Data_structures_and_algorithm_Lec_1.pptx

DATA STRUCTURES AND ALGORITHM
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Dr. Muhammad Idrees

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Books to Follow
 D.S.Malik, “Data Structures using C++”
 D.Samanta, “Classic Data Structures”, Prentice Hall
 Tenenbaum, M.Augenstein, and Y. Langman, “Data
Structures using C and C++”, Prentice Hall.

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Some General Comments
 Encouragement to ask questions during class
 Without your feedback, it is impossible for me to
know what you don’t know?
 There is no reason not to ask questions during class
 Of course, you could also send email.
 Encouragement to read course material prior to
class
 Kindly switch off your Mobile Phones during class

Introduction to Data Structure
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A data structure is a particular way of storing and
organizing data in a computer so that it can be
used efficiently

Need for Data Structures
 Data structures organize data  more efficient
programs.
 More powerful computers  more complex
applications.
 More complex applications demand more
calculations.

Organizing Data
 Any organization for a collection of records that
can be searched, processed in any order, or
modified.
 The choice of data structure and algorithm can
make the difference between a program
running in a few seconds or many days.

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What is Data Structure?
 Data structure is a representation of data and the
operations allowed on that data.
 A data structure is a way to store and organize
data in order to facilitate the access and
modifications.
 Data Structure is the method of representing of
logical relationships between individual data
elements related to the solution of a given problem.

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Fundamental Data Structures
Hash Tables
Basic Data Structures
Linear Data Structures Non-Linear Data Structures
Linked Lists Stacks Queues Trees
Graphs
Arrays

array
Linked list
tree
queue
stack

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Linear Data Structures
 A data structure is said to be linear if its elements
form a sequence or a linear list.
 Examples:
 Arrays
 Linked Lists
 Stacks
 Queues

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Non-Linear Data Structures
 A data structure is said to be non-linear if its
elements does not form a sequence or a linear list.
 Examples:
 Trees
 Graphs
 Hash Tables
 Each element may be connected with two or more
other nodes or items in a non-linear arrangement.

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Operations on Data Structures
 Traversal: Travel through the data structure
 Search: Traversal through the data structure for a
given element
 Insertion: Adding new elements to the data structure
 Deletion: Removing an element from the data
structure
 Sorting: Arranging the elements in some type of order
 Merging: Combining two similar data structures into
one

 Arrays
 Linked List
 Stacks
 Queues
Linear Data Structures
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Arrays
 A sequence of n items of the same data type that are
stored contiguously in computer memory and made
accessible by specifying a value of the array’s index.
 Properties:
 fixed length (need preliminary reservation of memory)
 contiguous memory locations
 direct access
 Insert/delete
a[0] a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9]
1 2 3 4 5 6 7 8 9 10
Array a with 10 integer elements

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Linked List
 A sequence of zero or more nodes each containing two kinds of
information: some data and one or more links called pointers to
other nodes of the linked list.
 Properties
 dynamic length
 arbitrary memory locations
 access by following links
 Insert/delete
 Types of Linked List
 Singly linked list (next pointer)
 Doubly linked list (next + previous pointers)

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Stacks
 A stack is a data structure that uses last-in, first-out
(LIFO) ordering and allows reading and writing on the
top element only.
 Properties
 insertion/deletion can be done only at the top
 LIFO
 Two operations
 Push (insertion)
 Pop (removal)

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Queues
 Collection with access only to the item that has been
present the longest
 Properties
 Insertion/enqueue from the rear (back) and deletion/
dequeue from the front.
 FIFO
 Two operations
 Enqueue
 Dequeue
20 30 10 60 57 29
Front Back

 Graphs
 Trees
 Hash Tables
Non-Linear Data Structures
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Graphs
 Formal definition: A graph G = <V, E> is defined by a
pair of two sets: a finite set V of items called vertices and a
set E of vertex pairs called edges.
 Undirected and directed graphs (digraphs).
 Complete, dense, and sparse graphs
Undirected Graph Directed Graph

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Trees
 A Tree is a way of representing the
hierarchical nature of a structure in a
graphical form.
 Properties of trees
 Root Node
 Child Node
 Parent Node
 Leaf Node
 Types
 Unordered Tree
 Binary Tree is an ordered tree data
structure in which each node has at most
two children.
Ordered Tree
Binary Tree

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Hash Tables
 A hash table is a data structure that uses a hash
function to map identifying values, known as keys
(e.g., a person's name), to their associated values.

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Summary
 A data structure is a particular way of storing and organizing
data in a computer so that it can be used efficiently.
 Linear Data Structures
 Arrays
 Linked List
 Stacks
 Queues
 Non Linear Data Structures
 Graphs
 Trees
 Hash Tables

Selecting a Data Structure
Select a data structure as follows:
1. Analyze the problem to determine the
resource constraints a solution must meet.
2. Determine the basic operations that must be
supported. Quantify the resource constraints
for each operation.
3. Select the data structure that best meets
these requirements.

Data Structure Philosophy
 Each data structure has costs and benefits.
 Rarely is one data structure better than another
in all situations.
 A data structure requires:
 space for each data item it stores,
 time to perform each basic operation,
 programming effort.

A precise rule (or set of rules) specifying
how to solve some problem.
Introduction to Algorithms
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What is an Algorithm?
 An algorithm is a sequence of unambiguous
instructions for solving a problem, i.e., for obtaining a
required output for any legitimate input in a finite
amount of time.
 Properties
 Can be represented various forms
 Unambiguity/clearness
 Effectiveness
 Finiteness/termination
 Correctness

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What is an Algorithm?
 Recipe, process, method, technique, procedure, routine,…
with the following requirements:
1. Finiteness
 terminates after a finite number of steps
2. Definiteness
 rigorously and unambiguously specified
3. Clearly specified input
 valid inputs are clearly specified
4. Clearly specified/expected output
 can be proved to produce the correct output given a valid input
5. Effectiveness
 steps are sufficiently simple and basic

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Why Study Algorithms?
 Algorithms solve problems
 Good choice: more efficient programs
 Bad choice: poor programs performance
 Example:
 Problem: Find the largest element ‘k’ out of ‘N’ integers
 Easy algorithms: sort all integers, then list the first or last element
 Better algorithm: take first element then read through the list
 Different algorithms perform better on different inputs
 Input size also affect the performance.

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Notion of Algorithm and Problem
“Computer”
Problem
Algorithm
Input Output

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Representation of an Algorithms
 An algorithm may be represented in different
forms:
 A description using English/other languages
 A real computer program, e.g. C++ or java
 A pseudo-code, C-like program, program-language-
like program.
 Program = algorithms + data structures

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Basic Issues Related to Algorithms
 How to design algorithms
 How to express algorithms
 Proving correctness
 Efficiency (or complexity) analysis
 Theoretical analysis
 Empirical analysis
 Optimality

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Analysis of Algorithms
 How good is the algorithm?
 Correctness
 Time efficiency
 Space efficiency

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Algorithm Efficiency
 There are often many algorithms for a given
problem. How do we choose the best?
 Goals of program design:
 Algorithm is to be easy to understand, code, debug
 Algorithm makes efficient use of computer’s resources
 How to measure the efficiency?
 Empirical comparison (run the program)
 Asymptotic algorithm analysis (without running the program)
 Factors affecting running time (size of the input)

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Best, Worst and Average Cases
 Not all inputs of a given size take the same time.
 Each algorithm has three cases:
 Best case:
 Worst Case:
 Average Case:

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Example: Best, Worst and Average Cases
 Sequential search for ‘k’ in an array of ‘n’ integers:
 Best case: ‘k’ is the first element of the array.
 Worst case: the search must visit every element once.
This happens when the value being searched for is
either the last element in the list, or is not in the list
 Average case: on average, assuming the value
searched for is in the list and each list element is
equally likely to be the value searched for, the search
visits only n/2 elements.

Data_structures_and_algorithm_Lec_1.pptx

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