1. CSE1301 Computer Programming Lecture 2: Introduction to Algorithms

2. Topics A little bit of History: Systematic problem solving Algorithms
The idea of a universal machine
Systematic problem solving
Algorithms

3. A “Universal” Machine Programmability
Binary Code (everything stored as “0” or “1”)
Program and Data are represented in the same form
Electronic Components
A washing machine is also programmed, but not universal…

4. Early Computing History in a Nutshell
200 BC - today
Abacus -
~1670
Leibniz’ “Rechenmaschine”
Fixed calculations
+, -, *, /, sqrt
~1750
Jacquard’s Loom
Punch Tape
1820
Babbage’s “Difference Engine”
Fixed Table Calculation
1838
Babbage’s “Analytical Engine”
Program & Data separate
1841
Ada Byron, Lady Lovelace
First program (Bernoulli-Numbers)

5. Leibniz’s Step Reckoner
Gottfried von Leibniz 1670
Add, subtract, multiply, divide, square roots

6. Jacquard’s punch card Joseph Marie Jacquard 1804
punch cards used to operate loom

7. Babbage’s analytical engine
Charles Babbage ( )
Design for the analytical engine
Motivated by error in vital tables.
British Empire -> Navy -> Navigation Tables
Industrial Revolution -> Life Insurance -> Risk Tables
Programmable, but mechanical.
Data+Program separate

8. One of the first Programmers
Lady Ada Augusta Byron, Countess of Lovelace ( ) ( )

9. Early Computing History in a Nutshell
200 BC - today
Abacus -
~1670
Leibniz’ “Rechenmaschine”
Fixed calculations
~1750
Jacquard’s Loom
Punch Tape
1820
Babbage’s “Difference Engine”
Fixed Table Calculation
1838
Babbage’s “Analytical Engine”
Program & Data separate
1841
Ada Byron, Lady Lovelace
First program (Bernoulli-Numbers)
However, what universal really means was only understood in the 1930’s
Babbage’s machines were never completed
First universal programmable machine

10. The Ancestors 1886 Hollerith Punch Cards 1936 Zuse Z1 Relais 1941-1944
Binary code
1886
Hollerith
Punch Cards
1936
Zuse Z1
Relais
Zuse Z3/Z4
“Plankalkül”
1944
Mark I
Partly mechanic
1943
Colossus
Not universal
1946
Eniac
Programmable with Re-wiring
1949
Manchester Universal Computer
Cathode-Ray Tube Memory
universal
electronic
Integration:
fully electronic
binary
Programmable
universal

11. Hollerith’s Tabulating Machine
Herman Hollerith ( )
Invented a punched card device to help analyse the 1890 US census data
Founded “Tabulating Machine Company” 1896
1924 – Tabulating Machine Company merges with others to form IBM
Reduced census effort from 10 years of manual counting to two years
Trying to find new markets, Hollerith then expanded his business to Railway companies
Binary but not really programmable

12. Konrad Zuse
1936: Z1 first binary computer using Erector Set parts, keyboard and lights for output (relay memory)
1938: Z2 – using punched tape and relays
Original motivation: solving simultaneous equations in aircraft construction problems (stability) Z1
Z3: fully binary, fully programmable, but partly mechanical

13. Colossus Fully electronic, but not universally programmable
1943 British Colossus – (1,500 vacuum tubes)
Decipher enigma coded messages at 5,000 chars/sec
At peak, 10 machines ran 24 hours a day in Bletchley Park
A German enigma coding machine
Fully electronic,
but not universally programmable

14. Harvard Mark 1 Universal, fully programmable But partly mechanical
Aiken at Harvard/IBM “Mark 1” – first electromechanical digital computer (electromagnetic relays – magnets open and close metal switches) (recreation of Analytical Engine)
8 ft tall, 50 ft long, 1 million parts
323 decimal-digit additions per sec
storage for digit numbers.
Developed at Harvard together with IBM and support of the Navy
Universal, fully programmable
But partly mechanical

15. ENIAC (1946) Fully electronic, programmable
18,000 tubes, 1500 sq ft
Programmed by wire plugs into panels
5,000 decimal-digit additions/sec
20 10-decimal digit “accumulators”
Original motivation: calculating tables required for aiming anti-aircraft fire
Von Neumann and ENIAC
Fully electronic, programmable
But extensive-wiring required

16. Experminental MUC (1949) First fully electronic universal computer
1941 Von Neumann proposes EDVAC – Electronic Discrete Variable Computer
Computer should
Use binary
Have stored programs
Be function-oriented
Team Members from Bletchley Park and EDVAC/ENIAC collaborate at Manchester
Add CRT display memory
First fully electronic universal computer

17. 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 …
Executable (solution)

18. 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. */
This Is not a linear process!
Program
Compilation
Executable (solution)

19. The Problem-solving Process
Analysis
Problem specification
Design
Algorithm
Implementation
Program
Compilation
Executable (solution)

20. 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 C.E. (Common Era)

21. Algorithm –History Muhammad ibn Musa Al-Khwarizmi Book on arithmetic:
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

22. Algorithm – Working Definition
A sequence of instructions describing how to do a task
[As opposed to actually executing
the instructions]

23. 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

24. Algorithm – Examples (cont)
Recipe for Almond and honey slice
Recipe for Arroz con pollo

25. 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 Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

26. 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 Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

27. 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.

28. 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.

29. 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 10 minutes.
Add beans and artichokes.
Cover, and bake for another 10 minutes or until rice is tender.

30. From Algorithms to Programs
Algorithm: A sequence of instructions describing how to do a task (or process)
Problem
C Program

31. Components of an Algorithm
Variables and values
Instructions
Sequences
Procedures
Selections
Repetitions
Also required: Documentation

32. 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

33. 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 Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

34. 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 Cook’s Companion, Viking/Penguin, Ringwood, Victoria, 1996, p. 349.

35. Variables Are containers for values – places to store values Example:
This jar
can contain
10 cookies
50 grams of sugar
3 slices of cake
etc.
Values
Variable
One form: strain the juices, put aside and let cool …(further instruction)… now add the reserved mix
In mathematics much more precisely: Call the sum of all items X. Call the number of items N… divide X by N

36. Restrictions on Variables
Variables may be restricted to contain a specific type of value

37. 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)

38. Summary Reading Deitel & Deitel, C: How to program
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