CS140 -- Final Exam. December 10, 2008

Please, write your answers on a separate sheet, not on the exam.

Remember your name, too...

Question 1

Behold the following B-tree for M = 5.

Question 2

You are given the hash table on the right.
  • Part 1: Suppose you are using Linear Probing. Draw the hash table that results when you insert the keys "Teachers" and "Critics", which have hash values of 47 and 170 respectively.

  • Part 2: Use the hash table on the right to demonstrate why quadratic probing can be a disastrous collision resolution technique if you don't select your parameters properly. Use a detailed example, and then tell me how you would change things to make quadratic probing work.

  • Extra Credit: Who wrote the song?

Question 3

Let f(x) = 2x, g(x) = 100x, h(x) = |x - 3|, and j(x) = -|x - 3|. Which of the following are true (answer all that are true, not just one):

A: f(x) = O(g(x)) D: g(x) = O(f(x)) G: h(x) = O(f(x)) J: j(x) = O(f(x))
B: f(x) = O(h(x)) E: g(x) = O(h(x)) H: h(x) = O(g(x)) K: j(x) = O(g(x))
C: f(x) = O(j(x)) F: g(x) = O(j(x)) I: h(x) = O(j(x)) L: j(x) = O(h(x))

Question 4

Given the following splay tree:

Which of the following is the tree that results when D is inserted into the splay tree:


A
B
C

D
E
F

G
H
I

Question 5

Given the following splay tree:

Which of the following is the tree that results when R is inserted into the splay tree:


A
B
C

D
E
F

G
H
I

Question 6

Given the following AVL tree:

Which of the following is the tree that results when G is inserted into the AVL tree:


A
B
C

D
E
F

G
H
I

Question 7

Recall the header file for Disjoint Sets, below left. 


typedef struct {
  int *links;
  int *sizes;
  int *ranks;
  int maxindex;
  int nsets;
} DisjointSet;
  
extern DisjointSet *new_disjoint_set(int maxindex);
extern void free_disjoint_set(DisjointSet *dj);
extern void disjoint_makeset(DisjointSet *dj, int index);
extern int disjoint_union(DisjointSet *dj, int s1, int s2);
extern int disjoint_find(DisjointSet *dj, int index);

Suppose we have a DisjointSet struct whose state is depicted above right, and we have a pointer to it in the variable dj. Answer the following questions:

Question 8

Write a program that takes two command line arguments, a and b, and prints out all strings that have a A's and b B's.

Question 9

Suppose we have the following typedef for a tree node: 

typedef struct node {
  char *key;
  int nchildren;
  struct node **children;
} Node;

The variable nchildren is the number of children that a node has, and children is an array of pointers to the children. Write a procedure tree_size(Node *n), which returns the number of nodes in the tree rooted at node n.