College of Computer and
Information Sciences
Design and Analysis of Algorithms
Lecturer:
Dr. Bandar Alshammari
https://sites.google.com/site/drbandaralshammari/
1
Fall 2013
Course References
1.
Required Text Book
Computer Algorithms, Ellis Horowitz, Startaj Sahni, &
Sanguthevar Rajasekaran, 1998 Computer Science U.S.A
2.
Another Recommended Text Book
Introduction to Algorithms, Thomas Cormen et al’s, Second
Edition, 2001, MIT Printing Press
Lecture Notes
3.
Available @
https://sites.google.com/site/drbandaralshammari/
4.
2
Notes taken during lectures
CSC413
Fall - 2013
Dr. Bandar Alshammari
Course Assessments
1.
Five (5) Homeworks worth: 10%
2.
Two (2) Midterms Exams: 15% each.
3.
Comprehensive Final Exam: 60%
3
CSC413
Fall - 2013
Dr. Bandar Alshammari
Course Motivation
 Need to run computer programs
efficiently!
INPUT
Computer program:
Accepts Input (Data)
Performs a Sequence of action
with the input
COMPUTER
PROGRAM
Generates Output (Data)
Efficient Sequence of Actions
OUTPUT
Algorithms
4
CSC413
Fall - 2013
Dr. Bandar Alshammari
Course Contents
Lecture Topic
Lecture Contents
Introduction
What is an algorithm? &
algorithm specification
Performance Analysis
Space Complexity, Time
Complexity and Asymptotic
Notations
Trees, Queues, Stack and Heaps
Data Structure
Searching and Sorting
Optimization in
Algorithms design
5
CSC413
Binary & Linear Searches,
Selection, Insertion, Quick and
Merge Sorts
Graphs & Greedy Algorithms.
Fall - 2013
Dr. Bandar Alshammari
Week
Date Hijri
Date
Lecture
3
9/11/1434
15/09/2013
Lecture 1 & 2
4
16/11/1434
22/09/2013
Lecture 3 & 4
5
23/11/1434
29/09/2013
Lecture 5
6
1/12/1434
6/10/2013
Lecture 6
Assessment Due
Homework 1
Mid Semester Break
6
7
22/12/1434
27/10/2013
Lecture 7 + Revision
Homework 2
8
29/12/1434
3/11/2013
Midterm Exam1
Lectures 1 - 6
9
6/1/1435
10/11/2013
Lecture 8 & 9
10
13/1/1435
17/11/2013
Lecture 10
11
20/1/1435
24/11/2013
Lecture 11
12
27/1/1435
1/12/2013
Lecture 12 + Revision
Homework 4
13
5/2/1435
8/12/2013
Midterm Exam 2
Lectures 7 - 12
14
12/2/1435
15/12/2013
Lecture 13
15
19/2/1435
22/12/2013
Revision
16
26/2/1435
29/12/2013
Revision
CSC413
Fall - 2013
Homework 3
Homework 5
Dr. Bandar Alshammari
Lecture (2)
Algorithms Basic Concepts
Introduction
II. Algorithm specification
I.
7
A.
Pseudocode Conventions
B.
Recursive Algorithm
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.1 Introduction
 An algorithm, named after the ninth century
scholar Abu Jafar Muhammad Ibn Musu AlKhowarizmi,
 An algorithm is “a finite set of instructions that
accomplishes a particular task”.
 Of course, there can be many algorithms for a
single problem, i.e., A single problem can be
solved by many techniques e.g., iteration and/or
8
recursion.
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.1 Introduction
 All algorithms must satisfy the following criteria:
 input: zero or more quantities that are externally supplied
 output: at least one quantity is produced
 definiteness: clear and unambiguous
 finiteness: terminate after a finite number of steps
 effectiveness: instruction is basic enough to be carried out
 A Computer Program is “a clearly specified series of
computer instructions implementing the algorithm”.
 A program does not have to satisfy the finiteness
criteria.
9
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.1 Introduction (More Definitions)
 Algorithm validation: Is the process which
shows that a certain algorithm can compute
the correct answer for all possible legal
inputs.
 Analysis of Algorithms (performance Analysis):
Is the task of determining how much
computing time and storage an algorithm
10
requires.
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2 Algorithm Specification
 Representation
 A natural language, like English or Chinese.
 A graphic, like flowcharts.
 A computer language, like C and JAVA.
11
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.1 Pseudocode (Assignment)
12
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.1 Pseudocode (Conditional)
Solution
13
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.1 Pseudocode (Loops)
Solution
14
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.1 Pseudocode (Selection Sort)
 Example 1.1 [Selection sort]:
 From those integers that are currently unsorted, find the smallest
and place it next in the sorted list.
i
0
1
2
3
15
CSC413
[0]
30
10
10
10
10
[1]
10
30
20
20
20
[2]
50
50
50
30
30
Fall - 2013
[3]
40
40
40
40
40
[4]
20
20
30
50
50
Dr. Bandar Alshammari
1.2.1 Java Code(Selection Sort)
Think about sorting an array in a decreasing order
(i.e., 10,9,8,.....,2,1,0)????
16
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.2 Recursion
 A Recursive function executes its code and
then returns control to the calling function.
 Similarly, an algorithm is said to be recursive,
if the same algorithm is invoked in the body.
17
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.2 Recursion
 This perspective ignores the fact that functions
can call themselves (direct recursion).
 They may call other functions that invoke the
calling function again (indirect recursion).
 extremely powerful
 frequently allow us to express an otherwise
complex process in very clear term
 We should express a recursive algorithm when
the problem itself is defined recursively.
18
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.2 Recursion Example
Consider the factorial function, N!, defined as the product of all
integers between 1 and N.
3! = 3 × 2 × 1 = 6
N! = N × (N − 1) × (N − 2) × . . . × 1
•
What is the base case? Look for the case that’s not defined
in terms of N: e.g. 1! = 1 or 0! = 1.
•
What is the recursive case? Define the problem in terms of
itself, while reducing the problem size (i.e., reduce N! to (N
− 1)!)
•
The factorial function can be expressed recursively as:
1! = 1 (base case)
N! = N × (N − 1)! for N > 1 (recursive case)
•
19
The base case is 1!. All other values of N! are defined
recursively as N × (N − 1)!
CSC413
Fall - 2013
Dr. Bandar Alshammari
1.2.2 Recursion Example
Given here in pseudocode:
Algorithm factorial(n)
{
if (n<=1) then
return 1;
else
return n * factorial(n-1);
}
Eventually the base case will be reached:
4! = 4 × 3!
= 4 × 3 × 2!
= 4 × 3 × 2 × 1! (base case reached)
= 4 × 3 × 2 × 1 (recursion is terminated)
20
CSC413
Fall - 2013
Dr. Bandar Alshammari
Tower of Hanoi

The Towers of Hanoi puzzle was invented in the 1880s
by Douard Lucas, a French mathematician.

The puzzle consists of three poles on which a set of
disks, each with a different diameter, may be placed.

Initially the disks are stacked on the leftmost pole, in
order of size, with the largest disk on the bottom.
21
CSC413
Fall - 2013
Dr. Bandar Alshammari
Rules for Tower of Hanoi
The goal of the puzzle is to move all the disks from the
leftmost pole to the rightmost pole, adhering to the
following rules:
1. Move only one disk at a time.
2. A larger disk may not be placed on top of a smaller
disk.
3. All disks, except the one being moved, must be on a
pole.
22
CSC413
Fall - 2013
Dr. Bandar Alshammari
Three-disk solution to the Tower of Hanoi puzzle
23
CSC413
Fall - 2013
Dr. Bandar Alshammari
Tower of Hanoi Solution (Code)
// Move the top n disks from tower A to tower C
Algorithm TowerOfHanoi(n,a,b,c)
{
if (n>=1) then
{
TowerOfHanoi(n-1,a,c,b);
Write(“move top disk from
tower”, a,”to top of tower”, c);
TowerOfHanoi(n-1,b,a,c);
}
}
24
CSC413
Fall - 2013
Dr. Bandar Alshammari
Tower of Hanoi Solution Property
Takes 2N- 1 steps to solve N disc problem.
• For example for 3 discs = 23- 1 = 7 moves.
• Another example for 4 discs = 24- 1 = 15 moves
• This is an example of exponential complexity.
• As the number of disks increases, the number
of required moves increases exponentially.
25
CSC413
Fall - 2013
Dr. Bandar Alshammari