3. 3 of 39Module 1 : Computing and Algorithms
What is Computational Thinking?
• It is a problem solving process that involves
• Analysis and modeling of data
• Understanding of how computers work
• Logic and procedure design
• Formulating a solution that we can use a
computer to work it out
• Automation
• Efficiency
• …
4. 4 of 39Module 1 : Computing and Algorithms
What is a problem?
• First… you may wonder…
What is a problem?
It is a question proposed for a solution.
Let’s start with a simple example:
Find the last 4 digits in factorial n or n!
5. 5 of 39Module 1 : Computing and Algorithms
What is a problem?
Before that… What is a factorial?
0! = 1
1! = 1
2! = 2 x 1! = 2 x 1
3! = 3 x 2! = 3 x 2 x 1 = 6
n! = n x (n-1)! = … = n x (n-1) x (n-2) x … x 2 x 1
6. 6 of 39Module 1 : Computing and Algorithms
What is a problem?
• So… we have to find out the last 4 digits in n!
Input: n
Output: 4 digits: could be 0000, 0001, …, 9999
Computational thinking is the problem-solving
process to devise a method to compute the solution
7. 7 of 39Module 1 : Computing and Algorithms
Let’s do Problem Solving!!!
• Now, let me give you a minute to think about
how to solve this problem?
…….
Don’t look at the next slides…
Think about it yourself first!!!!!!!
8. 8 of 39Module 1 : Computing and Algorithms
Method 1
Method 1: (Straight-forward)
Step 1: First, ask the user to input or tell you n
Step 2: We can compute n! by iteratively doing
the multiplication (like using a calculator)
Accumulator initialized to n
Accumulator ← Accumulator x (n-1)
Accumulator ← Accumulator x (n-2)
……
10. 10 of 39Module 1 : Computing and Algorithms
Any issue?
• How if we use a calculator to
compute it!!!
If n is large, say 50, the accumulator will
soon be too large, and not representable and
displayable with the finite precision on your
calculator: 50! = 3.0414…x1064.
• Any better or more efficient method?
Note: we only need to know the last 4 digits…
Do we really need to know the whole value of n!
11. 11 of 39Module 1 : Computing and Algorithms
Method 2
Home exercise: your problem solving time…
• Hints:
• Since we only need the last 4 digits as output…
• The computation ONLY involves a series of
multiplication…
• Whatever we multiply two numbers, we only
need to keep …… (think about this …)
• And any trick to speed up?
• It can be more efficient and independent of the
number representation precision!!!
12. 12 of 39Module 1 : Computing and Algorithms
Computational Thinking!!
Computational thinking is a mental process
aiming at solving a problem by formulating the
solution into a procedure/method that the
computer (like a calculator) can work on
This is the focus on this course!!!!!!!
Note!!! Generally, problem-solving is independent
of the choice of programming language!!!
13. 13 of 39Module 1 : Computing and Algorithms
Computational Thinking!!
And…
Computers and programming languages are
basically tools (like calculators) for you to
formulate your solution (algorithm/procedure)
into a program that a computer can run
Note: What is computer, hardware, software, …
you should learn these in course “Introduction to
Computing Systems” (which runs in parallel)
15. 15 of 39Module 1 : Computing and Algorithms
What is an Algorithm?
• Just like the example you saw…
When you formulate a method/procedure for
solving a problem, it is something computable
and it is also called an algorithm
Algorithm VS Program
• An algorithm is a description of the procedure
on how one can follow to solve the problem
• A program is an implementation of an algorithm
in a particular language for computers to run on
16. 16 of 39Module 1 : Computing and Algorithms
What is an Algorithm?
• So… Algorithm and computational thinking are
both independent of the programming
language we choose to implement the program
Problem Algorithm Program
Run on
Computational
Thinking
Programming
17. 17 of 39Module 1 : Computing and Algorithms
Why Algorithm?
• Hence, we can analyze the problem and derive
the solution independent of programming
• Furthermore, we can also examine how easily
or difficult a language allows us to realize the
algorithm
• And how different computers impact the
realization of an algorithm, e.g., efficiency
(in a course that you will take in the future:
“CZ2001 Algorithm” in 2nd year)
18. 18 of 39Module 1 : Computing and Algorithms
Aspects of an Algorithm
• How detail should an algorithm be:
• Provide enough detail to be implementable
• Can be tricky to define completely:
relies on “common sense” and the audience
19. 19 of 39Module 1 : Computing and Algorithms
• Example: Making scrambled eggs
1. Beating the eggs for 20 to 35 seconds in a bowl
2. Heating a frying pan over a medium-low heat
3. Melt some butter in the frying pan
4. Cook eggs on the pan and stir eggs while cooking
5. Add other ingredients
6. Serve the scrambled eggs
Aspects of an Algorithm
22. 22 of 39Module 1 : Computing and Algorithms
How to express an Algorithm?
• Algorithms is basically Sequential
(step after step)
• But may include
• Branching (making a selection)
• Looping (repeating certain operations)
Step 1 Step 2 Step 3 ……Sequence:
23. 23 of 39Module 1 : Computing and Algorithms
Algorithm can have Branching
• Branching (make a selection)
• E.g., if there are extra ingredients such as herbs
and cheese, then add them to the eggs before
serving the scrambled eggs; Else we skip this step.
Example: Making scrambled eggs
1. Beating the eggs for 20 to 35 seconds in a bowl
2. Heating a frying pan over a medium-low heat
3. Melt some butter in the frying pan
4. Cook eggs on the pan and stir eggs while cooking
5. Add other ingredients
6. Serve the scrambled eggs
24. 24 of 39Module 1 : Computing and Algorithms
Algorithm can have Looping
• Looping (certain operations needed to be
repeated again and again)
• E.g., while the eggs do not look like what you
desire, keep gently stirring them in the pan
Example: Making scrambled eggs
1. Beating the eggs for 20 to 35 seconds in a bowl
2. Heating a frying pan over a medium-low heat
3. Melt some butter in the frying pan
4. Cook eggs on the pan and stir eggs while cooking
5. Add other ingredients
6. Serve the scrambled eggs
26. 26 of 39Module 1 : Computing and Algorithms
General Notes
• No strict rules
• Informal language - mix of English and
keywords
• Common keywords: IF, ELSE, WHILE, etc.
• Other keywords: READ, PRINT, SET,
INITILAIZE, COMPUTE, ADD, SUBTRACT, etc.
• Usually start an operation sentence with a verb
(description should be concise and precise)
28. 28 of 39Module 1 : Computing and Algorithms
#1. Flowcharts
Beating the eggs in a bowl
Heating a frying pan
Melt butter and put eggs on pan
If eggs ok? Stir eggs
N
Y
Any ingredient? Add ingredients
Y
N
end
start
Decision blocks
(make choices)
Can do repetition
Can do selection
Serve Scrambled Eggs
Output!
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#2. Nassi-Schneiderman diagrams
• Similar to a flowchart but it is arrow-free
and so more space-friendly
Beating the eggs in a bowl
Heating a frying pan
Melt butter and put eggs on pan
#1: Sequential operations: Just stack them up
30. 30 of 39Module 1 : Computing and Algorithms
#2. Nassi-Schneiderman diagrams
#2: Selection operations: Make Branches
Any ingredient?
N Y
Serve Scrambled Eggs
Add ingredient
Here is empty,
meaning do nothing
but we may also put
operations here
#3: Looping operations: Repetition
Eggs not ok?
Stir eggsWhile condition is true,
keep running the
operations inside
Join again
31. 31 of 39Module 1 : Computing and Algorithms
#2. Nassi-Schneiderman diagrams
Beating the eggs in a bowl
Heating a frying pan
Melt butter and put eggs on pan
Putting them together:
Any ingredient?
N Y
Serve Scrambled Eggs
Add ingredient
Egg not ok?
Stir eggs
Can do repetition
Can do selection
32. 32 of 39Module 1 : Computing and Algorithms
#2. Nassi-Schneiderman diagrams
• One more example:
Computing factorial
Can do selection
(true or false)
Here I takes a value
of 3 up to N in different
iteration of this loop, which
Is repeated with different I
And accumulate to NFACT
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#3. Pseudo-code
Example #1: Making Scrambled Eggs
BEAT the eggs for 20 to 35 seconds in a bowl
HEAT a frying pan over a medium-low heat
MELT some butter in the frying pan
PUT eggs on pan
WHILE eggs not okay
STIR eggs while cooking
END WHILE
IF any ingredients
Add other ingredients
END IF
SERVE the scrambled eggs
37. 37 of 39Module 1 : Computing and Algorithms
More detail on
these techniques
later in this course
Expressing an Algorithm
• Important Note:
• Must be unambiguous
• Every step must be clear and precise
• Specify the order of steps precisely
[Sequence]
• Consider all possible decision points
[Branching and Looping]
• Must terminate
(No matter which representation you use)
38. 38 of 39Module 1 : Computing and Algorithms
Take Home Messages
• Computational thinking is a mental process, aiming at
solving a problem by formulating the solution into a
procedure/method that the computer can work on
• Problem-solving is independent of the choice of the
programming language
• An algorithm is a description of a procedure on how one
can follow to solve the problem, whereas a program is an
implementation of an algorithm in a particular language to
run on a computer
• Algorithms may not be sequential, they may include
branching and looping; Three basic techniques to express
algorithms: flowcharts, Nassi-Schneiderman diagrams,
and pseudo-code.
39. 39 of 39Module 1 : Computing and Algorithms
Reading Assignment
• Textbook
Chapter 0: The Study of Computer Science
0.1 to 0.4
Note: Though some material in textbook is not
directly related to the lecture material, you can
learn more from them.
• Exercise:
Write down the algorithm for the problem on P.4.
![1 of 39Module 1 : Computing and Algorithms
Introduction to
Computational Thinking
Module 1 :
Computing and Algorithms
Asst Prof Chi‐Wing FU, Philip
Office: N4‐02c‐104
email: cwfu[at]ntu.edu.sg](https://image.slidesharecdn.com/lecture1computingandalgorithms-130525013914-phpapp01/85/lecture-1-computing-and-algorithms-1-320.jpg)
