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CSE1301Computer Programming

Lecture 2:Introduction to Algorithms

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Topics

• Solving problems

• Algorithms

• Values and variables

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How do we solve problems?

• We "just do"

• Guesswork-and-luck

• Trial-and-error

• Experience (possibly someone else's)

• "Scientifically"

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0100111010110010101010101001010101010100110010101010101001011010011101010101010010010111010011110101010111110101010001101…

sterilize(saw,alcohol);raise_hammer();lower hammer(fast);start(saw);/* etc. etc. */

Patient has elevated pressure in anterior parietal lobe

The Problem-solving Process

Problem

specification

Algorithm

Program

Executable (solution)

Design

Implementation

Compilation

"Doctor, my head hurts"

Analysis

1. Sterilize cranial saw2. Anaesthetize patient3. Remove top of skull4. Get the big spoon...5. etc., etc.

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sterilize(saw,alcohol);raise_hammer();lower hammer(fast);start(saw);/* etc. etc. */

The Problem-solving Process

Problem specification

Algorithm

Program

Executable (solution)

Analysis

Design

Implementation

Compilation

"Doctor, my head hurts"

Patient has elevated pressure in anterior parietal lobe.

1. Sterilize cranial saw2. Anaesthetize patient3. Remove top of skull4. Get the big spoon...5. etc., etc.

010011101011001010101010100101010101010011001010101010100101101001110101010101001001011101001111010101011111010101000110100001101...

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The Problem-solving Process

Problem specification

Algorithm

Program

Executable (solution)

Analysis

Design

Implementation

Compilation

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• A sequence of instructions specifying the steps required to accomplish some task

• Named after: Muhammad ibn Musa al-Khwarizmi

of Khowarezm (now Khiva in Uzbekistan)

Circa 780-850 C.E. (Common Era)

Algorithm

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Algorithm –History

Muhammad ibn Musa Al-Khwarizmihttp://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Al-Khwarizmi.html

• Book on arithmetic:– Hindu numeration, decimal numbers, use of zero,

method for finding square root– Latin translation (c.1120 CE): “Algoritmi de

numero Indorum”

• Book on algebra– Hisab al-jabr w’al-muqabala

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• A sequence of instructions describing how to do a task

Algorithm – Working Definition

[As opposed to actually executing

the instructions]

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Algorithm -- Examples• A cooking recipe• Assembly instructions for a model• The rules of how to play a game• VCR instructions• Description of a martial arts technique• Directions for driving from A to B• A knitting pattern• A car repair manual

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Algorithm – Examples (cont)

• Recipe for Almond and honey slice

• Recipe for Arroz con pollo

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Almond and Honey Slice

1/2 quantity Shortcrust Pastry

185 g unsalted butter

100 g castor sugar

5 tablespoons honey

50 ml cream

50 ml brandy or any other liqueur or spirit

300 g flaked almonds

Preheat oven for 200° C

Line a 30 cm 20 cm baking tray with baking paper, and then with pastry

Bake blind for 20 minutes, then remove weights and foil

Turn oven up to 220° C.

Bring remaining ingredients to a boil, stirring.

Spread evenly over pastry.

Bake until topping is bubbling and has caramelised evenly, about 15 minutes.

Cool before cutting into fingers or squares.

From: Stephanie Alexander, The Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

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Almond and Honey Slice

1/2 quantity Shortcrust Pastry

185 g unsalted butter

100 g castor sugar

5 tablespoons honey

50 ml cream

50 ml brandy or any other liqueur or spirit

300 g flaked almonds

Preheat oven for 200° C

Line a 30 cm 20 cm baking tray with baking paper, and then with pastry

Bake blind for 20 minutes, then remove weights and foil

Turn oven up to 220° C.

Bring remaining ingredients to a boil, stirring.

Spread evenly over pastry.

Bake until topping is bubbling and has caramelised evenly, about 15 minutes.

Cool before cutting into fingers or squares.

From: Stephanie Alexander, The Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

Instructions are given in the order in which they are performed (“executed”)

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Correct Algorithm?Cut chicken into pieces and

brown the pieces on all sides in a casserole dish in hot olive oil.

Remove the chicken and to the juices in the casserole add garlic, onions and green peppers, and sauté until onion is golden.

Add bay leaf, whole tomatoes, and chicken broth.

When the broth boils add salt, saffron and rice.

Arrange chicken on rice, cover casserole and bake in a moderate oven (350°F) for 20 minutes or until the rice is tender.

Add beans and artichokes during last 10 minutes of cooking.

From: “Arroz Con Pollo” in The Margaret Fulton Cookbook, Hamlyn, Sydney, 1968.

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Cut chicken into pieces and brown the pieces on all sides in a casserole dish in hot olive oil.

Remove the chicken and to the juices in the casserole add garlic, onions and green peppers, and sauté until onion is golden.

Add bay leaf, whole tomatoes, and chicken broth.

When the broth boils add salt, saffron and rice.

Arrange chicken on rice, cover casserole and bake in a moderate oven (350°F) for 20 minutes or until the rice is tender.

Add beans and artichokes during last 10 minutes of cooking.

From: “Arroz Con Pollo” in The Margaret Fulton Cookbook, Hamlyn, Sydney, 1968.

Correct Algorithm?

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Cut chicken into pieces and brown the pieces on all sides in a casserole dish in hot olive oil.

Remove the chicken and to the juices in the casserole add garlic, onions and green peppers, and sauté until onion is golden.

Add bay leaf, whole tomatoes, and chicken broth.

When the broth boils add salt, saffron and rice.

Arrange chicken on rice, cover casserole and bake in a moderate oven (350°F) for 10 minutes.

Add beans and artichokes.

Cover, and bake for another 10 minutes or until rice is tender.

Correct Algorithm?

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From Algorithms to Programs

Problem

C ProgramC Program

AlgorithmAlgorithm: A sequence of instructions describing how to do a task (or process)

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Components of an Algorithm

• Variables and values

• Instructions

• Sequences

• Procedures

• Selections

• Repetitions

• Documentation

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Values

• Represent quantities, amounts or measurements

• May be numerical or alphabetical (or other things)

• Often have a unit related to their purpose

• Example:– Recipe ingredients

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Almond and Honey Slice

1/2 quantity Shortcrust Pastry

185 g unsalted butter100 g castor sugar5 tablespoons honey50 ml cream50 ml brandy or any other

liqueur or spirit300 g flaked almonds

Preheat oven for 200° C

Line a 30 cm 20 cm baking tray with baking paper, and then with pastry

Bake blind for 20 minutes, then remove weights and foil

Turn oven up to 220° C.

Bring remaining ingredients to a boil, stirring.

Spread evenly over pastry.

Bake until topping is bubbling and has caramelised evenly, about 15 minutes.

Cool before cutting into fingers or squares.

From: Stephanie Alexander, The Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

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Almond and Honey Slice

1/2 quantity Shotcrust Pastry

185 g unsalted butter

100 g castor sugar

5 tablespoons honey

50 ml cream

50 ml brandy or any other liqueur or spirit

300 g flaked almonds

Preheat oven for 200° C

Line a 30 cm 20 cm baking tray with baking paper, and then with pastry

Bake blind for 20 minutes, then remove weights and foil

Turn oven up to 220° C.

Bring remaining ingredients to a boil, stirring.

Spread evenly over pastry.

Bake until topping is bubbling and has caramelised evenly, about 15 minutes.

Cool before cutting into fingers or squares.

From: Stephanie Alexander, The Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

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Variables

This jarcan contain

10 cookies

50 grams of sugar

3 slices of cake

etc.

ValuesVariable

• Are containers for values – places to store values

• Example:

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Restrictions on Variables

• Variables may be restricted to contain a specific type of value

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Components of an AlgorithmValues and Variables

• Instruction (a.k.a. primitive)

• Sequence (of instructions)

• Procedure (involving instructions)

• Selection (between instructions)

• Repetition (of instructions)

• Documentation (beside instructions)

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Instructions (Primitives)

• Some action that is simple...

• ...and unambiguous...

• ...that the system knows about...

• ...and should be able to actually do

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Instructions – Examples

• Take off your shoes

• Count to 10

• Cut along dotted line

• Knit 1

• Purl 2

• Pull rip-cord firmly

• Sift 10 grams of arsenic

Directions to perform specific actions on values and variables.

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Instructions -- Application

• Some instructions can only be applied to a specific type of values or variables

• Examples:

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Instructions (Primitives) -- Recommendations

• When writing an algorithm, make each instruction simple and unambiguous

• Example:

Cut chicken into pieces and brown the pieces on all sides in a casserole dish in hot olive oil.

Cut chicken into pieces.

Heat olive oil in a casserole dish.

Brown the chicken pieces in the casserole dish.

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Instruction (Primitives)• When writing an algorithm, make the

instructions simple and unambiguous.

• Example:

Cut chicken into pieces and brown the pieces on all sides in a casserole dish in hot olive oil.

Cut chicken into pieces.

Heat olive oil in a casserole dish.

Brown the chicken pieces in the casserole dish.

A “sequence” of simple instructions

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Summary• Problem Solving Process• Algorithms• Components of Algorithms

– Values and Variables– Instructions– to be continued...

Reading• Deitel & Deitel, C: How to program

– Chapter 3, Sections 3.1 to 3.3