Final Exam Topics

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

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

Divide-and-Conquer................ 4
  The maximum-subarray problem.... 4.1
  Strassen's matrix-mult algorithm 4.2
  The substitution method......... 4.3
  The recursion-tree method....... 4.4
  The master method............... 4.5

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
    Fibonacci Heaps............... 19 (after midterm)
      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
  Red-Black Trees................. 13
    Red-Black Properties.......... 13.1
    Rotations..................... 13.2
    Insertion (and Fixup)......... 13.3
    Deletion (and Fixup).......... 13.4
 --------- Material above was on midterm ------
  B-Trees......................... 18
    Definition.................... 18.1
    Search........................ 18.2
    Insert........................ 18.2
      Split-Child
      Insert-Non-Full
    Delete........................ 18.3
  Data Structures for Disjoint Sets  21 (will not be on final)
    Disjoint Set Operations....... 21.1
    Linked-List Representation.... 21.2
    Disjoint Set Forests.......... 21.3


       Topic                   Text Chapter
--------------------           -------------

Algorithm Analysis
  Dynamic Programming.............  15
    What key ingredients are needed to solve
      a problem by dynamic programming? ans:
      optimal substructure + overlapping subproblems
    Rod-cutting problem...........  15.1
    Matrix-chain Multiplication...  15.2
    Elements of Dynamic Programming 15.3
      Memoization (what is it?)
  Greedy Algorithms...............  16
    What are two key ingredients are needed to solve
      a problem by a greedy algorithm? ans:
      greedy-choice property + optimal substructure
    Activity-selection Problem....  16.1
    Elements of Greedy Strategy...  16.2
    Huffman Codes.................  16.3
  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


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

Pages 22-23 Exercises:
2.1-1 (3)
2.1-2 (1)
2.1-3 (1,5)

Page 29 Exercises:
2.2-3 (2)

Pages 37-39 Exercises:
2.3-2 (1)*
2.3-5 (2)*

Page 53 Exercises:
3.1-4 (5)*
3.1-5 (5)*

Page 60 Exercises:
3.2-3 (5)*
3.2-7 (5)*

Page 60 Problems:
3-1 parts a., b., and c. (5)*

Page 74 Exercises:
4.1-1 (4)

Page 82 Exercises:
4.2-1 (3)

Page 87 Exercises:
4.3-1 (5)

Pages 92-93 Exercises:
4.4-1 (5)
4.4-2 (5)

Pages 96-97 Exercises:
4.5-1 (4)
4.5-3 (5)

Pages 153-154 Exercises:
6.1-1 (4)
6.1-2 (5)*
6.1-5 (4)
6.1-6 (4)

Page 159 Exercises:
6.3-1 (3)
6.3-2 (4)
6.3-3 (5)* (too hard for exam)

Pages 160,162 Exercises:
6.4-1 (3)

Pages 164-166 Exercises:
6.5-1 (3)
6.5-2 (3)
6.5-3 (1)* (In Part 1, Assignment 4)

Pages 173-174 Exercises:
7.1-1 (3)

Page 178 Exercises:
7.2-1 (5)
7.2-2 (2)
7.2-3 (5)
7.2-4 (5)

Pages 184-185 Exercises:
7.4-2 (2)* (too hard for exams)
7.4-4 (2)* (too hard for exams)

Pages 193-194 Exercises:
8.1-1 (4)
8.1-2 (5) (in Ex. 3.2-3 above)

Pages 199-200 Exercises:
8.3-1 (3)

Page 204 Exercises:
8.4-1 (3)

Pages 240-241 Exercises:
10.2-1 (4)
10.2-2 (5)
10.2-3 (5)

Pages 248-249 Exercises:
10.4-4 (4)

Page 261 Exercises:
11.2-2 (3)

Page 277 Exercises:
11.4-1 (3)
11.4-2 (1)

Page 289 Exercises:
12.1-1 (4)
12.1-2 (4)
12.1-4 (1)
12.1-5 (5)*

Pages 293-294 Exercises:
12.2-1 (4)
12.2-2 (1)*
12.2-3 (1)*
12.2-5 (5)*

Trace BST insertion/deletion (3)

Pages 311-312 Exercises:
13.1-2 (3,4)
13.1-4 (4)*
13.1-5 (5)*
13.1-6 (4)*
13.1-7 (4)

Pages 313-314 Exercises:
13.2-1 (1)* (In Assignment 8, Part 1)

Page 322 Exercises:
13.3-1 (4)
13.3-2 (3) (trace RB-tree insertion)*
13.3-3 (4)

Page 330 Exercises:
13.4-3 (3) (trace RB-tree deletion)*
13.4-5 (4)

 -------- material above was on midterm ------------

Pages 369-370 Exercises:
15.1-1 (5)             
15.1-2 (4)
15.1-3 (1)
15.1-5 (1,4)

Page 378 Exercises:
15.2-1 (3) (a bit too hard for an exam)
15.2-2 (1)
15.2-6 (5)

Pages 389-390 Exercises:
15.3-2 (4) (but for 8 elements)
15.3-4 (4) (a bit too hard for an exam)

Pages 421-422 Exercises:
16.1-1 (1,2) (too hard for an exam)

Pages 427-428 Exercises:
16.2-1 (5) (too hard for an exam)
16.2-2 (1,2) (too hard for an exam)

Pages 436-437 Exercises:
16.3-1 (5) (too hard for an exam)
16.3-2 (5) (too hard for an exam)
16.3-3 (3,4) (i.e. trace Huffman)

Page 456 Exercises:
17.1-1 (4)
17.1-2 (4)
17.1-3 (4) * (Assignment 10)

Page 459 Exercises:
17.2-2 (4) * (Assignment 10)

Pages 462-463 Exercises:
17.3-1 (5)
17.3-2 (4) * (Assignment 10)
17.3-2 (5) (too hard for an exam)

Pages 490-491 Exercises:
18.1-1 (4)
18.1-2 (4)
18.1-4 (5)
18.1-5 (4) * (Assignment 8)

Pages 497-499 Exercises:
18.2-1 (3) (Trace B-tree insertion/deletion)
18.2-3 (1) 
18.2-6 (5) (too hard for an exam)

Page 502 Exercises:
18.3-1 (3) (Trace B-tree insertion/deletion)
18.3-2 (1)* (Assignment 9, I won't ask it on the final)

Page 518
19.2-1 (3)

Page 522
19.3-1 (5) (too hard for an exam)

Page 522
19.4-1 (5) (too hard for an exam)
19.4-2 (5) (interesting, but way too hard for an exam)

Page 564 Exercises: (will not be on final)
21.1-1 (3) (too long for an exam)
21.1-3 (2)

Pages 567-568 Exercises: (will not be on final)
21.2-1 (1) (a bit too long for an exam)
21.2-2 (3) (a bit too long for an exam)
21.2-4 (2)

Page 572 Exercises: (will not be on final)
21.3-1 (3) (too long for an exam)
21.3-2 (1)

Pages 592-593 Exercises:
22.1-1 (4)
22.1-2 (4)
22.1-5 (1,2)

Pages 601-602 Exercises:
22.2-1 (3)
22.2-2 (3)
22.2-3 (2)

Pages 610-612 Exercises:
22.3-2 (3)
22.3-3 (3)
22.3-5 (5) (a bit hard for an exam)
22.3-7 (1)

Pages 614-615 Exercises:
22.4-1 (3) (won't ask this one)

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

Pages 654-655 Exercises:
24.1-1 (3)

Pages 662-664 Exercises:
24.3-1 (3)*
24.3-3 (4)

Pages 691-693 Exercises:
25.1-6 (1) (too hard for an exam)
25.1-7 (1) (too hard for an exam)

Pages 699-700 Exercises:
25.2-1 (3)* (like Part II of Assignment 14)
25.2-4 (5) (Useful, but won't ask it)