Introduction to Data Structures & Algorithms

Data Structures and Alglorithms
Prepared by: Afaq Mansoor Khan
BSSE III- Group A
Session 2017-21
IMSciences, Peshawar.

Course Details
• Course Title: Data Structures
• Credit Hours: 3 + 1
• Course Objectives:
The course is designed to teach students
structures and schemes, which allow them to
write programs to efficiently manipulate,
store, and retrieve data.

Course Description
• In recent years the subject of computer programming
has been recognized as a discipline whose mastery is
fundamental and crucial to the success of many
engineering projects and which is close to scientific
treatment and presentation.
• It has advanced from a skill to an academic discipline
• it is abundantly clear that a systematic and scientific
approach to program construction primarily has a
bearing in the case of large, complex programs which
involve complicated sets of data.
• Hence, a methodology of programming is also bound to
include all aspects of data structuring.

Course Objectives
• To extend and deepen the student's knowledge and
understanding of algorithms and data structures
• To examine previously studied algorithms and data
structures more rigorously and introduce the
students to "new" algorithms and data structures.
• It focuses the student's attention on the design of
program structures that are correct, efficient in both
time and space utilization, and defined in terms of
appropriate abstractions.

Course Goals
• Upon completion of this course, a successful student will
be able to:
▫ Describe the strengths and limitations of linear data
structures, trees, graphs
▫ Select appropriate data structures for a speciﬁed problem
▫ Compare and contrast the basic data structures used in
Computer Science: lists, stacks, queues, trees and graphs
▫ Describe classic sorting techniques
▫ Recognize when and how to use the following data
structures: arrays, linked lists, stacks, queues and binary
trees.
▫ Identify and implement the basic operations for
manipulating each type of data structure

Course Goals
• Upon completion of this course, a successful student
will be able to:
▫ Perform sequential searching, binary searching and hashing
algorithms.
▫ Apply various sorting algorithms including bubble,
insertion, selection and quick sort.
▫ Understand recursion and be able to give examples of its
use
▫ Use dynamic data structures

Course Outline - I
• Introduction to data structures
• Linear and non-linear data structures
• Arrays and pointers
• List data structure
• Singly linked list
• Doubly linked list
• Circular linked list
• Stack; Implementation of stack using arrays and
linked list
• Applications of a stack

Course Outline - II
• Infix to postfix conversion
• Evaluation of postfix expressions
• Queues; Implementation of queues using arrays and
linked list
• Circular Queues; Priority Queues;
• Trees; Tree traversals; Binary search trees and
implementation
• Heaps and Heap sort;
• Graphs; Minimum spanning trees;
• Hashing
• Files

Recommended Books
Textbook:
• Robert L. Kruse, Alexander J. Ryba, Data Structures & Program Design in C++,
Prentice Hall, New Jersey, USA
Reference Books:
• Debasis Samanta, Classic Data Structures, 2nd Edition, Prentice Hall India,
2009
• ISRD Group, Data Structures Using C, Tata McGraw-Hill Publishing Company,
New Delhi, India, 2006.

Marks Distribution of Course
 Assignments ……….……… 10%
 Quizzes ..…………….. 10%
 Midterm Exam .………….….. 30%
 Final Exam .……………… 50%

Objectives Overview for this Lecture
• Introduction to Data Structures & Algorithms
• One Dimensional Arrays
• Two Dimensional Arrays

12
What is it all about?
• Solving problems
▫ Get me from home to work
▫ Balance my checkbook
▫ Simulate a jet engine
▫ Graduate from SPU
• Using a computer to help solve problems
▫ Designing programs (architecture, algorithms)
▫ Writing programs
▫ Verifying programs
▫ Documenting programs

13
Data Structures and Algorithms
• Algorithm
▫ Outline, the essence of a computational procedure,
step-by-step instructions
• Program – an implementation of an algorithm in
some programming language
• Data structure
▫ Organization of data needed to solve the problem

14
Overall Picture
• This course is not about:
▫ Programming languages
▫ Computer architecture
▫ Software architecture
▫ Software design and implementation principles
 Issues concerning small and large scale programming
• We will only touch upon the theory of complexity
and computability

What is Data Structures?
• Example:library
▫ is composed of elements
(books)
▫ Accessing a particular book
requires knowledge of the
arrangement of the books
▫ Users access books only
through the librarian
the logical arrangement of data
elements, combined with
the set of operations we need to access
the elements.

Basic Data Structures
• Structures include
▫ linked lists
▫ Stack, Queue
▫ binary trees
▫ …and others

What is Algorithm?
• Algorithm:
▫ A computable set of steps to achieve a desired result
▫ Ralationship to Data Structure
 Example: Find an element
1 2 3 4 5 6 7
1
2
3
4
5
6
7

Introducing Arrays
Array is a data structure that represents a collection
of the same types of data.
myList[0]
myList[1]
myList[2]
myList[3]
myList[4]
myList[5]
myList[6]
myList[7]
myList[8]
myList[9]
double[] myList = new double[10];
myList reference
An Array of 10
Elements
of type double

Declaring Array Variables
• datatype[] arrayname;
Example:
double[] myList;
• datatype arrayname[];
Example:
double myList[];

Creating Arrays
arrayName = new datatype[arraySize];
Example:
myList = new double[10];
myList[0] references the first element in the array.
myList[9] references the last element in the array.

Declaring and Creating in One Step
• datatype[] arrayname = new
datatype[arraySize];
• datatype arrayname[] = new
datatype[arraySize];
double myList[] = new double[10];

The Length of Arrays
• Once an array is created, its size is fixed. It
cannot be changed. You can find its size using
arrayVariable.length
For example,
myList.length returns 10

Initializing Arrays
• Using a loop:
for (int i = 0; i < myList.length; i++)
myList[i] = i;
• Declaring, creating, initializing in one step:
double[] myList = {1.9, 2.9, 3.4, 3.5};
This shorthand syntax must be in one statement.

Declaring, creating, initializing Using the
Shorthand Notation
double[] myList = {1.9, 2.9, 3.4, 3.5};
This shorthand notation is equivalent to the following
statements:
myList[0] = 1.9;
myList[1] = 2.9;
myList[2] = 3.4;
myList[3] = 3.5;

CAUTION
Using the shorthand notation, you have to
declare, create, and initialize the array all in
one statement. Splitting it would cause a
syntax error. For example, the following is
wrong:
double[] myList;
myList = {1.9, 2.9, 3.4, 3.5};

Testing Arrays
• Objective: The program receives 6 numbers from
the keyboard, finds the largest number and
counts the occurrence of the largest number
entered from the keyboard.
Suppose you entered 3, 5, 2, 5, 5, and 5, the
largest number is 5 and its occurrence count is 4.
TestArray Run

Assigning Grades
• Objective: read student scores (int) from the
keyboard, get the best score, and then assign
grades based on the following scheme:
▫ Grade is A if score is >= best–10;
▫ Grade is B if score is >= best–20;
▫ Grade is C if score is >= best–30;
▫ Grade is D if score is >= best–40;
▫ Grade is F otherwise.
AssignGrade
Run

Passing Arrays as Arguments
• Objective: Demonstrate differences of
passing primitive data type variables
and array variables.
TestPassArray Run

Example
swapFirstTwoInArray(a)
swapFirstTwoInArray(array)
Pass by value (Reference value)
a Reference
:
a[0]
a[1]
array Reference
swap(a[0], a[1])
swap( n1, n2)
Pass by value
a[0] 1 2
n1 n21 2
a[1]

Copying Arrays
In this example, you will see that a simple
assignment cannot copy arrays in the
following program. The program simply
creates two arrays and attempts to copy one
to the other, using an assignment statement.
TestCopyArray Run

Copying Arrays
Contents
of list1
list1
Contents
of list2
list2
Before the assignment
list2 = list1;
Contents
of list1
list1
Contents
of list2
list2
After the assignment
list2 = list1;
Garbage

Copying Arrays
Using a loop:
int[] sourceArray = {2, 3, 1, 5, 10};
int[] targetArray = new int[sourceArray.length];
for (int i = 0; i < sourceArrays.length; i++)
targetArray[i] = sourceArray[i];

Multidimensional Arrays
Declaring Variables of Multidimensional Arrays and Creating
Multidimensional Arrays
int[][] matrix = new int[10][10];
or
int matrix[][] = new int[10][10];
matrix[0][0] = 3;
for (int i=0; i<matrix.length; i++)
for (int j=0; j<matrix[i].length; j++)
{
matrix[i][j] = (int)(Math.random()*1000);
}
double[][] x;

Multidimensional Array Illustration
0 1 2 3 4
0
7
0 1 2 3 4
1
2
3
4
0
1
2
3
4
matrix[2][1] = 7;matrix = new int[5][5];
3
7
0 1 2
0
1
2
int[][] array = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12}
};
1 2 3
4 5 6
8 9
10 11 12

Declaring, Creating, and Initializing Using Shorthand
Notations
You can also use a shorthand notation to declare, create and initialize a two-dimensional
array. For example,
int[][] array = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12}
};
This is equivalent to the following statements:
int[][] array = new int[4][3];
array[0][0] = 1; array[0][1] = 2; array[0][2] = 3;

Lengths of Multidimensional Arrays
int[][] array = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12}
};
array.length
array[0].length
array[1].length
array[2].length

Definition – Pointer
• A value indicating the number of (the first byte of)
a data object
▫ Also called an Address or a Location
• Used in machine language to identify which data
to access
 E.g., stack pointer is address of most recent entry of The Stack
• Usually 2, 4, or 8 bytes, depending upon machine
architecture
∙∙∙
2n-10 1 2 3 4 5 6 7 8 9 10 11
11

Memory Addressing
0x00000000
0xFFFFFFFF
address space
program code
(text)
static data
heap
(dynamically allocated)
stack
(dynamically allocated)
PC
SP

Declaring Pointers in C
• int *p; — a pointer to an int
• double *q; — a pointer to a double
• char **r; — a pointer to a pointer to a
char
• type *s; — a pointer to an object of
type type
 E.g, a struct, union, function, something defined by a typedef, etc.

Declaring Pointers in C (continued)
• Pointer declarations:–read from right to left
• const int *p;
 p is a pointer to an integer constant
 I.e., pointer can change, thing it points to cannot
• int * const q;
 q is a constant pointer to an integer variable
 I.e., pointer cannot change, thing it points to can!
• const int * const r;
 r is a constant pointer to an integer constant

Pointer Operations in C
• Creation
& variable Returns variable’s memory address
• Dereference
* pointer Returns contents stored at address
• Indirect assignment
• pointer = val Stores value at address
• Of course, still have...
• Assignment
pointer = ptr Stores pointer in another variable

Using Pointers
int i1;
int i2;
int *ptr1;
int *ptr2;
i1 = 1;
i2 = 2;
ptr1 = &i1;
ptr2 = ptr1;
*ptr1 = 3;
i2 = *ptr2;
i1:
i2:
ptr1:
0x1000
0x1004
0x1008
…
ptr2:
…
0x100C
0x1010
0x1014
1
2
0x1000
0x1000
3
3

Pointer Arithmetic
• int *p, *q;
q = p + 1;
▫ Construct a pointer to the next integer after *p and
assign it to q
• double *p, *r;
int n;
r = p + n;
▫ Construct a pointer to a double that is n doubles beyond
*p, and assign it to r
▫ n may be negative

Pointer Arithmetic (continued)
• long int *p, *q;
p++; q--;
▫ Increment p to point to the next long int; decrement q to
point to the previous long int
• float *p, *q;
int n;
n = p – q;
▫ n is the number of floats between *p and *q; i.e., what
would be added to q to get p

Pointer Arithmetic
pointer + number pointer – number
E.g., pointer + 1 adds 1 something to a pointer
char *p;
char a;
char b;
p = &a;
p += 1;
int *p;
int a;
int b;
p = &a;
p += 1;In each, p now points to b
(Assuming compiler doesn’t
reorder variables in memory)
Adds 1*sizeof(char) to
the memory address
Adds 1*sizeof(int) to
the memory address
Pointer arithmetic should be used cautiously

46
Pass-by-Reference
void
set_x_and_y(int *x,
int *y)
{
*x = 1001;
*y = 1002;
}
void
f(void)
{
int a = 1;
int b = 2;
set_x_and_y(&a,&b);
}
1
2
a
b
x
y
1001
1002

Arrays and Pointers
• Arrays and pointers are closely related in C
▫ In fact, they are essentially the same thing!
▫ Esp. when used as parameters of functions
• int A[10];
int *p;
▫ Type of A is int *
▫ p = A; and A = p; are legal assignments
▫ *p refers to A[0]
*(p + n) refers to A[n]
▫ p = &A[5]; is the same as p = A + 5;

Arrays and Pointers (continued)
• double A[10]; vs. double *A;
• Only difference:–
▫ double A[10] sets aside ten units of memory, each large
enough to hold a double
▫ double *A sets aside one pointer-sized unit of memory
 You are expected to come up with the memory elsewhere!
▫ Note:– all pointer variables are the same size in any given
machine architecture
 Regardless of what types they point to

Note
• C does not assign arrays to each other
• E.g,
▫ double A[10];
double B[10];
A = B;
 assigns the pointer value B to the pointer value A
 Contents of array A are untouched

Arrays as Function Parameters
• void init(float A[], int arraySize);
void init(float *A, int arraySize);
• Are identical function prototypes!
• Pointer is passed by value
• I.e. caller copies the value of a pointer to float into the
parameter A
• Called function can reference through that pointer to
reach thing pointed to

Arrays as Function Parameters (continued)
• void init(float A[], int arraySize){
int n;
for(n = 0; n < arraySize; n++)
A[n] = (float)n;
} //init
• Assigns values to the array A in place
▫ So that caller can see the changes!

Examples
while ((rc = scanf("%lf", &array[count])) !=EOF && rc==0)
…
double getLargest(const double A[], const int sizeA) {
double d;
if (sizeA > 0) {
d = getLargest(&A[1], sizeA-1);
return (d > A[0]) ? d : A[0];
} else
return A[0];
} // getLargest

Result
• Even though all arguments are passed by value to
functions …
• … pointers allow functions to assign back to data of
caller
• Arrays are pointers passed by value

Safety Note
• When passing arrays to functions, always specify const
if you don’t want function changing the value of any
elements
• Reason:– you don’t know whether your function would
pass array to another before returning to you
 Exception – many software packages don’t specify const in
their own headers, so you can’t either!

Summary
• Introduction to Data Structures & Algorithms
• One Dimensional Arrays:
• Multi Dimensional Arrays:
▫ Declaration
▫ Initialization
▫ Representation
▫ Operations
▫ Arrays and functions
• Pointers
▫ Declaration, Initialization
▫ Arrays and pointers

References
• www.cse.ust.hk/~liao/comp102/PPT/array.ppt
• https://www.geeksforgeeks.org/array-data-
structure/
• http://www.cplusplus.com/doc/tutorial/arrays/
• https://cs.nyu.edu/courses/fall03/V22.0101-
002/05slide.ppt
• https://processing.org/tutorials/arrays/

Introduction to Data Structures & Algorithms

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