Final Exam Topics

       Topic                   Text Chapter
--------------------           -------------
Algorithmic Pseudo-code........... 2

Rate of Growth of Functions
and Asymptotic Notation........... 3

Recurrences....................... 4
  The substitution method......... 4.1
  The recursion-tree method....... 4.2
  The master method............... 4.3

Sorting Algorithms
  Insertion-sort.................. 2
  Merge-sort...................... 2
  Heap-sort....................... 6.1-6.4
  Quicksort....................... 7
    Quicksort and Partition....... 7.1
    Quicksort performance......... 7.2
    Randomized Quicksort.......... 7.3
  Sorting in Linear Time.......... 8
    Lower bounds for sorting...... 8.1
    Counting sort................. 8.2
    Radix sort.................... 8.3
    Bucket sort................... 8.4

Dynamic sets
  Priority Queue Implementations
    Binary Heaps.................. 6.5
      Insert
      Extract-Min
    Binomial Heaps................ 19
      Binomial Trees
        Binomial-Link
        Union
      Insert
      Extract-Min
      Decrease-Key
      Delete
    Fibonacci Heaps............... 20
      Structure of Fibonacci Heaps
        Unordered binomial trees
        The potential function
        The maximum degree
      Mergeable-heap operations
        Insert, Find Minimum, Union
        Extract-Min, Consolidate
      Decrease-Key, Delete
      Bounding the maximum degree
  Elementary Data Structures...... 10
    Stacks and Queues............. 10.1
    Linked Lists.................. 10.2
    Implementing Pointers & Objs.. 10.3
    Representing Rooted Trees..... 10.4
  Hash Tables..................... 11
    Direct-address tables......... 11.1
    Hash Tables................... 11.2
      Collision Resolution
        Chaining
        Open Addressing........... 11.4
    Hash Functions (skip 11.3.3).. 11.3
  Binary Search Trees............. 12.1-12.3
    Tree-Walk
    Search
    Insert
    Delete
      Minimum
      Successor

       Topic                   Text Chapter
--------------------           -------------
  Red-Black Trees................. 13
    Red-Black Properties.......... 13.1
    Rotations..................... 13.2
    Insertion (and Fixup)......... 13.3
    Deletion (and Fixup).......... 13.4
  B-Trees......................... 18
    Search
    Insert
      Split-Child
    Insert-Non-Full
    Delete

Algorithm Analysis
  Dynamic Programming............. 15.1
    Assembly-line scheduling                 <--- skip this spring 04
  Amortized Analysis.............. 17.1-17.3
    Aggregate analysis
    The accounting method
    The potential method

Graphs
  Implementations................. 22.1
    Adjacency List
    Adjacency Matrix
  Graph Search
    Breadth-First................. 22.2
    Depth-First................... 22.3
      Topological Sort............ 22.4

  Minimum Spanning Trees.......... 23
    Generic-MST
      safe edges
      light edges
    MST-Kruskal
    MST-Prim

  Single-Source Shortest Paths.... 24.1-24.3
    Bellman-Ford Algorithm
    DAG Algorithm
    Dijkstra's Algorithm

  All-Pairs Shortest Paths........ 25.1-25.2
    Shortest paths and matrix multiplication
    The Floyd-Warshall Algorithm

Number-Theoretic Algorithms....... 31.0
  Measure of input size
  Elementary notions.............. 31.1
    Z = integers
    Z_n = integers mod n
    Z_n*
    Euler's phi function
  Powers of an element............ 31.6
    Euler's theorem
    Fermat's theorem
    Powers by repeated squaring
  The RSA Cryptosystem............ 31.7
    Public-key Cryptosystems
    The RSA Cryptosystem


Possible Types of Exam Problems:

  (1) Writing Pseudocode

  (2) Runtime analysis of algorithms

  (3) You should be able to trace the
   algorithms and operations on the data
   structures that we have discussed.

  (4) Short answer

  (5) "Prove that ..."

Especially questions from the Exercises and
Problems in the Assignments.

Materials allowed at exam: Two 4"x6" note cards
(or equivalent)


The following list contains examples of the
kinds of questions listed above.  
The following is a list of Exercises and
Problems from the text.  Questions like these
will appear on exams (in a slightly altered
form).  If they fall into one of the
categories above, that is noted; the ones
that have appeared in class assignments are
marked with *'s.

Page 13 Exercises:
1.2-2 (4)   (but easier to calculate)
1.2-3 (4)*  (but easier to calculate)
Problems: 1-1 (first column) (4)* 

Pages 20-21 Exercises:
2.1-1 (3)
2.1-2 (1)
2.1-3 (1,5)

Page 27 Exercises:
2.2-3 (2)

Pages 36-37 Exercises:
2.3-2 (1)*
2.3-5 (2)*

Page 50 Exercises:
3.1-4 (5)*
3.1-5 (5)*

Page 57 Exercises:
3.2-3 (5)*
3.2-7 (5)*

Pages 57-58 Problems:
3-1 parts a., b., and c. (5)*

Page 67 Exercises:
4.1-1 (5)

Page 75 Exercises:
4.3-1 (4)
4.3-3 (5)

Pages 129-130 Exercises:
6.1-1 (4)
6.1-2 (5)*
6.1-5 (4)
6.1-6 (4)

Page 135 Exercises:
6.3-1 (3)
6.3-2 (4)
6.3-3 (5)* (too hard for exam)

Pages 136,138 Exercises:
6.4-1 (3)

Pages 140-142 Exercises:
6.5-1 (3)
6.5-2 (3)
6.5-3 (1)* (Part 1, Assignment 3)

Page 148 Exercises:
7.1-1 (3)

Page 153 Exercises:
7.2-1 (5)

Pages 167-168 Exercises:
8.1-1 (4)
8.1-2 (5) (in Ex. 3.2-3 above)

Pages 167-168 Exercises:
8.3-1 (3)

Page 177 Exercises:
8.4-1 (3)

Pages 228-229 Exercises:
11.2-2 (3)

Pages 244-245 Exercises:
11.4-1 (3)
11.4-2 (1)

Page 256 Exercises:
12.1-1 (4)
12.1-2 (4)
12.1-4 (1)
12.1-5 (5)

Pages 259-260 Exercises:
12.2-1 (4)
12.2-2 (1)
12.2-3 (1)
12.2-5 (5)

Trace BST insertion/deletion (3)

Pages 276-277 Exercises:
13.1-2 (3,4)
13.1-5 (5)*
13.1-6 (4)*
13.1-7 (4)

Pages 278-279 Exercises:
13.2-1 (1)* (Assignment 4)

Page 287 Exercises:
13.3-1 (4)
13.3-2 (3)*
13.3-3 (4)

Pages 293-294 Exercises:
13.4-3 (3) (like Assignment 4, last problem) 
13.4-5 (4)

Pages 330-331 Exercises:  <-- won't ask for spring 04, but 15.1.1 is a
15.1-1 (1)                good kind of question; ans: like Print-Path p. 538
15.1-2 (5)
15.1-3 (5) (Too hard for an exam)

Pages 409-410 Exercises:
17.1-1 (4)
17.1-3 (4)

Pages 409-410 Exercises:
17.3-2 (4)

Pages 440-441 Exercises:
18.1-1 (4)
18.1-2 (4)
18.1-4 (5)
18.1-5 (4)

Pages 447-449 Exercises:
18.2-1 (3) (Trace B-tree insertion/deletion)
18.2-3 (1) 

Page 452 Exercises:
18.3-1 (3) (Trace B-tree insertion/deletion)
18.3-2 (1)* (Assignment 5, I won't ask it on the final)

Page 461 Exercises:
19.1-1 (4)
19.2-1 (4)

Pages 471-473 Exercises:
19.2-1 (1)* (merge linked list)
19.2-2 (3)
19.2-3 (3)

Pages 488-489 Exercises:
20.2-1 (3)

Pages 530-531 Exercises:
22.1-1 (4)
22.1-2 (4)
22.1-5 (1,2)

Pages 538-539 Exercises:
22.2-1 (3)
22.2-2 (3)
22.2-3 (2)

Pages 547-549 Exercises:
22.3-2 (3)
22.3-3 (3)
22.3-6 (1)

Pages 551-552 Exercises:
22.4-1 (3) (won't ask this one)

Chapter 23:
Be able to trace Prim's and Kruskal's algorithms (3)

Pages 591-592 Exercises:
24.1-1 (3)

Pages 600-601 Exercises:
24.3-1 (3)*
24.3-3 (4)

Pages 634-635 Exercises:
25.2-1 (3)* (like Part II of Assignment 9)
25.2-4 (5) (Useful, but won't ask it)

Pages 855-856 Exercises:
31.1-1 (5) (Important, but won't ask it)
31.1-3 (5) (Important, but won't ask it)

Pages 880-881 Exercises:
31.6-2 (1)

Page 887 Exercises:
31.7-1 (3) (Interesting, but too long for an exam)