What NOT to do

1. I get sooooo Frustrated! Marking the SAME wrong answer hundreds of times! What NOT to do I will give a list of mistakes which I particularly hate marking& for which there is no excuse. If you do any of these thingsyou will get -20% on the question.

2. 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.

3. Types of Questions • Easy algorithmic problems testing whether you get the correct structure of iterative & recursive programs. • Get the structure correct, even if you can’t get the details of the algorithm correct. • Tell me that you know what you need to doand where you get stuck

4. Types of Questions In high school, I hated teachers who marked answers wrong if not done their way. Now I do the same. The method of thinking abstractly is important. 99% of other types of answers are wrong.

5. Types of Questions • Did you learn the basics of the algorithms taught in class? Can you trace them? • Did you do the homework? Did you read the solution set? • Math: summing, recurrence relations,  & , running time

6. Give the exact time complexity (running time). No one gave the correctanswer! Do not measure running time using the value of the input. Size = log n = s. n = 2s. Time = 2n2 + 3n + 4 = 2·22s + 3·2s + 4.

7. Give the exact time complexity (running time). T(n) = T(n/ 4) + T(n-5) + 3. Not T(n) = 3 T(n/ 4) + T(n-5) + 3. Not Eg(n) = Eg(n/ 4) + Eg(n-5) + 3.

8. Give the exact time complexity (running time). T(n) = T(n/ 4) + T(n-5) + n+ 3. Not T(n) = T(n/ 4) + T(n-5) + T(n)+ 3.

9. Loop Invariants are picturesof current state. Not actionsNot algorithms Typical Loop Invariant If the input consists of an array of objects Each iteration considers the next input item.

10. What about elements [1...i]? Typical Loop Invariant If the input consists of an array of objects We have considered the ith input element.

11. So? Typical Loop Invariant If the input consists of an array of objects We have considered input elements [1..i].

12. Typical Loop Invariant If the input consists of an array of objects We have a solution for theprefix consisting of elements [1..i]. plus some additional information

13. I have produced the first i objects. Typical Loop Invariant If the output consists of an array of objects

14. For all major algorithms covered. Learn pre and post conditions. Learn the Loop Invariant Learn how to make progress while maintaining the LI.

15. I am obsessed with the Friends - Strong Induction View of Recursion. • Trust your friends to solve subinstances. • The subinstance given must be smaller and must be an instance to the same problem. • Combine solution given by friend to construct your own solution for your instance. • Focus on one step. • Do not talk of their friends friends friends. • Solve small instances on your own.

16. generic generic generic I am obsessed with the Friends - Strong Induction View of Recursion. For binary trees, make sure that your program works for

17. Don't have inputs or outputs that are not explained! Typical Test Answer Define pre & post conditions

18. k,num,v Typical Test Answer Call recursively on the correct types of input

19. returning the correct types of output Save the results (or don't bother calling) Typical Test Answer Call recursively

20. Typical Test Answer Combine solutions given by friends to construct your own solution.

21. Not an element the root? Typical Test Answer Return things of the correct types. In every path through code

22. Typical Test Answer Subinstancesneed to be smaller. “Size” is size of the tree

23. Typical Test Answer Subinstancesneed to be smaller. When the instance sufficiently smallsolve on your own. This does not actas base casebecause k is not getting smaller

24. Typical Test Answer Subinstancesneed to be smaller. When the instance sufficiently smallsolve on your own. Code does not checkwhether the tree is empty.

25. Local variables don't change outside of the current stack frame. n = 2 Typical Test Answer No global variables allowed! Local variables (other than those holding and combining solutions) are not usually needed. Value of n?

26. Typical Test Answer No global returns. Things returned by your friends do not get returned to your boss unless you do the returning. My friend finds and returns the answer. I drop his answer. And return nothing!

27. Typical Test Answer Loops are rarely used in recursive programs. Called n times on the same input getting the same result each time! Returns the root??

28. Typical Test Answer Don’t expect your markerto be a compiler!

29. Hard to write a recursive program that implements an iterative algorithm. Typical Test Answer Reasonable Sounding Alg Traverse nodes in in-order. Count the nodes. Output the kth one. This is an iterative alg not a recursive alg. Fine (though asked for recursive)

30. Greedy Algorithms Don’ts What is the loop invariant of any greedy algorithm? We prove that the algorithm's solution is … The algorithm has made some commitments already, but this does not yet constitute a valid solution.

31. Greedy Algorithms Don’ts What is the loop invariant of any greedy algorithm? What the algorithm has done so far is optimal. What does this mean? The “More of the Input” loop invariantdoes not work.

32. Greedy Algorithms Don’ts What is the loop invariant of any greedy algorithm? “There exists an opt solution consistent with choices made so far.”

33. Greedy Algorithms Don’ts We prove it is consistent, optimal, and valid. The loop invariant of any greedy algorithm is “There exists an opt solution consistent with choices made so far.” How we prove that this loop invariant is maintained? Don't say "it" without saying what "it" is.

34. Greedy Algorithms Don’ts Great, but what does this mean? The loop invariant of any greedy algorithm is “There exists an opt solution consistent with choices made so far.” How we prove that this loop invariant is maintained? We tell the fairy god mother to change her solution optSLI into optSours. We must prove optSours is consistent, optimal, and valid.

35. Greedy Algorithms Don’ts How do we prove optSoursis consistent? The Prover compares the Fairy Godmother's optimal solution to what the algorithm has done. The Prover is unable to see the Fairy Godmother's optimal solution.

36. Greedy Algorithms Don’ts How do we prove optSoursis consistent? By the LI, optSLI is consistent with what the algorithm did in the first i steps. The Prover instructs the Fairy Godmother to change it to optSours to make it consistent with the i+1st step without missing up the earlier commitments.

37. Greedy Algorithms Don’ts How do we prove optSoursis valid? Show that the steps taken by the algorithm are valid. It is true that is important.But it is not what we need here.

38. Greedy Algorithms Don’ts How do we prove optSoursis valid? By the LI, optSLI is valid (ie does not contain conflicts within it.) The Prover instructs the Fairy Godmother to change it to optSours in a way that provably does not introduce conflicts.

39. Greedy Algorithms Don’ts How do we prove optSoursis optimal? Show that the steps taken by the algorithm are the best choice available. It is true that is important.But it is not what we need here.

40. Greedy Algorithms Don’ts How do we prove optSoursis valid? By the LI, optSLI is optimal (ie there is not a valid solution worth more.) The Prover instructs the Fairy Godmother to change it to optSours in a way that provably does not decrease its worth. Good

41. Optimization Problems • Don’t mix up the following • What is an instance • What are the objects in an instance • What is a solution • What are the objects in a solution • What is the cost of a solution • Greedy algorithm • What does the algorithm do & know • What does the prover do & know • What does the fairy god mother do & know • Recursive Backtracking / Dynamic Programming • What does the algorithm do & know • What does the little bird do & know • What does the friend do & know

42. Dynamic Programmingdon’ts • Yes, the code has a basic structure that you should learn. • But don’t copy other code verbatim • Don’t say if(ai = bj) (i.e. Longest Common Subsequence) when our problem has not bj

43. Dynamic Programmingdon’ts • When looping over the subinstances • be clear what the set of subinstances are • which is currently being solved, i.e. which instance is cost(i,j)? • If you know that the set of subinstances are the prefixes of the input, i.e. <a1,a2, …, ai>, then don’t have a two dimensional table. Table[1..n,1..n]. • Don’t loop over i and loop over j if j never gets mentioned again.

44. Dynamic Programmingdon’ts • .When trying all bird answers • be clear what the set of bird answers are, • which is currently being tried, • & what it says about the solution being looked for. • When getting help from your friend, • be clear what the subinstance is that you are giving him • How do you use the current instance and the birds answer to form his subinstance. • Don’t simply say cost(i-1,j-1)

45. Dynamic Programmingdon’ts • .Think about what the base cases should be. • Don’t make an instances a base cases if they can be solved using the general method. • % is used to start a comment. Don’t put it in front of code.

46. End