CS107: Introduction to Computer Science

Lecture 2 Jan 29th

• Last time – What is not Computer Science – What is Computer Science – Algorithms, properties and examples • Today – Expressing algorithms: Pseudocode – Examples • Algorithm for adding two m-digit numbers • Algorithm for computing miles-per-gallon

What is Computer Science?

The study of

algorithms

: – their formal properties • correctness, limits • efficiency/cost (Chapters 2, 3, 10) – their hardware realizations • computer design (Chapters 4-6) – their linguistic realizations • programming languages (Chapters 7-9) – their applications • network design, ocean modeling, bioinformatics, ...

What is an algorithm?

Algorithm = well-defined procedure that allows an agent to solve a problem.

Algorithms must: 1. Be well-ordered and unambiguous 2. Be executable (understandable), 3. Solve the problem, and 4. Terminate.

Note: often the agent is a computer or a robot…

Example Algorithms

• Cooking a dish • Making a peanut-butter jelly sandwich • Shampooing hair • Adding two numbers (p 7) • Programming a VCR (p 6) • Making a pie (p 13)

Designing Algorithms

We need: • A

problem

for which an effective algorithm can be written (i.e., one that is tractable), • A

language

(e.g., “pseudocode” or C++), A

methodology

for translating the problem into an algorithm, and • A computing “

agent

” that can understand and execute such algorithms.

Expressing algorithms

• Is natural language good? – For daily life, yes…but for CS is lacks structure and would be hard to follow – Too rich, ambiguous, depends on context • How about a programming language? – Good, but not when we try to solve a problem..we want to think at an abstract level – It shifts the emphasis from how to solve the problem to tedious details of syntax and grammar.

Pseudocode

• Pseudocode = English but looks like programming • Good compromise – Simple, readable, no rules, don’t worry about punctuation. Lets you think at an abstract level about the problem. – Contains only instructions that have a well-defined structure and resemble programming languages

Pseudocode elements

Basic (primitive) operations – Read the input from user – Print the output to the user – Cary out basic arithmetical computations • Conditional operations – Execute an operation if a condition is true • Sequential operations • Repeat operations – Execute a block of operation multiple times until a certain condition is met

Variables

Variable – A named memory location that can store a value – Think of it as a box into which you can store a value, and from which you can retrieve a value Examples: i carry – List variables: used when the input comes as a list of elements a m-1 a m-2 … a 1 a 0 … a 1 a 2 … a m-1 a m …

Expression and assignment statements

Function: change the value of a variable by evaluating arithmetic expressions • can use any arithmetic expression, just like on a typical calculator: +. -. *, /, … Examples

set the value of m to 2 set the value of i to 6.

set the value of carry to i+2*m set the value of a i to 0

a 1 a 2 … a m-1 a m …

Input/Output Statements

Function: transfer values from the user to a variable, or vice versa

get values for print value of

• Examples – Get the value of

n

from the user – Get value of the list of elements

a 1 , a 2 , …,a m

the user – Print the value of

result

to the user from

Sequential statements

The steps of an algorithm are carried out in the order they are written.

Conditional statements

Function: specifying a statement that may or may not be done:

if then else

Example if the value of

carry

is 0 then set the value of a to else set the vale of a to a+1 0

Loop statements

Function

:

specify a group of statements that may be done several times (repeated):

repeat until < statements to be repeated >

• How does this work? – Condition is evaluated – If it is true than the loop terminates and the next instruction to be executed will be the instruction immediately following the loop – If it is false, then the algorithm executes the <

statements to be repeated>

in order, one by one

Example

Step 1: set count to 1 Step 2: repeat step 3 to step 5 until count is > 10 Step 3: set square to count *count Step 4: print value of square and value of count Step 5: add 1 to count Step 6: end • What does this algorithm do? • Note: indentation – Not necessary, but makes reading/understanding algorithms easier

An example pseudocode algorithm (Fig 1.2)

Given: m ≥ 1 and two positive numbers a and b, each containing m digits, compute the sum c = a + b.

0 Get values for

m, a m-1 … a 0

and

b m-1 … b 0

1 Set the value of

carry

to

0

.

2 Set the value of

i

to

0

.

3 4 5 Repeat steps 4-6 until i > m-1 Set the value of if

c i ≥ 10

then

c i

to

a i + b i + carry

subtract

10

from

c i

to

1

and set the value of

carry

7 8 6 else set the value of

carry

to

0

1

to

i

Set the value of

c m

to

carry

Print value of

c = c m c m-1 c m-2 … c 0

So, how does this work???

For example, the input is m = 4, a = 3276, and b = 7345.

After step 0, the variables

m, a

, and

b

have those values: m 4 3 2 7 6 a 3 a 2 a 1 a 0 b 7 3 4 5 3 b 2 b 1 b 0 After steps 1 and 2, the variables

i

and

carry

are initialized.

i 0 carry 0 Next, steps 4-6 are repeated until the value of

i > 3

. Each repetition computes a single digit of

c

.

c 4 c 3 c 2 c 1 c 0

A model for visualizing an algorithm’s behavior

Computer Algorithm Input (keyboard) Output (screen) Variables

E.g., Visualizing Fig 1.2

Computer

0 Get values for … … 8 Print value of …

Input (keyboard)

4 3276 7345 m 4 i 0 carry 3 2 7 6 a 3 a 2 a 1 a 0 7 3 4 5 b 3 b 2 b 1 b 0 0 c 4 c 3 c 2 c 1 c 0

Output (screen)

Another example: computing MPG (Fig 2.5)

0 1 2 Set

response

to “Yes” Repeat steps 2-10 until

response

= “No” Get

gallons

,

start

,

end

11 3 4 5 Set

distance

to

end - start

Set

mpg

to

distance

÷

gallons

Print 6 7 8 9 if

mpg

> 25.0 then print “You are getting good gas mileage” else print “You are NOT getting good gas mileage” Print “Do you want to do this again, Yes or No?” 10 Get

response

Stop

mpg

So, how does this work???

For example, suppose we use 25 gallons, beginning at 12000 and ending at 13000 on the odometer. Then, after step 2, some variables have the following values: Yes

response

25

gallons

12000

start

13000

end

After step 4, the variables

distance

and

mpg

are computed.

distance

1000

mpg

40 Steps 5-9 displays these results on the output screen: 40 You are getting good gas mileage Do you want to do this again, Yes or No?

Visualizing Fig 2.5

Computer

0 Set response … … 11 Stop

Input (keyboard)

25 12000 13000 response Yes gallons start end distance mpg

Output (screen)

Summary

• Pseudocode – Get/print statements (input/output statements) – Conditional statements – Sequential statements – Loops • Algoritms – Compute sum of two m-digit numbers – Compute miles-per-gallon

Over the weekend…

1. Get the textbook.

2. Read Chapter 1, 2.1 and 2.2

3. Discuss and solve the problems in the Lab 1 (in groups or individually).

Lab 1 is due on Monday in class. If you have questions we’ll discuss them in class on Monday.

4.

Bring a digital picture for the lab tomorrow. You will need it for your website.