1. Welcome Thinking about Algorithms Abstractly
Jeff Edmonds
CSB 3044, ext  
Jeff Edmonds
York University
Lecture 1
COSC 3101

2. Course Material Text Slides Videos
Steps, Practice Tests, Unit Tests, Exam
Extra Text: Cormen, Leiserson, Rivest, and Stein  "Introductin to Algorithms",
Good to have, but not needed for this course. 2

3. Course Material

4. Course Material Steps:
For each unit, I spoon feed you the key ideas from each unit as a set of steps.
Learn them! Understand them!
With only them, you are on your way to passing. Without them, you are on your way to failing.
Lectures consists of many examples of using these steps.
Practice Tests: Do them!
Text “How to Think about Algorithms”: If you prefer reading. 4

5. What do you think about 3101?
Was by far the hardest course ever.
I got the worst midterm mark ever.
I almost gave up.
But opened a door to such an interesting world for me.
Learned to see things abstractly and from different angles
After working a few years, I realized that 3101 was the most useful course I took.

6. What do you think about 3101?
Hey Jeff,
Never thought I would say this but I missed you a little bit.
I was able to solve some interesting business programming problems - all by myself by just thinking back to the course.
The main thing I got out of the course is belief in higher self and the ability to relax.
If taken professionally, you weren't kidding that the course would be helpful for us in life and not just academically.

7. I request that you do everything in your power.
A Contract to Learn
It deeply saddens me when a third of the class does not learn the material sufficiently to pass.
I will do everything in my power to help you learn this material.
I request that you do everything in your power.
Everyone can learn it.

8. Tough Love The last few years I threatened them every day.
They performed better than ever before!
And my course evaluations were better.

9. Think about Algorithms Abstractly
This course requires completely changing the way you think about algorithms.
Though I keep warning people,
they tend not to get it until they are
Devastated by the midterm
Change your thinking now.

10. Study Now! You spend 50hrs/week on your programming courses.
Study the material deeply before fail the tests.

11. Marks We will work you HARD: 5 practice tests 5 unit tests
Participation
An exam
Mark =
0% (only threats) 4
5%*4=20%  14%*4=56%   
2%  10%  
34%  78%  
Σi=1..4 [ 0.05 Ti  Max(Ti,E) ] 
+ [ 0.02 P Max(P,E) ] + 0.34 E 
Which is ever best for me!
Excess marks go on the exam.

12. Marks
5 unit tests:
Each unit test, half the class fails “Fail early, fail often”
Then almost everyone starts to listen and passes the exam.
Don’t want to people who fail the midterms to give up
Want people to work on the midterms
5%*4=20%  14%*4=56%   
9% max(Ti,E)
5% Ti 12

13. Basically, does he recognize you.
Marks
Class Participation:
Asking/Answering questions in class
Attending office hours
Talking to me outside of class
Submitting a photo *
Basically, does he recognize you.

14. I get frustrated reexplaining the marking scheme
Marks
I get frustrated reexplaining the marking scheme % P1 P2 T1 5% 60 25
Max(T1,E) 9% 70 95 T2 80 30
Max(T2,E) …
Participation 2% 90 20
Max(P,E) 8%
Exam
36%
Σi=1..4 [ 0.05 Ti  Max(Ti,E) ] 
+ [ 0.02 P Max(P,E) ] + 0.36 E 

15. Together
I think it is important for people to not feel isolated with the material.

16. Together Yes! The best way to learn is to teach each other!
You’re cool! Are you free sometime this weekend?
Yes! The best way to learn is to teach each other!

17. Together Some students feel too intimidated to talk to the professor.
Actually, he is just a guy who has been doing this for a while.

18. Together
Office hours: Before/after class tend to be the best time. Longer or private questions, when requested, can be taken back to my office, CSB 3044. 18

19. Together Pros Don’t have to take notes.
Lower fear level that you will miss something.
Flexible to miss a class or two if working, parenting, sick, …
Read/watch ahead to be prepared for a good discussion.
Read/watch after to review and as a reference. 19

20. Test every other week! Cant be delayed.
Together
Pros
REALLY good students might feel they don’t have to come to class (some might be right).
Cons
Cocky students will think they don’t need to come class but are wrong.
Lazy students will use them as an excuse to skip class and then never really get to them.
Test every other week! Cant be delayed. 20

21. Together Please interact with me in class.
Help me know what people are not understanding
Slow down the slides
(Though we do have a lot of material to cover)

22. Together Please ask questions! To keep the flow going
Wiggly hand: relevant to current slide.
Stationary hand: question about past material.
Avoid getting off topic.

23. Together When I ask a question to the class.
Please don’t shout out answers. So others can think.

24. Together In every class, there is one student I don’t like.
The key when talking in class is
Are you trying to help me and the class or win some compitition?

25. Together Please ask questions!
Winter 06, the average of one section was much higher than the average of the other.   (I taught them both)
My theory was that it was because a student, Gertruda, constantly asked great questions and everyone learned from them.
Ask questions for everyone’s sake.
10% of your mark is class participation!

26. Together Submit a Photo
What: 
Submit a photo on line
Add a photo to your forum account
If you would like a better rapport with your s, please include a photo.
Why:
I am very bad with names. (Sorry)
s and tests are effectively anonymous.
Needed for 10% participation mark.
You can see the class list.
How:
Submit
     - cp photo.jpg Smith_John.jpg 
- submit 3101Z photos Smith_John.jpg (or line) 26

27. Together Forum I communicate to you via the Forum.
You are also encouraged to talk to each other this way.
To be sure that you know when something has been posted, it is important to subscribe to the course forum.
Be sure to subscribe to the course forum and not just to one of its topics 27

28. Together
When you me something in topic

29. Together Two years from now:
May I have a letter of reference for grad school?
I find it awkward to write letters for people that I don’t recognize.
Make yourself KNOWN today to SOME professor.

30. Together Two years from now:
May I have a letter of reference for grad school?
I find it awkward to write letters for people that I don’t recognize.
Make yourself KNOWN today to SOME professor.
Sorry does not help as I don’t remember names

31. Together HATE that doctors charge you for a doctor's note.
And then it does not actually say that they know you were sick enough to have missed a test.
So dont tell anyone, but dont pay for a note for me.

32. So you want to be a computer scientist?

33. Is your goal to be a mundane programmer?

34. Or a great leader and thinker?

35. Original Thinking

36. Everyday industry asks these questions.
Boss assigns task:
Given today’s prices of pork, grain, sawdust, …
Given constraints on what constitutes a hotdog.
Make the cheapest hotdog.
Everyday industry asks these questions.

37. Your answer: Um? Tell me what to code.
With more sophisticated software engineering systems, the demand for mundane programmers will diminish.

38. Soon all known algorithms will be available in libraries.
Your answer:
I learned this great algorithm that will work.
Soon all known algorithms will be available in libraries.

39. Great thinkers will always be needed.
Your answer:
I can develop a new algorithm for you.
Great thinkers will always be needed.

40. Course Content A list of algorithms. Learn their code.
Trace them until you are convinced that they work.
Implement them.
Worry about details.
class InsertionSortAlgorithm extends SortAlgorithm {
void sort(int a[]) throws Exception {
for (int i = 1; i < a.length; i++) {
int j = i;
int B = a[i];
while ((j > 0) && (a[j-1] > B)) {
a[j] = a[j-1];
j--; }
a[j] = B; }}

41. Course Content A survey of algorithmic design techniques.
Abstract thinking.
How to develop new algorithms for any problem that may arise.

42. Course Content
Goal: To provide a number of different notations, analogies, and abstractions within which to develop, think about, and describe algorithms.

43. Levels of Abstraction
Given a concrete algorithm, eg. MergeSort and a concrete input, eg. <4,2,6,1,7> trace it and prove that it works.
Given a concrete algorithm, eg. MergeSort and an abstract input, eg. <x1, … xn> trace it and prove that it works.
Given a “Meta Algorithm”, eg. Iterative Algs and an abstract input, eg. <x1, … xn> trace it and prove that it works.

44. Levels of Abstraction
Given a new computational problem on exam, design a new concrete algorithm that solves it following the “Meta Algorithm” steps.
If you do not get all the details of the new algorithm correct, it wont be a disaster.
If you do not get the steps of the “Meta Algorithm correct, it will be a disaster.
There are only a few “Meta Algorithms” Learn them!

45. Levels of Abstraction “Meta Algorithms” Iterative Algorithms
Recursive Algorithms
Greedy Algorithms
Recursive Back Tracking
Dynamic Programming.
NP-Completeness

46. Levels of Abstraction “Meta Math”
Existential and Universal Quantifiers
Asymptotic Growth
Adding Made Easy Approximations
Recurrence Relations

47. Value Correctness
Don’t tack on a formal proof of correctness after coding to make the professor happy.
It need not be mathematical mumbo jumbo.
Goal: To think about algorithms in such way that their correctness is transparent.

48. Study:
Many experienced programmers were asked to code up binary search.

49. Good thing is was not for a nuclear power plant.
Study:
Many experienced programmers were asked to code up binary search.
80% got it wrong
Good thing is was not for a nuclear power plant.

50. What did they lack?

51. What did they lack?
Formal proof methods?

52. What did they lack? Formal proof methods? Yes, likely
Industry is starting to realize that formal methods are important.
But even without formal methods …. ?

53. What did they lack?
Fundamental understanding of the algorithmic design techniques.
Abstract thinking.

54. Thinking Abstractly
The psychological profiling of a successful person is mostly the ability to shift levels of abstraction, from low level to high level.
To understand the detailed workings.
To understand the big picture.
Donald Kunth

55. Thinking Abstractly
The psychological profiling of a successful person is mostly the ability to shift levels of abstraction, from low level to high level.
To understand the detailed workings.
To understand the big picture.
To understand complex things in simple ways.
Donald Kunth =

56. It is hard to think of love in terms of the firing of neurons.
Thinking Abstractly vs
It is hard to think of love in terms of the firing of neurons.
Software developers view subsystems as entities with separate personalities, roles, and interactions,
not details of code. vs

57. Thinking Abstractly
Better for communicating to friend

58. Thinking Abstractly
A form that can peculate down and dwell in your subconscious
where the miracle leaps of inspiration happen
Your subconscious does not understand JAVA code.

59. Thinking Abstractly Paradigm Shift
Is the black the form and the green the background?
Is the green the form and the black the background?
It is helpful to have different ways of looking at it.

60. Course Content Notations, analogies, and abstractions for developing,
thinking about,
and describing algorithms
so correctness is transparent

61. A survey of fundamental ideas and algorithmic design techniques
For example . . .

62. Some Math g "b Loves(b,g) "b g Loves(b,g) 2a × 2b = 2a+b 2log n = n
Input Size
Time
Classifying Functions
f(i) = nQ(n)
Logic Quantifiers
g "b Loves(b,g) "b g Loves(b,g)
Time Complexity
t(n) = Q(n2)
Adding Made Easy
∑i=1 f(i).
Logs and Exps
2a × 2b = 2a+b 2log n = n
Recurrence Relations
T(n) = a T(n/b) + f(n)

63. Iterative Algorithms Loop Invariants
<preCond>
codeA
loop
<loop-invariant>
exit when <exit Cond>
codeB
codeC
<postCond>
i-1 i
T+1
9 km
5 km
One step at a time
Code
Relay Race

64. Recursive Algorithms ?

65. Graph Search Algorithms

66. Network Flows

67. Greedy Algorithms
NEED A PIC HERE
(NOT POOH)

68. Recursive Back Tracking

69. Dynamic Programing

70. Rudich www.discretemath.com
Reduction =
Rudich

71. Course Material

72. Course Material Steps:
For each unit, I spoon feed you the key ideas from each unit as a set of steps.
Learn them! Understand them!
With only them, you are on your way to passing. Without them, you are on your way to failing.
Lectures consists of many examples of using these steps.
Practice Tests: Do them!
Text “How to Think about Algorithms”: If you prefer reading. 72

73. End

74. Useful Learning Techniques74

75. Read Ahead
You are expected to read the lecture notes before the lecture.
This will facilitate more productive discussion during class.
Also please proof read assignments & tests.
Like in an English class

76. Explaining
We are going to test you on your ability to explain the material.
Hence, the best way of studying is to explain the material over and over again out loud to yourself, to each other, and to your stuffed bear.

77. Day Dream While going along with your day
Mathematics is not all linear thinking.
Allow the essence of the material to seep into your subconscious
Pursue ideas that percolate up and flashes of inspiration that appear.

78. Ask questions. Why is it done this way and not that way?
Be Creative
Ask questions.
Why is it done this way and not that way?

79. Guesses and Counter Examples
Guess at potential algorithms for solving a problem.
Look for input instances for which your algorithm gives the wrong answer.
Treat it as a game between these two players.

80. Rudich www.discretemath.com
Refinement: The best solution comes from a process of repeatedly refining and inventing alternative solutions
Rudich

81. Together Ask me anything!
This term we will provide two hours a week of contact hours with the TA.
Ask me anything!
Class material
Help YOU solve the assignment questions.
Material missed from previous courses
Your love life

82. Yes! I will be sure to attend.
Together
This term we will provide two hours a week of contact hours with the TA.
We can have
Practice Tests
Lectures
One-on-one time
Group discussions
Yes! I will be sure to attend.

83. I will take attendance! This will effect your participation mark!
Together
I will take attendance! This will effect your participation mark!
Yes! I will be sure to attend. 83

84. Together Sorry! I will not have time to mark the assignments.
But we can I read your solution together during the TA hours.
This might be better anyway.

85. Lets schedule the office hours now.
Together
Lets schedule the office hours now.

86. Marks We will work you HARD: 6 assignments 5 practice tests
5 unit tests
Participation
An exam
Mark = 0%
0%  -4%   
4%*5=20%  11%*5=55%   
2%  10%  
35%  78%  
Σi=1..5 [ 0.04 Ti  Max(Ti,E) ] 
+ [ 0.02 P Max(P,E) ] + 0.35 E 

87. Marks
5 unit tests:
Each unit test, half the class fails “Fail early, fail often”
Then almost everyone starts to listen and passes the exam.
Don’t want to people who fail the midterms to give up
Want people to work on the midterms
4%*5=20%  11%*5=55%   
7% max(Ti,E)
4% Ti 87

88. Marks Class Participation: Asking/Answering questions in class
Attending office hours
Talking to me outside of class
Submitting a photo *

89. Marks Σi=1..5 [ 0.04 Ti + 0.07 Max(Ti,E) ] % P1 P2 T1 4% 60 25
Max(T1,E) 7% 70 95 T2 80 30
Max(T2,E) …
Participation 2% 90 20
Max(P,E) 8%
Exam
35%
Σi=1..5 [ 0.04 Ti  Max(Ti,E) ] 
+ [ 0.02 P Max(P,E) ] + 0.35 E