sessions 2-3 (algorithms and flowchart)

7/30/2019 Sessions 2-3 (Algorithms and Flowchart)

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Introduction to Programming

Sessions 2 & 3: Introduction to Algorithms and Flowchart

Instructor: Arash [email protected]

Sharif University of TechnologyDepartment of Computer Engineering

Spring 2008


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Sharif University ofTechnology

Introduction to ProgrammingSessions 2,3: Alg. & Flow Chart

2

Outline

Algorithm Basic Blocks

Conditional Statements

Examples of Algorithm Design

Flowcharts Flowchart Symbols

Flowchart Examples

Arrays in Algorithms


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Basics of Algorithms

4 types of statements :


If statements

Calculation Statements

Assignment statements

Explanation Statements

Begin, End

Input/Output Statements


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Conditional statements:

Simple conditional statement: If then Changes the order of statements execution

An algorithm to calculate even numbersbetween 10 and 99

1. Start2. I 103. Write I in standard output

4. I I+25. If (I


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Conditional Statements (contd)

Design an algorithm which gets a natural value, n,

as its input and calculates odd numbers equal orless than n. Then write them in the standardoutput:

1. Start

2. Read n3. I 1

4. Write I

5. I I + 2

6. If ( I


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Second type of conditional statements:

If Then Else Design an algorithm which generates even numbers

between 1000 and 2000 and then prints them in thestandard output. It should also print total sum:

1. Start2. I 1000 and S 03. Write I4. S S + I5. I I + 2

6. If (I


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Design an algorithm with a natural number, n, as its

input which calculates the following formula andwrites the result in the standard output:

S = + + +1/n

1. Start

2. Read n3. I 2 and S 0

4. S= S + 1/I

5. I I + 2

6. If (I


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Loop: A sequence of statements which will

be repeated in the algorithm execution.

Counter: A variable which defines thenumber of repeats.

Increment or decrement counter in eachexecution

Check the value of the counter to find out end ofexecution

Usually named: I

Most of previous examples


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Determine the value of loop counter in each step of the

following algorithm:1. Start

2. N 2

3. Read i, j and k

4. t i + j + k5. Write t

6. N N+2

7. If (N


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Algorithm Design

Design an algorithm which gets a natural number, N,

and determines if is it complete or not? Complete number (N): If the sum of all the denominators(less than N) equals to N itself. for example: 6 = 1 + 2 + 3

1. Start

2. Read N

3. S 04. I 1

5. R N-I*[N/I]

6. If (R=0) then S S+I

7. I I + 1

8. If ( I


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Algorithm Design (contd)

Design an algorithm which gets a natural number, n,and determines that if it is prime or not? what is the idea?1. Start2. Read N3. I 2

4. R N-I*[N/I]5. If ( R = 0) then write N is not prime

and go to line 96. I I + 1

7. If ( I < N) then go to line 48. Write N is prime9. End This algorithm works for numbers greater than 2

N/2 or N could beused but N

reduces numberof iteration


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Flowcharts

Flowchart: A set of graphical symbols to

give a simple description of algorithms. Design algorithm

Draw flow chart

Convert flow chart to programming languagestatements


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Flowchart Symbols

Start and End

use arrows to connect components of a flow chart

the end symbol can have multiple input arrows

Assignment and Process

Input and Output

Start

End

R [N/I] A 2 S S+I

Read N Write R


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Flowchart Symbols (contd)

Conditional Decision Symbol

multiple input or output arrows

Continue If the chart is to complex

You need to cut it some where and continue it in

the another partition

N < 5 Npositivenegative

zero

true

false

A

A


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Flowchart Examples

A very simple example:

Flowchart for an algorithm which gets twonumbers and prints sum of their value

1. Start

2. Read A and B3. C A + B

4. Print C

5. End

Start

End

Read A , B

C A + B

Print C


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Flowchart Examples (contd) Flowchart which calculates the real roots of a quadratic equation

and then prints them: ax2+bx+c=0

1. Start2. Read a3. If ( a =0) then go to line 24. Read C and b5. D b2-4ac6. If ( D >0) then

6.1. X1 (-b+D)/2a and X2 (-b-D)/2a6.2. Write X1, X26.3. go to line 9

7. If ( D = 0) then7.1. X -b/(2a)7.2. Write X

7.3. go to line 98. Write no real root9. End

Start

End

Db2-4ac

Read a

a=0

Read c,b

no

Yes

D

X-b/2a

= 0

X1(-b+D)/2aX2(-b-D)/2a

> 0

write x1,x2

A

write no rootA

write X


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Flowchart Examples (contd)

Flowchart for the problem of printing even numbers

between 9 and 100:Start

End

Write I

I 10

I I+2

I


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Flowchart for the problem of printing odd numbers less

than a given number. It should also calculate their sumand count.

Put multiple statements in just one symbol

Use lower number of

symbols you can

Start

S0

W

0I 1

Read n

I


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Flowchart for the problem of determining prime number:

Start

I 2

Read N

write N isprime

B

N=2

no

Yes

R N-I*[N/I]

R=0no

I I+1

A

I


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Flowchart Examples (contd) Quiz? Draw a flowchart which generates first 50 items of the Fibonacci

series.

1, 1, 2, 3, 5, 8,

1. Start2. Write 13. Write 14. I35. F1 16. F2 17. F3 F1+F28. Write F39. I I+110. If (I


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Arrays in Algorithms

Design an algorithm to convert a decimal

number, n, to binary format: division idea

1. Start

2. Read N

3. R N-2[N/2]

4. Write R

5. N[N/2]

6. If N>0 then go to line 3

7. End

12

12

2

6

6

2

2

2

3

10 01

2

01 The result will be

(0011) instead of(1100)We need a

mechanism to saveintermediateresults


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Arrays in Algorithms (contd)

Index: A symbol which is used to differentiate

between variables with the same major name

Array (indexed variable): A set of variables with the

same name but different indices

In your algorithms you

can refer to A1 as A(1)

X1 X2

A

A1 A3 A5

A2 A4


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Arrays in Algorithms (contd) The corrected algorithm:

1. Start

2. Read N3. I14. If N0) then

12.1. J J+112.2. Go to line 9

13. Write A(J)

14. J J-115. If J>0 the go to line 1316. End

This line is only used forbetter understanding,you should not use themin your algorithms


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Arrays in Algorithms (contd)

Flowchart Start

I 1

Read N

write A(J)

BN0

J 1

A

N>0

A

End

B

no

Yes

I I+1

A(J) R

N [N/2]

J J+1

J J-1

no

Yes

sessions 2-3 (algorithms and flowchart)

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