Algorithm 1: The Morning Routine Get out of bed Shower Bathe kids Prepare cereal. Algorithm 1: The Morning Routine Get out of bed Shower Bathe kids Prepare.

Algorithm 1: The Morning RoutineGet out of bedShowerBathe kidsPrepare cereal...

Algorithm 1: The Morning RoutineGet out of bedShowerBathe kidsPrepare cereal...

Math 130 Intro to Computer Programming

AlgorithmsLecture # 01

01/21/05

Math 130 Intro to Computer Programming

AlgorithmsLecture # 01

01/21/05

B Smith:

Required 45 to 50 minutes. Stirred up few questions. Needs to be more interactive and less general/abastract. Score 3 with improv, 2.5 if used as is.

B Smith:

Required 45 to 50 minutes. Stirred up few questions. Needs to be more interactive and less general/abastract. Score 3 with improv, 2.5 if used as is.

B Smith:

Great for independent study; not so great otherwise.

B Smith:

Great for independent study; not so great otherwise.

B Smith:

Not used Fall05. Not needed; not helpful

B Smith:

Not used Fall05. Not needed; not helpful

2

Overview

• Solving problems– mysterious or methodical– luck or by design

• Algorithms– recipes

• Values and variables– quantity and place holders

3

How do we solve problems?

• Largely empirical– “Doing heart surgery in this manner works”

• History– “This is how Alice did it…”

• Inspiration– “I don’t know how, but I solved it!”

• Brute force– Trial-and-error

• The scientific method

4

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.

B Smith:

Use math as a useful application. How about finding the roots of 2x^2+3x-4 = 0? What would be the algorithm.

B Smith:

Use math as a useful application. How about finding the roots of 2x^2+3x-4 = 0? What would be the algorithm.

5

The Problem-solving Process

Problem specification

Algorithm

Program

Executable (solution)

Analysis

Design

Implementation

Compilation

6

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

• Named after:– Muhammad ibn Mūsā al-

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

http://jeff560.tripod.com/khowar.jpg

Algorithm

7

Algorithm –History

Muhammad ibn Musa al-Khwarizmihttp://www-gap.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– “Kitāb al-jabr wa’l-muqābala”

• (“Rules of restoring and equating”)

8

• A sequence of instructions describing how to do a task

Algorithm – Working Definition

As opposed to actually executing the instructions!

9

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...

10

Algorithm -- Examples

• A cooking recipe• Assembly instructions for a model car,

boat, etc.• 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

11

Algorithm – Examples (cont)

• Recipe for Almond and honey slice• Recipe for Arroz con pollo

12

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° CLine 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 caramelized 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.

13

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° CLine 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 caramelized 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”)

14

Correct Algorithm?Cut chicken into pieces

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

Remove the chicken; 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.

15

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?

16

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?

17

From Algorithms to Programs

Problem

C ProgramC Program

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

18

Components of an Algorithm

• Variables and values• Instructions• Sequences• Procedures• Selections• Repetitions• Documentation

19

Values

• Represent quantities, amounts, rates, etc.• May be numerical, alphabetical or even

other items• A related unit may or may not be specified

– Add 3 cups of flour – Pull rip-cord

• Example:– Recipe ingredients (how big, how hot, how long)

20

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° CLine 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.

21

Almond and Honey Slice

1/2 quantity Shotcrust 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° CLine 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.

22

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:

23

Restrictions on Variables

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

24

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)

25

Instructions (Primitives)

• Some action that is simple......and unambiguous......that the system knows about......and should be able to actually do

26

Instructions – Examples

• Take off your shoes• Count to 10 • Cut along dotted line• Knit 1• Purl 2• Firmly Pull rip-cord • Sift 10 grams of sulfur

Directions to perform specific actions on values and variables.

27

Instructions -- Application• Some instructions can only be

applied to specific types of values or variables

• Examples:

28

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.

29

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

30

Summary

• Problem Solving Process• Algorithms• Components of Algorithms

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

Reading

Bronson, Ch 1 and Ch 2