DCP2073 Asas Pengaturcaraan C Lecture 2: Introduction to Algorithms

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DCP2073Asas Pengaturcaraan CLecture
2Introduction to Algorithms
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Topics

• A little bit of History
• The idea of a universal machine
• Systematic problem solving
• Algorithms

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A Universal Machine

• Programmability
• Binary Code (everything stored as 0 or 1)
• Program and Data are represented in the same
  form
• Electronic Components

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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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The Problem-solving Process
"Doctor, my head hurts"
Patient has elevated pressure in anterior
parietal lobe
1. Sterilize cranial saw 2. Anaesthetize
patient 3. Remove top of skull 4. Get the big
spoon... 5. etc., etc.
sterilize(saw,alcohol) raise_hammer() lower
hammer(fast) start(saw) / etc. etc. /
01001110101100101010101010010101010101001100101010
10101001011010011101010101010010010111010011110101
010111110101010001101
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The Problem-solving Process
"Doctor, my head hurts"
Patient has elevated pressure in anterior
parietal lobe.
Analysis
Problem specification
1. Sterilize cranial saw 2. Anaesthetize
patient 3. Remove top of skull 4. Get the big
spoon... 5. etc., etc.
Design
Algorithm
Implementation
sterilize(saw,alcohol) raise_hammer() lower
hammer(fast) start(saw) / etc. etc. /
Program
Compilation
01001110101100101010101010010101010101001100101010
10101001011010011101010101010010010111010011110101
01011111010101000110100001101...
Executable (solution)
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The Problem-solving Process
Analysis
Problem specification
Design
Algorithm
Implementation
Program
Compilation
Executable (solution)
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Algorithm

• 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)

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Algorithm History

• Muhammad ibn Musa Al-Khwarizmi
• http//www-groups.dcs.st-andrews.ac.uk/history/Ma
  thematicians/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 wal-muqabala

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Algorithm Working Definition

• A sequence of instructions describing how to do a
  task

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

• 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.

• 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

From Stephanie Alexander, The Cooks Companion,
Viking/Penguin, Ringwood, Victoria, 1996, p. 349.
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Almond and Honey Slice

• 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.

• 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

Instructions are given in the order in which they
are performed (executed)
From Stephanie Alexander, The Cooks Companion,
Viking/Penguin, Ringwood, Victoria, 1996, p. 349.
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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 (350F) 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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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 (350F) 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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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 (350F) for 10 minutes.
• Add beans and artichokes.
• Cover, and bake for another 10 minutes or until
  rice is tender.

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From Algorithms to Programs
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Components of an Algorithm

• Variables and values
• Instructions
• Sequences
• Procedures
• Selections
• Repetitions
• Also required 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

• 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.

• 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

From Stephanie Alexander, The Cooks Companion,
Viking/Penguin, Ringwood, Victoria, 1996, p. 349.
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Almond and Honey Slice

• 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.

• 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

From Stephanie Alexander, The Cooks Companion,
Viking/Penguin, Ringwood, Victoria, 1996, p. 349.
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Variables

• 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 Algorithm

• Values 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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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