Itc lec5-24+sep+2012

Introduction To Computer Science
(ITC)
Lecture 05
Introduction to Algorithms
24 September 2012

Instructor: Adeela Waqar
adeela.waqar@nu.edu.pk, adeela.abbas@gmail.com

National University of Computer and Emerging Sciences, Islamabad
1

Algorithm
Algorithm is a step by step procedure for solving a
problem

It represents a process that a computer carries
out, in order to complete a well defined task

The objective of computer science is to solve
problems by developing, analyzing, and
implementing algorithmic solutions

2

Al-Khwarizmi Principle
• All complex problems can be broken into
simpler sub-problems.
• Solve a complex problem by breaking it down
into smaller sub-problems and then solve them
(in a specified order), one at a time.
• When all the steps are solved, the original
problem itself has also been solved.
• This process is called Algorithm.
(Originating from al-Khwārizmī)

3

Computer Programming
• Computer is a powerful tool
• It is not intelligent!
• In order to use computer to solve our problems,
we must tell it what we want done and the order
in which we want it done.
• These instructions are called computer program.
• Writing these instructions is called computer
programming.
• The person giving these instructions is called a
computer programmer.
4

Computer Programming
• Analyze the problem
• Develop a sequence of instructions for
solving the problem.
• Communicate it to the computer.

5

Phases of the software life cycle

• Requirement definition
• Analysis and design
• Coding
• Testing
• Implementation
• Maintenance

6

Problem Solving Techniques
• Ask questions
• Look for things that are similar
• Means-ends analysis
• Divide and Conquer
• Merging solutions

7

Ask Questions
• Ask questions until you have developed a clear
understanding of the problem.
• Who, What, Why, Where, When.
– What do I have to work with? (my data or input)
– How much data is there?
– What should my output look like?
– How many times is the process going to be
repeated?
– What are the exceptions to the main course?
– What special error condition might come up?
8

Look for things that are Similar
• Do not reinvent the wheel!
• Draw Analogies

9

Means-Ends analysis
• Starting point and ending state are known.
• You need to devise the transformation
function.
• Ends are defined – you need to analyze
your means of getting between them.
• Lahore to Islamabad
– What are the options?
– Narrow down the options?
– Figure out the details?
10

Divide and Conquer
• Same as the Al-khwarizmi Principle.
• Breakup the large problem into smaller
units and then solve them one at a time.
• Building block approach.

11

Divide and Conquer
Hard Problem

Easy Sub-problem Hard Sub-problem Easy Sub-problem

Easy Sub-problem Easy Sub-problem

12

Merging Solution
• Sometimes merging two independent
solutions solves the problem more
efficiently?
• Calculate Average
– Count values
– Sum Values
– Divide sum by count
• Alternative approach
– calculate partial sum as you count
13

Problem Solving Techniques
• What is the unknown?
– What is required?

• What are the data?
– What is given?

• What is the condition?
– By what condition the unknown is linked to the
data?
14

Conversion from Fahrenheit to Celsius

• Output
– Temperature in Celsius (C)

• Inputs
– Temperature in Fahrenheit (F)

• Process
5
C = (F − 32)
9

15

Calculate and print the average grade of 3
tests for the entire class
• Input
– 3 test scores for each student
• output
– Average of 3 tests for each student
• Process
1. Get three scores
2. Add them together
3. Divide by three to get the average
4. Print the average
5. Repeat step 1 to 4 for next student
6. Stop if there are no more students

16

Flow Charts

 A flowchart is a visual or graphical
representation of an algorithm.
 The arrows, each of which represents a
flowchart employs a series of blocks
and
particular operation or step in the
algorithm.
 The arrows represent the sequence in
which the operations are implemented.
17

Flowcharts – Most Common Symbols
Symbol Name Function
Terminal Represents the beginning or end of a
program.
Flow-line Represents the flow of logic.

Process Represents calculations or data
manipulation.

Input/Output Represents inputs or outputs of data
and information.

Decision Represents a comparison, question,
or decision that determines
alternative paths to be followed.

18

Flowcharts – An Example
Find the solution of a quadratic equation
Ax2+Bx+C=0, given A, B and C.
A
START

INPUT X1 = (-B+R)/(2A)
A, B, C X2 = (-B-R)/(2A)

Calculate PRINT
R = SQRT(B2-4AC) A, B, C, X1, X2

A
END

19

Flow Charting
Expresses the flow of processing in a
structured pictorial format.
Flow
Input and Processing of
Output Steps Steps data

Decision Terminator
Connectors

20

Begin
Flow chart for
Converting
Get temp. in ‘F’
Fahrenheit
into Celsius
Calculate 5
C = (F − 32)
9

Print ‘C’

Stop

21

Flow chart for
Get three scores
calculating
Add them together average of
three scores
Divide the result by three

Print the average

Yes No
More students? Stop

22

Comparison of Algorithm representations in Natural
language, flowchart and Pseudo-code
START

INPUT
Step 1: Begin the calculations A, B
BEGIN Adder
Step 2: Input two values A and B Input A and B
C = A + B
Add A to B
Step 3: Add the values PRINT C
and store in C
END Adder
Step 4: Display the result
OUTPUT
Step 5: End the calculation
C

END
Natural language Flowchart Pseudo-code
23

Algorithm Representation
(Natural Languages)

• English or some other natural language.
• Are not particularly good:
– too verbose
– unstructured
– too rich in interpretation (ambiguous)
– imprecise

24

Algorithm Representation
(Using Programming Language)
{
int I, m, Carry;
int a[100], b[100], c[100];
cin >> m;
for ( int j = 0 ; k <= m-1 ; j++ ) {
cin >> a[j];
cin >> b[j];
}
Carry = 0;
i = 0; 25

while ( i < m ) { …

Programming Languages

• Are not particularly good either
– Too many implementation details to worry
about
– Too rigid syntax
• Easy to lose sight of the real task

26

Pseudo-code
• We need a compromise between the two:
 Pseudo-code
• Computer scientists use pseudo-code to
express algorithms:
– English like constructs (or other natural
language), but
– modeled to look like statements in typical
programming languages.

27

Pseudo-code Primitives
Three basic kind of operations:
• Sequential
– Computation ( Set … )
– Input/Output ( Get ... / Print ... )
• Conditional
– If … Else
– If …
• Iterative / looping
– Repeat ...
– While ...
28

Computation
General format:
Set the value of <variable> to <expression>

Performs a computation and stores the
result.
Example:
Set the value of C to (A + B)
Set the value of location to 0
Set the value of GPA to (sum / count) 29

Variables
A variable is a named storage.
- A value can be stored into it, overwriting
the previous value
- Its value can be copied
Examples:
Set the value of A to 3
The variable A holds the value 3 after its
execution
Set the value of A to (A+1)
Same as: add 1 to the value of A ( A is now 4) 30

Not too Strict on Syntax
• Pseudo-code is kind of a programming language
without a rigid syntax, for example we can write:
– Set the value of A to (B+C)
• as
– Set A to (B+C)
• or even:
• Set the value of sum to 0
• Set the value of GPA to 0
• as
• Set sum and GPA to 0

31

Sequential Operations - Input/Output

Input
Outside world
Output

•The Computer needs to communicate with
the outside world:
INPUT operations allow the computing agent to
receive from the outside world data values to use in
subsequent computations.
OUTPUT operations allow the computing agent to
communicate results of computations to the outside
world.
32

Input
General format:
Get a value for <variable>

The computing agent (computer) suspends
executions and waits for an input value.

33

Input - Examples
• Examples:
– Get value for grade
– Get values for N, M
• Can write:
– Get value for N1
– ...
– Get value for N100
• as
– Get value for N1,..., N100

34

Output
General format:
Print the value of <variable>
Print the message, "<text>"

The computing agent (computer) displays the value
of the variable(s).

35

Output - Examples
• Examples:
– Print the value of grade
– Print the message, "Hello"
• Can write:
– Print the value of N1
– ...
– Print the value of N100
• as
– Print the values of N1,..., N100

36

Example
• Write an algorithm to calculate the
average of three numbers.
Steps Operations
1 Get values for N1, N2, and N3
2 Set the value of Average to (N1+N2+N3)/3
3 Print the value of Average
4 Stop

37

Conditional Operations

If <condition> then
operations for the then-part
Else
operations for the else-part

1. Evaluate <condition> expression to see
whether it is true or false.
2. If true, then execute operations in then-part
3. Otherwise, execute operations in else-part.
38

Conditions, or Boolean Expressions

• A condition is one whose value is true or
false, for example:
3>2 is greater than (true)
 3=2 is equal to (false)
 A>2 is true if A’s value is greater
than 2 (at the time this is
executed), false otherwise.

39

Conditions may be compounded
E1 or E2
true if at least one of them is true; false
otherwise.
E.g. 3 > 2 or 2 > 3 is true
E1 and E2
true if both are true; false otherwise
E.g. 3 > 2 and 2 > 3 is false
not E
true if E is false, false if E is true
40

Example
1. Get a value for A
2. If A = 0 then
3. Print the message, “The input is zero”

Else
4. Print the message, “The input is not zero”
1. Get a value for grade
2. If grade < 1 or grade > 9 then
3. Print the message, “Invalid grade”
Else
4. Set the value of total to (grade + total) 41

Iterative Operation - While
While <condition> remains true do steps i to j
step i: operation
step i+1: operation
…
step j: operation
1. Evaluate <condition>
2. If condition is true, execute steps i to j,
then go back to i.
3. Otherwise, if condition is false,continue
execution from step j+1. 42

Example
1 Get a value for count
2 While count < 10 do
3 Set square to (count * count)
4 Print the values of count and square
5 Add 1 to count
6 Stop

43

While Loops
What happens when it gets executed?
If count starts with 7, we get printout
7 49
8 64
9 81
What if count starts with 11?
Nothing is printed, loop is executed 0 times.

44

Exercise
What does the following algorithm do?

Set value of A equal to 1
While A > 0
Print message, “Enter an integer”
Get a value for A
End of the loop
Stop

45

Tracing an algorithm

The current values of algorithm variables at
various points during execution can be
known by tracing the algorithm with a table
called Trace Table

46

Trace Table
Problem: Determine the value of the variable x and y
after the following algorithm is executed
Pseudocode:

Ne
x=5

st
Y=7

in
If x = 5 then

g?
y= 8

? ?
else
y= 0
if y = 7 then
x=6
else
x=3
if x = y then 47
y=0

… Continued
Trace table for algorithm

Step X y
No.
1 5 -
2 5 7
3 5 8
4.1 5 8
4.2 3 8
4.3 3 8
48

Sequential Search: an Example
Find the phone number of a given Name in an
(unsorted) list of names and their phone numbers
Names Phone numbers
N1 T1
N2 T2
…
N1000 T1000

49

Sequential Search: an Example
d:
fin
to
e o hn
Nam ,J
it h
1 553614
Sm
2 442563
3 521463
4 541236
5 452361
6 442563
7 551123
8 441155
9 521364
10 528975
11 541258 50

Sequential Search: 1st Attempt
1. Get value for Name
2. Get values for N1,…,N1000
3. Get values for T1,…,T1000
4. If Name = N1 then print the value of T1
…
1003. If Name = N1000 then print the value of 1000
1005. Stop
51

Sequential Search: Using a Loop
Get values for Name, N1,…, N1000, T1,…, T1000
Set the value i to 1 and the value of Found to 0
While Found = 0 AND i <= 1000 do
If Name = Ni then
Print the value of Ti
Set the value of Found to 1
Else
Add 1 to the value of I
EndIF
End of While loop
52
Stop

Selection: Find the Largest Number

Given a list of variables A1, A2, …, An, find the
largest value and its (first) location

Location A1 A2 A3 A4 A5 A6 A7
Value 5 2 8 4 8 6 4
The largest is 8 at location 3
Idea (sketch): Go through the entire list, at each
iteration find the largest-so-far and record its
location
53

i

Value 5 2 8 4 8 6 4

To begin with,
set largest-so-far to (the value of) A1
set location to 1
set i to 2
54

i

Value 5 2 8 4 8 6 4

Compare A1 and A2
largest-so-far still holds the value of A1
set i to i+1

55

i

Value 5 2 8 4 8 6 4

Compare A1 and A3
largest-so-far now holds the value of A3
location is 3
set i to i+1
56

i

Value 5 2 8 4 8 6 4

Continue the similar process until i = 8

57

Selection: Find The Largest Number
Get a value for n, the size of the list
Get values for A1, A2, …, An, the list to be searched
Set largest_so_far to A1 and set location to 1
Set the value of i to 2
While i is less or equal to n do
If Ai > largest_so_far then
Set the value of largest_so_far to Ai
Set the value of location to I
EndIF
Add 1 to the value of i
End of While loop
Print the values of largest_so_far and location
58

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