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, Philip
Office: 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 loop
Generally, 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)

Visualize them by a flow chart!!!
1. Initialize
2. Test
3. Loop body
4. Update
Initialize
Statement
Update
Test
true
false
4
3
2
1
Loop

main:
SET sum TO 0 // Initialize
SET counter TO 0
WHILE counter < N // Test
READ height // Loop body
ADD height TO sum
INCREMENT counter BY 1 // Update
ENDWHILE
COMPUTE average = sum/counter
PRINT average
Example: Compute average height of N students
1
2
3
4

Two kinds of loop
1. 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 = 0
time = get current time
WHILE time < Canteen A closing time
height = get height of next guy
sum += height
count += 1
time = 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
Initialize
Test
Loop Body
Update
Note: time is the loop control variable

In Python
We 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

Topics
• Basic concepts
• Syntax
• Syntax: while
• Syntax: for
• Nested loops

Python Syntax: while
• Similar to an IF statement but repeat the
block till the condition becomes false
Syntax:
while <boolean expression> :
suite (one or more
indented statements)
Example:
while a > b:
print(a," > ",b)
a = a - 10
MUST use colon followed
by proper indentation
the whole
while structure
Test
true
Statement
false

Any difference? Try them!!!
Order is important
The control FLOW!!!
Indentation is important
It 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

Implementation
New while
In the new loop:
( ) is ok but
redundant

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…
• Any issue to ensure for this design?
[Make sure: sentinel value will not appear in normal cases]
while
structure

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:
suite1
else:
suite2
rest of the program
the whole
while
structure

Python Syntax: while with else

Topics
• Basic concepts
• Syntax
• Syntax: while
• Syntax: for
• Nested loops

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 from
start 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 ] ?
[ 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 ] ?
[ 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?

Topics
• Basic concepts
• Syntax
• Syntax: while
• Syntax: for
• Nested loops

Python Syntax: for
• Control flow: loop through the objects
according to their order in the sequence
Syntax:
for <element> in <sequence> :
suite (one or more indented statements)
Example:
for each element in it
two for
structures
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 element
i.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!
x
1
10432
+−+−+− LL
Basic idea to implement it:
Sum the terms one by one by using a for loop,
i.e., one term per iteration

• 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!
x
1
10432
+−+−+− LL

• 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!
x
1
10432
+−+−+− LL

• Hence, we have:
Note:
- Make sure use float for
x and term
- The negative sign before
term 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
• 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
… …

Topics
• Basic concepts
• Syntax
• Syntax: while
• Syntax: for
• Nested loops

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 entire
suite/block inside
the 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 from
the program:
How many times each
of these print statements
is executed?

• Print a pattern, e.g., triangular pattern:
First… observe and
analyze the pattern…
How many stars on each level?
How many leading white spaces?

• Implementation

Case study: Example #2.5.1
• Use while loops inside instead
How many times these print functions are called?
Change
to
while

More Patterns?
• Can you write programs
to print out each of these
patterns?

Topics
• Basic concepts
• Syntax
• Syntax: while
• Syntax: for
• Nested loops

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 we
run this program?
- How many times the loop
is iterated?
- Note the else: statement
for 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 more
here3!

break
• How if we include everything in a for loop?
This time, we add the outer for
Basically a for statement
The print-out doubled!!
Note: break affects only the
inner 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 sure
loop control variable can be
updated. Else infinite loop!
here3’s
back!

pass
• It has no effects (do nothing), but help
indicates an empty statement/suite/block
We add else: and pass
No
change!

Topics
• Basic concepts
• Syntax
• Syntax: while
• Syntax: for
• Nested loops

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 velocity
a – angle
• 2D Coordinate System:
x – along horizon
y – height
0
y
x
u
horizon
a
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
a
u 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 = 0
Thus, 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 compute
the parabola path; change
this value yourself and try
Need radian for
cos 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 computed
parabola 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:

• 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

• 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 ask
yourselves “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: Control
2.1 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)

Lecture 6.2 flow control repetition

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