Final Exam Review

1. Final Exam Review 6 December 2010

2. Assignment #5 • Will be due tonight @ 11:59 p.m. • Take a look at my “Review Notes” if you still have no idea how to approach the problem • Stars in cells with no dependencies • Runtime issue • We will not impose runtime constraints, but you have to use backtracking • Be aware that we will do less bug-fixing

3. Final Exam Information • On Monday, 13 December @ 4:00 p.m. – 6:50 p.m. (NOT 4:30 p.m.) • You are allowed 3 sheets of letter-sized paper with notes • Review Sessions: • Tuesday, 7 December @ 1:00 p.m. – 3:00 p.m. in HEC 101 with Remo • Wednesday, 8 December @ 1:00 p.m. – 3:00 p.m. in HEC 101 with Chris

4. Review Question 1 • Network Flow • Proposed Solution:

5. Review Question 1 • Counter Example: • Maximum Flow will be 10 • BUT: book is “split up” between boxes x1 and x2

6. Review Question 2 • Edit Distance • Remember:

7. Review Question 3 • Backtracking • You are given a set of letters, in random order, e.g. “OFCEFI” • You have to determine whether or not there exists a way to reorder those letters to form a valid word. • Given: A function “startswith(a)”, that determines if there are any words that start with the string “a”

8. Review Question 3 • Backtracking function jumbledLetters(a, b) takes in a set of letters, a, already ordered, and set of letters, b, that needs to be added • Base Cases: • If startswith(a) == FALSE, return FALSE • If b is empty string, return startswith(a) • Recursively call jumbledLetters()with next set of letters • If any of recursive calls return TRUE, return TRUE • If all return FALSE, return FALSE

9. Review Question 3 • Example: • Call to jumbledLetters(“OF”, “CEFI”)

10. Review Question 4 • Single Room Scheduling (Lecture 11) • Greedy Solution: • Sort the requests by finish time. • Go through the requests in order of finish time, scheduling them in the room if the room is unoccupied at its start time.

11. Review Question 4

12. Review Question 5 • MakeHeap (Lecture 4) • Place all the unsorted elements in a complete binary tree. • Going through the nodes in backwards order, and skipping the leaf nodes, run Percolate Down on each of these nodes. • If one of the children is less than the node, swap the lowest. • Continue until node has only larger (or equal) children or until leaf node

13. Review Question 5 • Initial Heap:

14. Review Question 5 • Final Heap:

15. Review Question 6

16. Review Question 6 • Solution:

17. Review Question 6 • Usually a good idea to break down initial equation as much as possible before proceeding

18. Review Question 7 • Code Analysis • What problem does this code solve? • Symbolically, what does the variable “m” represent? Matrix Chain Multiplication At which matrix you want to split your multiplication a the top level.

19. Review Question 7 • Explain conceptually what is stored in the variables “one”, “two”, and “three”. • Is the method “function” efficient? Justify. • “one” stores number of multiplications to do the left-side product • “two” stores number of multiplications to do the right-side product • “three” stores number of multiplications to take the two products from two recursive calls and multiply them No. The exact same recursive call gets made multiple times.

20. Review Question 8

21. Review Question 8

22. Review Question 8

23. Review Question 9

24. Review Question 9 • Which row (0 – 9) is this in the path array? • Determine the vertices traversed in the shortest path from vertex 3 to vertex 0. • From the information given, can we determine which vertex is farthest away from vertex 3? Why or why not? 3 3  7  6  2  0 No. Because of insufficient weight info.

25. Review Question 10 • CHEESE!

26. Good Luck on the Final Exam