m01 computing and algorithms

1 of 39Module 1 : Computing and Algorithms

Introduction to

Computational Thinking

Module 1 :

Computing and Algorithms

Assoc Prof Chi-Wing FU, Philip

Office: N4-02c-104

email: cwfu[at]ntu.edu.sg


Topics

• What is Computational Thinking?

• What is an Algorithm

• How to Express an Algorithm?

• Flowcharts

• Nassi-Schneiderman Diagrams

• Pseudo-code


What is Computational Thinking?

• It is a “problem solving” process that involves

• Analysis and modeling of the problem and the data

• Understand of how computers work

• Acquire logic and procedural design concepts

• Formulate a computational solution that one

can use a computer to resolve the problem

• Automation

• Efficiency

• …


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!


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


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


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!!!!!!!


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)

……

Accumulator


Method 1

……

Accumulator ← Accumulator x 3



Step 3: Lastly, output last 4 digits in Accumulator


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!


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!!!


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!!!


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, …

See course “Introduction to Computing Systems”

(which runs in parallel)

http://en.wikipedia.org/wiki/Human_computer



• What is an Algorithm?

• How to Express an Algorithm?

• Flowcharts

• Nassi-Schneiderman Diagrams

• Pseudo-code

Topics


What is an Algorithm?

• Just like the example you saw…

When you formulate a method/procedure for

solving a problem, it has to be computable;

such a procedure 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


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 onComputational

Thinking

Programming


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 may take in the future:

“CZ2001 Algorithm” in 2nd year)


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


• 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


• Example: Making scrambled eggs

More detail? it depends, e.g., audience

Source: http://whatscookingamerica.net/Eggs/ScrambledOmelette.htm


Topics


• What is an Algorithm?

• How to Express an algorithm?

• Flowcharts

• Nassi-Schneiderman diagrams

• Pseudo-code


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:


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








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








How to express an Algorithm?

• Three general (and very common) techniques to express algorithms:

• Flowcharts

• Nassi-Schneiderman diagrams

• Pseudo-code


General Notes

• No strict rules

• Informal language - mix of English and keywords

• Common keywords: IF, ELSE, WHILE, etc.

• Other keywords: READ, PRINT, SET, INITIALIZE, COMPUTE, ADD, SUBTRACT, etc.

• Usually start an operation sentence with a verb

(description should be concise and precise)


#1. Flowcharts

• Represent an algorithm by a diagram for effective visualization

Symbol Name

Process

Decision

Input / Output

Terminal

Flowlines


#1. Flowcharts

Beating the eggs in a bowl

Heating a frying pan

Melt butter and put eggs on pan

If eggs ok? Stir eggsN

Y

Any ingredient? Add ingredientsY

N

end

start

Decision blocks(make choices)

Can do repetition

Can do selectionServe Scrambled Eggs

Output!


#2. Nassi-Schneiderman diagrams

• Similar to a flowchart but it is arrow-free and so more space-friendly




#1: Sequential operations: Just stack them up



#2: Selection operations: Make Branches

Any ingredient?

N Y

Serve Scrambled Eggs

Add ingredient

Here is empty,meaning do nothingbut we may also putoperations here

#3: Looping operations: Repetition

Eggs not ok?

Stir eggsWhile condition is true,keep running theoperations inside

Join again






Putting them together:

Any ingredient?

N Y

Serve Scrambled Eggs

Add ingredient

Egg not ok?

Stir eggs

Can do repetition

Can do selection



• 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[skip if N is smaller than 3]

And accumulate to NFACT


#3. Pseudo-code

• How to pronounce?

sy-ooooooooooooo-doh! code

• IDEA: directly use informal English to describe an algorithm step by step with one step per line


#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


#3. Pseudo-code

Example #2: factorial

READ N from user input

IF N <= 1

nfact = 1

ELSE

nfact = 2

REPEAT I = 3 to N

nfact = nfact x I

END IF

OUTPUT nfact


#3. Pseudo-code

Guidelines:

• Write only one statement per line

• Capitalize the keywords

• Indent to show hierarchy

• End multi-line structures

• Keep statements programming-language independent


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)


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.


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.

m01 computing and algorithms

Documents

naccumulator accumulator

factorial n

value of n

computational solution

problem automation efficiency

computational thinkingmodule

problemsolving process

efficient method