Remember from the Transition Week! Hardware Software ...Computer Science Hardware + Software + Algorithms COSC 1100 Freshman Seminar Fall 2017 Remember from the Transition Week! Algorithm

Computer Science

Hardware

+ Software

+ Algorithms

COSC 1100 Freshman Seminar Fall 2017

Remember from the Transition Week!

Algorithm = Sequence of simple steps, combined with decisions and loops.

We presented algorithms for:

• Performing simple arithmetic (multiply by 9 and 11, divide or multiply by 5)

• River-crossing (Wolf-Goat-Cabbage, Light-Medium-Heavy, Missionaries and Cannibals)

• Building hardware (adders)

• Adding a sequence of numbers (until a negative one is encountered)

All algorithms are about

breaking a problem into sub-problems

When do we stop in the “breaking” process?

When the sub-problems are simple enough for us to solve!

Algorithm for extracting parts of a string

Given a string, say Computer Science, let’s assume that we know how to split it into two parts:

• The first character, a.k.a. the head

• All the remaining characters, a.k.a. the body

We express these basic operations with functions

head(‘Computer science’) = ‘C’

body(‘Computer science’) = ‘omputer Science’

head and body are the sub-problems! (simple enough for us to solve)

Devise an algorithm to extract the secondcharacter of the string!

head(body(‘Computer Science’)) = ‘o’

Devise an algorithm to extract all but the firsttwo characters of the string!

body(body(‘Computer Science’))

= ‘mputer Science’

Devise an algorithm to extract the third character of the string!

The fourth?

All but the first three?

All but the first four?

For individual work (do not turn in!)

A: We can do it provided we know the length of the string!

Food for thought:

What if we need to extract the last character in the string?

Do you remember the function len from Python?

A: To save us a lot of writing, we need a loop!

Food for thought:

What if we need to extract the 1000th character in a (long) string?

Algorithm for buying a car

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

Which car is best?

a. Car 1 d. Not enough information

b. Car 2

c. Same

Inspired by : Udacity – Introduction to ProgrammingCOSC 1100 Freshman Seminar Fall 2017

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

Which car is best? – Best for what/whom?

b. Car 2

c. Same

Inspired by : Udacity – Introduction to ProgrammingCOSC 1100 Freshman Seminar Fall 2017

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

Which car is best for minimizing total owner’s cost ?

b. Car 2

c. Same

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

Which car is best for minimizing total owner’s cost ?

b. Car 2

c. Same

How many miles will I drive?Repairs?Insurance?Resell value?Environmental impact?

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

All we care about is the gas price!

Total miles to drive: 60,000

Average cost of gasoline: $3.10/gal

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

1. Calculate cost for each car.

2. Choose the one with lower cost.

miles: 60,000 gas price: $3.10/gal

Use Python!

winner

Use Python!

winner

Use Python to make the calculation for the current price of gas in S’ville!

To do for next time (do not turn in!)

Let’s assume that my algebra is really bad

1. Ask a friend for formula.

2. If friend doesn’t know, GO TO step 1.

3. Plug in numbers for each car.

4. Choose car with lower cost.

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

What’s wrong with this algorithm?

Cost: $35,000

MPG: 45

Cost: $10,000

MPG: 10

Still, this loop could take forever to complete!

What if I run out of

friends?

Find new friends?

An algorithm must:

1. Be guaranteed to terminate.

2. Consume finite resources.

3. Be unambiguous, i.e. precise enough to be implemented (in a programming language).

An algorithm must:

1. Be guaranteed to terminate in “reasonable” time.

2. Consume finite and “reasonable” resources.

From a practical perspective, we have additional constraints!

Example!

Hint: Ask at most 5 friends!

How would you change this algorithm so it’s guaranteed to terminate?

2. If friend doesn’t know and I asked less than 5 friends

1. GO TO step 1.

3. If # of friends asked is less or equal to 5

4. Else

1. Give up

Is this unambiguous/precise enough?

1. GO TO step 1.

4. Else

1. Give up

Add steps to keep track of the number of friends we have asked

Hint: Add a variable nr_friends

1. GO TO step 1.

4. Else

1. Give up

1. nr_friends = 0

3. nr_friends = nr_friends + 1

4. If friend doesn’t know and nr_friends < 5

1. GO TO step 2.

5. If nr_friends ≤ 5

4. Else

1. Give up

1. nr_friends = 0

3. nr_friends = nr_friends + 1

4. If friend doesn’t know and nr_friends ≤ 5

1. GO TO step 1.

5. If nr_friends ≤ 5

4. Else

1. Give up

Why do we need to ask this again

Conclusion

• Developing an algorithm is hard work!

• We call this algorithm design.

• It is not uncommon for the algorithm design phase to account for 50% or more of the total time needed for a computer project!

EOL1COSC 1100 Freshman Seminar Fall 2017

What are the three conditions any algorithm must satisfy?

An algorithm must:

1. Be guaranteed to terminate.

2. Consume finite resources.

A better algorithm for buying a car

Is this a valid algorithm?

1. For each car:

1. gas_cost = miles/mpg*gallon_price

2. total_cost = gas_cost + purchase_cost

2. If total_cost1 < total_cost2

1. Buy car 1

3. Else

1. Buy car 2

Is this a valid algorithm?

1. For each car:

1. Buy car 1

3. Else

1. Buy car 2

No, it’s not precise enough: the variables have not been initialized!

1. gallon_price = 3.10

2. miles = 60000

3. mpg1 = 45, mpg2 = 10

4. purchase_cost1 = 35000, purchase_cost2 = 10000

5. For each car:

1. Output “Buy car 1”

7. Else

Now we can follow the algorithm and decide!

Conclusion: Decision-making statements (a.k.a. if or conditional) enable algorithms to perform different operations, based on the input data.

Without the ability to make decisions, computers are just calculators!

Source: "FX-77" by Sergei Frolov, Soviet Calculators Collection - Own work. Licensed under Public domain via Wikimedia Commons http://commons.wikimedia.org/wiki/File:FX-77.JPG#mediaviewer/File:FX-77.JPG

The presence of conditional statements is what makes a computer language a programming language (e.g., HTML, XML and P3P are not programming languages)

Source: AP CS Principles – Course and Exam DescriptionsCOSC 1100 Freshman Seminar Fall 2017

Flowchart Symbols

Flowchart Rules

• Always have a Start and a Stop

• Blocks are connected with lines and arrows indicating the direction of process flow

• Try to orient all flows top to bottom or left to right

Input/Output

Process stepor instruction

Conditional Test(decision)

Start/Stop

Algorithms are built from three basic structures

• Sequential Actions

– Series of actions performed in the same order

• Decision (Conditional, or Selection)

– Two possible outcomes; one is selected based on a condition

• Loop (Repetition)

– An action is repeated until a condition is met

Nesting: Any of the structures can be inside any other, on multiple levels!

Building blocks for algorithms

Examples of sequential algorithms

The algorithm always goes through exactly the same steps, no matter what inputs are provided

Follow this algorithm, assuming the values input are x = 3 and y = 4. What is the output?

PseudocodeFlowchart

Devise a similar algorithm to find the volume of a rectangular box. (pseudocode and flowchart)

Draw the flowchart for this pseudocode:

Examples of algorithms with selection/decision

The algorithm branches into alternate paths.

Each time it’s executed, the concrete path is selected based on the inputs provided.

COSC 1100 Freshman Seminar Fall 2017Source: http://cs.iupui.edu/~telliott/n100/images/flowChart.html

COSC 1100 Freshman Seminar Fall 2017Source: http://www.the-diy-income-investor.com/2011_11_01_archive.html

Exchange-Traded Funds

What conditions must be true in order to pay down debts?

COSC 1100 Freshman Seminar Fall 2017Source: http://www.the-diy-income-investor.com/2011_11_01_archive.html

Exchange-Traded Funds

What conditions must be true in order to invest in ETFs?

Examples of algorithms with loops

The algorithm can “move backwards” and repeat the same steps multiple times.

Explain in your own words what this algorithm does

Modify the algorithm to count backwardsfrom 42 to 30 (inclusive!)

1. gallon_price = 3.10

2. mpg1 = 45, mpg2 = 10

3. miles = 60000

4. purchase_cost1 = 35000, purchase_cost2 = 10000

5. For each car:

7. Else

Is there a loop in this algorithm?

Explain in your own words what this algorithm does

Handout

Source: AP CS Principles – Course and Exam DescriptionsCOSC 1100 Freshman Seminar Fall 2017

Remember from the Transition Week! Hardware Software ...Computer Science Hardware + Software + Algorithms COSC 1100 Freshman Seminar Fall 2017 Remember from the Transition Week! Algorithm

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