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

More Related Content

Viewers also liked (16)

Similar to Lecture 6.2 flow control repetition (20)

Recently uploaded (20)

Lecture 6.2 flow control repetition