Lecture 6.2 flow control repetition

1 of 81Module 6 : Flow control

Introduction to Computational Thinking

Module 6 : Flow control #2

Asst Prof Chi‐Wing FU, PhilipOffice: N4‐02c‐104

email: cwfu[at]ntu.edu.sg


Topics• Basic Concepts: Why Selection and Repetition• Selection (Branching)

• Basic concepts• Case study: Paper Scissor Rock• Syntax• Examples in Python

• Repetition (Looping)• Basic concepts: for and while• Syntax: while• The range function• Syntax: for• Nested loops• break, continue, and pass

• Case Study: Visual Example - Path of a projectile


Basic Concepts• Recall the motivation example to compute

average student height in a class


Basic Concepts• With the looping mechanism, we can

repeat certain code arbitrarily number of times based on the need


General structure of a loopGenerally, four steps:1. Initialize: loop control variable

2. Test: continue the loop or not?

3. Loop body: main computation being repeated

4. Update: modify the value of loop control variable so that next time when we test, we MAY exit the loop

Sometimes a loop may not have all of them,e.g., infinite loop (test is always true)


General structure of a loopVisualize them by a flow chart!!!

1. Initialize2. Test3. Loop body4. Update

Initialize

Statement

Update

Testtrue

false

4

3

2

1

Loop


main:SET sum TO 0 // InitializeSET counter TO 0WHILE counter < N // Test

READ height // Loop bodyADD height TO sumINCREMENT counter BY 1 // Update

ENDWHILECOMPUTE average = sum/counterPRINT average

General structure of a loopExample: Compute average height of N students

12

3

4


Two kinds of loop1. Counter-controlled loop – the number of

repetitions is known before the loop starts execution; just repeat the loop on each element in a preset sequence

2. Sentinel-controlled loop – the number of repetitions is NOT known before the loop starts. For example, a sentinel value (e.g., –1, different from the regular data) is used to determine whether to execute the loop body


Examples:• Counter-controlled loops

Compute average student height in a class…

Assumption: we know the number of students before we start the loop


Examples:• Sentinel-controlled loops

Compute average height of people entering Canteen A in a day…

sum = count = 0time = get current timeWHILE time < Canteen A closing time

height = get height of next guysum += heightcount += 1time = get current time

END WHILE

Cannot know ahead how many people entering canteen A before we start the loop body


Examples:• A Sentinel-controlled loop

usually contains all four loop elements

InitializeTest

Loop Body

UpdateNote: time is the loop control variable


In PythonWe can implement loops by:• for – usually for counter-controlled loops• while – usually for sentinel-controlled

loop, but may also be used to implement counter-controlled loops







Python Syntax: while• Similar to an IF statement but repeat the

block till the condition becomes falseSyntax:while <boolean expression> :

suite (one or moreindented statements)

Example:while a > b:print(a," > ",b)a = a - 10

MUST use colon followedby proper indentation

the wholewhile structure

Test

true

Statement

false


Any difference? Try them!!!

Order is importantThe control FLOW!!!

Indentation is importantIt defines a block


Example #1.1• Compute and print a conversion table between

Fahrenheit and Celsius, starting from 0 deg. C


Print message

Read tempLimit

Start

fahren = 32.0

fahren<=tempLimit ?

true

fahren += 10

Print fahren, celsius

false

End

Initialize

while (Test)Statement

Update

Loop Body

Test

celsius = (fahren– 32.0) * 5.0 / 9.0


Implementation

• Who is the loop control variable?• Counter-controlled or sentinel-controlled?

Note: You will learn how to format the output as below for print() by using % in module 8 on Strings

\t - a tab space (nicer formatting)


Check loop iteration: table

False122.0

44.4True112.0

………

5.6True42.0

0True32.0

Output Celsiusfahren < tempLimitfahren


Any issue?

• Any potential issue in this program?

How if the user enters a value smaller than 32? Or? Then?What will happen? So… Any idea to fix it?


Example #1.2• Maybe… we can force the user to input

again? But how?• Idea:

• Keep asking until he/she enters a number that is at least 32 and at most a certain reasonable limit

•Now… we can add a while loop


ImplementationNew while

In the new loop:• Who is the loop control variable?• Counter-controlled or sentinel-controlled?

( ) is ok butredundant


Note:• while loop is useful if we want to

repeatedly ask user for input until the input fulfills our requirement


Example #1.3• Write a program to read numbers from

user; sum them up until the input is -1 (sentinel value)

Indicate an end


Implementation• Again, we can use while loop to

continue asking for user input…

• Who is the loop control variable?• Counter-controlled or sentinel-controlled?• Any issue to ensure for this design?

[Make sure: sentinel value will not appear in normal cases]

whilestructure


Python Syntax: while with else• while loop, oddly, can have an associated else statement

• else statement is executed when the loop finishes under normal conditions• The last thing the loop does as it exits

• Syntax:while booleanExpression:

suite1else:

suite2rest of the program

the wholewhilestructure


Python Syntax: while with else







range• Before we discuss "for" loop, we first

learn a useful built-in function in Python called range()•Note: range() is often used in "for" loop


What is range?• Generates a list of integers from start up to end (but excluding end) with stepsize step

• Syntax: it has three forms:range( end )range( start , end )range( start , end , step )

i.e., we can use/call it in three different ways…


Meaning• range( end )

- Python puts start to 0 and step to 1 (default values)- range(11) gives [ 0 , 1 , 2 , … , 10 ]

• range( start , end )- Python puts step to 1 (default value)- range(1,11) gives [ 1 , 2 , 3 , … , 10 ]

• range( start , end , step )- Python returns a list (sequence) of integers fromstart to end-1 with stepsize step

- range(1,11,2) gives [ 1 , 3 , 5 , …, 9 ]

However, range() returns a memory efficient object implicitly rather than an explicit list; we can use list to see its contents, see next page


count down

Infinite! returns an empty list (“list” is a

Error! Only integers!

start from 0 and step 1

sequence)

returns a memory efficient object


Exercises for you• How can you create a list containing

[ 0, 3, 6, 9, 12, 15 ] ?

• How can you create a list containing[ 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 ] ?

• How can you create a list containing[ 4, 2, 0, -2, -4 ] ?


What is memory efficient object?• range() returns a “range object” (memory

efficient object) that pretends to be the sequence• It is an opaque sequence which yields the same

values as "list(range())”,but NOT storing every single value explicitly; it generates values for you only when you use its contents (on demand)

• Any advantage? Think about…

Try range(1,1000000)and list(range(1,1000000))Which one consumes more memory?







Python Syntax: for• Control flow: loop through the objects

according to their order in the sequenceSyntax:for <element> in <sequence> :

suite (one or more indented statements)

Example:

for each element in it

two forstructures

can be a list also…


Note:Main issue:• Variable x (or y) in the example “for” loops will take

different values in different loop iterations

Other issues:• First, remember the colon!!!• Second, why it is always counter-controlled?• Lastly, remember range in Python!!

Excluding the ending elementi.e., not symmetric!!!range(1,5,1) != range(5,1,-1)


Example #2.1• Problem: print a multiplication table of a certain

number, e.g., 9, see below:


Example #2.1 – Algorithm?• First, ask user for a number• Then, loop from 1 to 10, compute the

multiplication, and display the formulae


Example #2.1 – Implementation• In Python, just a few lines…

Use comma to separate different elements for printEnd with 11 instead

of 10 if we want the last value to be 10


Case Study: Example #2.2• Summing a series of data using for loop

!10

x

!4

x

!3

x

!2

x

1!

x1

10432

+−+−+− LL

Basic idea to implement it:Sum the terms one by one by using a for loop,

i.e., one term per iteration


Case Study: Example #2.2• Let’s analyze the term

Observation:• First, check the terms…• 1st term is 1; 2nd term is

• Multiply 1st term with x, divide by 1 and flip the sign• Third term is

• Multiply 2nd term with x, divide by 2 and flip the sign……

!10

x

!4

x

!3

x

!2

x

1!

x1

10432

+−+−+− LL


Case Study: Example #2.2• More detailed idea to implement it

So...• We may have one variable to keep track of the term,

say term• One more variable to keep track of what to be

divided next, say divisor• Another variable to accumulate the sum, say total

!10

x

!4

x

!3

x

!2

x

1!

x1

10432

+−+−+− LL


Case Study: Example #2.2• Hence, we have:

Note:- Make sure use float forx and term

- The negative sign beforeterm can flip the sign of the term in each iteration

- I put in this “print(term)”for testing purpose;note: testing is important to verify your code!!!(after that, can just comment it)


Inputs/initialization:x = 0.9, total= 1.0, term = 1.0

Case Study: Example #2.2• We can trace each iteration to verify also:

Outputs:Result = 0.406569

…

+1

-1

sign

0.4065699.609e-0810

…

0.5050.4052

0.0999-0.91

totaltermdivisor

… …







Nested Loops• Sometimes… one level of loop is not sufficient

for the algorithmic need; an outer loop may enclose an inner loop (or even more), e.g.,

Two levels of loops!!!


Example #2.3• Note: This additional argument is used in

Python 3 to avoid the default ending \n

This is the entiresuite/block insidethe outer for loop

Only one statement inside the inner for loop

Question:How many times each print is executed?What is the control flow?


Case study: Example #2.4• Printing the full Multiplication Table

Print out fromthe program:

How many times each of these print statements is executed?


Case study: Example #2.5• Print a pattern, e.g., triangular pattern:

First… observe and analyze the pattern…How many stars on each level?How many leading white spaces?


Case study: Example #2.5• Implementation


Case study: Example #2.5.1• Use while loops inside instead

How many times these print functions are called?

Changeto

while


More Patterns?• Can you write programs

to print out each of these patterns?







What are break and continue?• Python keywords that can alter control flow

in a loop• Let’s start with the following simple loop:

- What will be printed if werun this program?

- How many times the loopis iterated?

- Note the else: statementfor while


What are break and continue?• Print out of running this program


break• Meaning: Executing break exits the immediate

loop that contains it

Compared to prev. page:We add if and break

Control flow knowledge:Go after the whole enclosing loop


break• And break is considered as an abnormal exit

from the loop… so?

No morehere3!


break• How if we include everything in a for loop?

This time, we add the outer forBasically a for statement

The print-out doubled!!Note: break affects only theinner loop that contains it


continue• To understand continue…

Let’s go back to the basic example:


continue• Skips the rest of the loop body and goes back to

the test in the loop that contains it

Compare to prev. page:We add if and continue

Control flow knowledge:Go immediately to test

in the enclosing loop


continue• If we run the program, print “here2” will only

be reached two times… why?

For continue, make sureloop control variable can be updated. Else infinite loop!

here3’sback!


pass• It has no effects (do nothing), but help

indicates an empty statement/suite/block

We add else: and pass

Nochange!







Case Study: Path of a projectile• In many computer games, we can see parabolas,

which are the trajectories of throwing objects

But how to compute a parabola?From http://www.youtube.com/watch?v=bNNzRyd1xz0

You are advised to try and go through this example yourself with Python and Excel


Input and coordinate system• First, what is our input?• Let’s say:

u – initial velocitya – angle

• 2D Coordinate System:x – along horizony – height

0

y

x

u

horizona

x

y u

a


Initial velocity along x and y• In Physics, we know that we can decompose

u into two components (vector decomposition):ux – initial velocity along x, which is u cos(a)uy – initial velocity along y, which is u sin(a)

u sin(a) u

au cos(a)


The Physics• First, let’s look at the Physics…• We can use the following formula:

s = u t + ½ a t2

where• s = distance travelled (in m)• u = initial velocity (in ms-1)• t = time (in s)• a = acceleration (in ms-2)

(unit: m – meter, s – second)


The Physics• Along x, we assume no external forces, i.e.,

a = 0Thus, traveled distance along x at time t is:

x = ux t

• Along y, we have gravity, and so, we put a = g, which is the gravitational field constant:

a = g = -9.8ms-2

Thus, traveled distance along x at time t is:y = uy t – 4.9 t2


To compute the parabola…• To compute the parabola, we need looping to

incrementally compute the x and y locations of the object over time

More important things…• Loop control variable: time t and t starts from 0• When to stop?

Ans: object reaches the ground again or y < 0(of course, you may have more complicated stopping criteria, say hitting an object)


Implementation #1: Initialization

(note: implementation continues on in next page)

How detail we computethe parabola path; changethis value yourself and try

Need radian forcos and sin

Need math module


Implementation #2: Loop

(note: implementation continues from previous page)

Report parabola coordinates

Update loop control variable


Results• A long list of coordinates, output in IDLE shell

How can we know that the computedparabola is correct?Perhaps error here?How to verify?


Verify… Plot it with Excel #1• We can first select the coordinate outputs (with

mouse) in IDLE and click copy in IDLE• Then, we can open a text editor, and paste the

coordinates into a brand-new text file as follows:


Verify… Plot it with Excel #2• After that, we may load the text file into Excel

as a space-delimited text file:

Open the text file by Excel check delimited, and next

Then check space, next and finish


Verify… Plot it with Excel #3• Then, we can use the graph plotting function in

Excel to plot the two lists of coordinates:

y

x

I just use XY scatter plot


More to try…• You can change the initial velocity and plot more

series in the same plot: u = 100,80,60

When you verify, you have to askyourselves “Does it make sense?”


Or… to try…• You can change the initial angle and plot more

series in the same plot: a = 45,60,75

What is the angle for the optimal distance along X?You can try the code (or try implement yourself) on Edventure


Take Home Messages• General structure of a loop:

– Initialize; Test; Loop body; Update• Concepts: loop control variable, counter-controlled and

sentinel-controlled loops, nested loops• Syntax: while, for, and range• Reminders:

– Dry run and check the number of iterations!!!One more or one less iteration can kill the program… bug!!!

– Understand how and when to stop!!!– Use break and continue very carefully!!!– Read (trace code and logic) and try (work it out) more examples... – Always test and verify your code

Think and try test data that causes different consequences!!!

Practice! Practice!! Practice!!!


More…• Again the four levels of skills

like module 6.1– #1 Understand: trace and

understand code: control flow– #2 Analysis: Given a problem,

think and analyze carefully the logic

– #3 Apply: Transform the logic appropriately into for or while loops

– #4 Test: test data to evaluate with different consequences

• Practice!Practice!!Practice!!!

What is/are to be printed out?


Reading Assignment • Textbook

Chapter 2: Control2.1 to 2.4

Note: Though some material (2.3 and 2.4) in textbook is not directly related to the lecture material, you can learn more from them. Note: other than using Excel, Python has module pylab for graph plotting (see 2.4)

Technology

Lecture 6.2 flow control repetition