list), then we can perform the sublist
search to find it.
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

15. Fibonacci Search:
fibonacci search technique is a method of searching
algorithms where a sorted array uses a divide and
conquer algorithm that narrows down possible
locations with the aid of fibonacci numbers.
• compared to binary search where the sorted array is
divided into two equal-sized parts, one of which is
examined further, fibonacci search divides the array
into two parts that have sizes that are
consecutive fibonacci numbers
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

16. Fibonacci Search:
• fibonacci search is a comparison-based technique
that uses fibonacci numbers to search an element
in a sorted array.
• similarities with binary search:
• works for sorted arrays
• a divide and conquer algorithm.
• has log n time complexity
• for range elimination, and hence for the o(log(n))
complexity
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

17. The Ubiquitous Binary Search:
problem statement: given a sorted array of n
distinct elements. find a key in the array using
least number of comparisons.
Theoretically we need log N + 1 comparisons in
worst case. If we observe, we are using two
comparisons per iteration except during final
successful match, if any
SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

18. SEARCHING ALGORITHMS AND THEIR
EFFICIENCY

19. THANKS