CS107Introduction to Computer

ScienceLecture 2

Administrativia

• Lab access– Searles 128: daily until 4pm unless class in progress– Searles 117: 6-10pm, Sat-Sun 12-10pm

• Office hours– M, W 4-5 pm – Quick questions: Anytime I am in the office– Email to set up appointment

• My office: Searles 219• Study group

– Mondays 8-9pm in Searles 224

Last time– What is (not) Computer Science– Algorithms, properties and examples– Expressing algorithms: Pseudocode

• Who was Alan Turing and what is he famous for?

• Today– More pseudocode elements– Algorithm examples

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 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

• Repeat operations– Execute a block of operation multiple times until a certain

condition is met

Basic operations

– Read the input from user• Get x • Get a, b, c

– Print the output to the user• Print x• Print “Your mileage is ” x

– Cary out basic arithmetical computations• Set x to 10• Set y to x*x/3

Conditional statementsSpecify a statement that may or may not be done:

if <condition> then<statement to be done>

else <statement to be done otherwise>

Example

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

Loop statements

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

repeat until <condition>< 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

ExampleVariables: countStep 1: set count to 1Step 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 countStep 5: add 1 to count

Step 6: end

• What does this algorithm do? • Note: indentation

– Not necessary, but makes reading/understanding algorithms easier

Pseudocode examplesEquivalent:

– Set the value of a to 1– Set a to 1– a=1

Equivalent– Add 1 to count– Set count to count + 1– Increment the value of count by 1– count = count + 1

Writing in pseudocode gives you the freedom to choose any of these!

• Incorrect– Set 1 to a– Add a + b (what do you do with the result?)– Set a+b +3

• Note: not the same– set a to b – set b to a

• Example: what is the output of the following algorithms?set a to 2 set a to 2set b to 4 set b to 4set a to b set b to aprint a, b print a, b

A model for visualizing an algorithm’s behavior

Algorithm

Computer

Input (keyboard)

Output (screen)

Variables

Algorithm for computing MPG (Fig 2.5)

Write a pseudocode algorithm to compute the distance traveled and the average miles per gallon on a trip when given as input the number of gallons used and the starting and ending mileage readings on the odometer.

Variables: response, gallons, start, end, distance, mpg0 Set response to “Yes”1 Repeat steps 2-8 until response = “No”

2 Get gallons, start, end3 Set distance to end - start4 Set mpg to distance ÷ gallons5 Print mpg6 if mpg > 25.0 then print “You are getting good

gas mileage” else print “You are NOT getting good gas mileage”7 Print “Do you want to do this again, Yes or No?”8 Get response

9 Stop

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:

response gallons12000start

Yes 25

After step 4, the variables distance and mpg are computed.

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?

end

distance

13000

1000

Visualizing Fig 2.5

response

end

distance

Yes gallons

start

mpg

0 Set response ……11 Stop

Computer

Input (keyboard)

Output (screen)

251200013000

Designing Algorithms: A Methodology

1. Read the problem, identifying the input and the output.

2. What variables are needed?3. What computations are required to achieve the

output?4. Usually, the first steps in your algorithm bring

input values to the variables.5. Usually, the last steps display the output6. So, the middle steps will do the computation.7. If the process is to be repeated, add loops.

How was the MPG program (Fig 2.5) designed?

Problem statement: Write a pseudocode algorithm to compute the distance traveled and the average miles per gallon on a trip when given as input the number of gallons used and the starting and ending mileage readings on the odometer.

Input: number of gallons, starting mileage, ending mileageOutput: distance traveled, average miles per gallonVariables: gallons, start, end, distance, mpgCalculate: distance = end - start

mpg = distance / gallonsPut the steps in order: input, calculate, output (steps 2-8)Determine if a loop is needed (steps 0, 1, 9, 10)

Problem

• Adding two n-digit numbers

7597831 + 1287525-------------------

8885356

How would you write an algorithm to solve this problem? Assume the basic operation is adding one-digit numbers.

Computing the sum 1+2+….+n

Problem: Write an algorithm which reads a positive integer from the user and computes the sum of all positive integers smaller than or equal to te number entered by the user.

– Example: if the user enters 10, the algorithm should compute 1+2+3+…+10

Gauss formula

• Find a formula for 1 + 2 + ……. + n

Gauss noticed that • 1 + n = n+1• 2 + (n-1) = n+1• ….

==> 1 + 2 + … + (n-1) + n = n(n+1)/2