CS483 - Russell
Final Exam Preparation Guide
Spring 2023
CS483 Final Exam Topics List
Problems [things we are trying to solve/discover…]
Graph Problems
Optimal Substructure Problems
Data Compression
Sorting
Hard Problems
analyzing of and matching in bipartite graphs
independent sets in graphs
traversing a graph
cycle detection in a graph
topological sorting of a directed graph
paths and shortest paths
spanning trees and minimum spanning trees
connected components of a graph
flows and max flow in flow graphs
cuts and min cuts of flow graphs (inc. capacity and net
flow across a cut)
finding negative cycles [book]
disjoint paths [book]
flows/circulations [book – optional, but in lecture]
with demands
with demands and lower bounds
with circulations and source/sink [lecture only]
activity/interval selection (and variations)
optimal caching [book]
knapsack [0-1, fractional]
kth Fibonacci number [lecture]
egg drops
longest common subsequence
segmented least squares [book]
subset sum [book]
RNA secondary structure [book]
sequence alignment [book]
… also some of the graph problems
… also data compression problems
concept of and goals of data compression
prefix codes
comparison vs. non-comparison sorts
lower bound time complexity on comparison sorts
general terms (reducibility, decidable/undecidable,
tractable/intractable, optimization vs. decision
problems, P/NP/NP-Complete/NP-Hard)
Independent Set
Vertex Cover
SAT and 3SAT
Circuit SAT [book]
Set Packing [book]
CS483 - Russell
Final Exam Preparation Guide
Other Problems
Spring 2023
Travelling Salesman Problem
Hamiltonian Cycle Problem
Hamiltonian Path Problem [book]
3D Matching Problem [book]
Graph Coloring and 3-Color
Subset Sum [book]
Scheduling with Release Times and Deadlines [book]
Halting Problem [lecture]
Euler Tour [lecture]
competitive facility locations
counting inversions [book – ch5]
closest pair of points [book – ch5]
integer multiplication [book – ch5]
convolutions for the Fast Fourier Transform [book – ch5]
image segmentation [book – ch 7 + lecture]
survey design [book – ch 7 optional]
project selection [book – ch 7 optional]
baseball elimination [book – ch 7 optional]
median finding [book – ch 13]
2-3 from this list for randomized algorithms [ch 13]:
Contention Resolution
Finding the Global Min Cut
Hashing
Random Caching
Load Balancing
Packet Routing
Techniques [ways to solve problems we have…]
Review: Formal Proofs
Algorithm Analysis Basics
Amortized Analysis
Approaches for Optimal Substructure
Problems
Divide and Conquer
basic formal proofs for algorithms (by contradiction,
induction, etc.)
empirical vs. mathematical vs. approximation analysis
asymptotic notation
methods/approaches (aggregate, accounting, potential)
[lecture]
greedy (including requirements on subproblems, and
greedy choice property)
dynamic programming (including elements of DP)
memoization
basic approach and methods
analysis using recurrences using:
substitution
recursion trees
master method [lecture]
CS483 - Russell
Final Exam Preparation Guide
Randomized Algorithms
Techniques for Harder Problems
Spring 2023
indicator random variables
probabilistic analysis
Reductions (general idea of)
Proving equivalence
Proving special case of a more general problem
Proofs using gadgets
Data Structures (with Their Analysis!!!) [for support…]
Review: Dynamic Array Lists
Review: Stacks and Queues
Review: Tree Data Structures
Review: Priority Queues w/ Heaps
Review: Sets and Maps
Review: Graph Data Structures
Disjoint Set Data Structures
expansion [lecture – amortized analysis]
building queues using only stacks [lecture – amortized
analysis]
stacks with occasional backups [book]
tree basic terminology / properties [homework]
tree storage [homework]
basic operations: add (enqueue)
basic operations: remove (dequeue)
concept of sets and maps
graph basic terminology / properties (e.g. vertices,
edges, weights, directed, connected, cycles, paths,
degrees, etc.) [book]
graph storage (adjacency matrix, adjacency list, edge list,
map-of-maps, map-of-sets) and add/remove and
vertex/edge operations for each
concept of union-able disjoint sets
disjoint sets with union find [lecture version]
basic operations: find [w/ path-comp]
basic operations: union [by-rank-size]
use in Kruskal’s MST algorithm
Algorithms (with Their Analysis!!!) [to solve problems…]
Greedy
activity/interval selection algorithms for:
scheduling a single resource
scheduling all intervals (w/ fewest resources)
[book]
scheduling with minimum lateness [book]
fractional knapsack greedy algorithm [lecture]
Huffman coding:
creating an encoding tree
encoding and decoding messages
CS483 - Russell
Final Exam Preparation Guide
Dynamic Programming
Memoization
Comparison Sorts
Non-Comparison Sorts
Review: Graph Basics
Graph Algorithms using Basic Walks
More Graph Algorithms
Spring 2023
kth Fibonacci number DP algorithm [lecture + HW]
egg drop DP algorithm [lecture]
0-1 knapsack DP algorithm
longest common subsequence DP algorithm
segmented least squares [book]
subset sum [book]
RNA secondary structure [book]
sequence alignment [book]
kth Fibonacci number MEMO algorithm [HW]
insertion sort [lecture]
merge sort
quick sort (inc. randomized algorithm analysis)
counting sort [lecture]
radix sort [lecture]
bucket sort [lecture]
walks: breadth-first
walks: depth-first [and edge types created]
path detection
cycle detection
topological sort
D-F method [lecture + homework]
Kahn’s method [book + homework]
shortest paths in unweighted graphs
connected components
finding connected components [book]
strongly connected components [book +
homework]
bipartite graphs: testing bipartiteness [book]
shortest paths in weighted graphs
Dijkstra’s algorithm
Bellman-Ford algorithm
-- and when to use which one!
minimum spanning trees
Prim’s algorithm [book]
Kruskal’s algorithm
all-pairs shortest path
BFS for unweighted (run repeatedly)
Dijkstra’s SP algorithm (run repeatedly)
Floyd-Warshall algorithm
-- and when to use which one!
max-flow and min-cut
Ford-Fulkerson “method”
Edmonds-Karp algorithm
finding negative cycles using DP [book]
CS483 - Russell
Final Exam Preparation Guide
Algorithms Using Max Flow / Min Cut
Additional Algorithms from the Book
Spring 2023
max bipartite graph matching
airplane scheduling
image segmentation
finding disjoint paths
solving flows/circulations (including with demands,
lower bounds, and original sources/sinks) [book – ch 7
+ lecture]
survey design [book – ch 7 optional]
project selection [book – ch 7 optional]
baseball elimination [book – ch 7 optional]
divide and conquer algorithms from ch 5:
counting inversions [book]
closest pair of points [book]
integer multiplication [book]
convolutions for the FFT [book]
median finding using randomized algorithm [ch 13]
2-3 from this list for randomized algorithms [ch 13]:
Contention Resolution
Finding the Global Min Cut
A Randomized Approx. of MAX 3-SAT
Hashing
Closest Pair of Points (Randomized)
Random Caching
Load Balancing
Packet Routing
CS483 - Russell
Final Exam Preparation Guide
Spring 2023
CS483 Final Exam Sample Questions
You should COMBINE these with the sample questions from the midterm.
Important:
This part of the guide contains SAMPLE questions for the midterm. The actual exam will have DIFFERENT
questions, DIFFERENT question difficulties, a DIFFERENT number of questions, and questions will have
weights (DIFFERENT number of points per problem). On the actual exam you will also likely have questions
on topics which are not shown here (see the Topics List).
Memorizing the answers to these questions will NOT result in a good grade on the exam. However, being
able to solve these TYPES of questions WITHOUT assistance is a good sign.
Exception: The extra credit question is the same question you will get on the actual exam, and worth the
same number of points. It will be given as an anonymous survey question at a later date.
What to Bring to the Exam:
•
•
Required: A photo ID, preferably your GMU ID. If you do not have a GMU ID, or your GMU ID is
damaged so that the name or picture can’t be read, or you only have a “virtual” GMU ID, you can
use another form of photo ID. Driver’s license, learner’s permit, state ID card, or passport are all
acceptable. If anyone does not have a photo ID at the time of the exam, I will take a picture of
that person and the exam will not be graded until a photo ID is shown (so please don’t skip the
exam because you forgot your ID at home).
Required: ONE side of an 8.5"x11" sheet of paper with HAND-WRITEN notes (you will submit this
with the exam so please put your name on it). The back side is going to be used for scratch paper,
so if you choose not to bring notes, you must still bring a blank sheet of paper for scratch paper.
EXAMPLE Question Instructions:
MULTIPLE CHOICE: Select the correct answer as indicated. If you are directed to select only one item and
select more than one, it will be marked as wrong. Not selecting an answer is the same as getting it wrong.
ALL OTHER QUESTIONS: Write as much as indicated by the question. ALL words you write will be graded
(you can lose points for adding incorrect information).
EXAMPLE Exam Timing:
The set of sample questions listed below COMBINED with the midterm sample questions for the first half
of the semester, should be doable in about three and a half hours WITHOUT any notes or other resources.
If it’s taking longer than this (or you need notes to do them quickly), you may need more practice with
certain topics. The actual exam will be approximately TWO AND A HALF hours.
CS483 - Russell
Final Exam Preparation Guide
Spring 2023
SAMPLE QUESTIONS WITH ANSWERS (AND TIME ESTIMATES) As part of the midterm review and as part
of the last day of class we did (or will do) timed exercises for about 40 minutes. Provided after those
classes are longer versions. The combined long versions add up to about 75+ minutes of practice. In
addition, below is a template question and a few “new algorithm design” questions which do not have
answers (since, as stated, one is only a template and on the others the design is up to you).
[Graph Algorithm Template Question] Given
the graph on the right perform [a DFT, a BFT,
Prim’s, Kruskal’s, Dijkstra’s, Bellman-Ford,
Floyd-Warshall] algorithm showing your steps
and the final state of any supporting data
structures. If you need a starting place for the
algorithm, choose node three. [Note that this
is a “template question”, choose whichever
one you are LEAST comfortable with for
practice. You can convert this to a max-flow
min-cut problem by choosing a source/sink
and directions for the edges.]
[New Algorithm Example 1] Design an algorithm for determining the longest monotonically increasing
subsequence of a sequence of n numbers. For example, assume the input is 3 7 4 2 8 6. Then the
longest monotonically increasing subsequence is 3 4 6 or 3 4 8 both of which have a size of 3, so your
algorithm should return a value 3. Note that this is not asking for the longest monotonically increasing
consecutive-number sequence, the numbers do not have to be next to each other (as in the example:
3 7 4 2 8 6). This algorithm is solvable in O(n2) time, where n is the number of numbers in the
sequence. For your solution, prove your runtime.
[New Algorithm Example 2] You want to flip a coin to make decisions in a board meeting (heads with
probability 0.5 and tails with probability 0.5). Unfortunately, you have only a “trick coin” that is weighted
so that it lands on heads with probability p, and tails with probability 1-p (where 0 < p < 1). Even more
unfortunately, you do not know what p is (you can’t remember what was on the instructions when you
bought the coin at the joke shop).
Give an algorithm that uses the unfair coin to produce a fair coin flip (i.e. you want to tell the board
members “it has determined head” or “it has determined tails” with equal probability). You may be as
inefficient as you’d like (e.g. flip the unfair coin as many times as you’d like) and you may use scrap paper
to track results of coin flips and do some math, but you cannot use other things (such as go to the bank
and get a better coin, bend the coin, etc.). State and prove the runtime of your new algorithm.
[New Algorithm Example 3] You have a network shaped like a rooted tree, with the root as a source, the
leaves as its sinks. All the edges are directed along the paths from the root to the leaves and the edges
have various weights. Design an efficient algorithm for finding of a maximum flow in such a network (note
this must be more efficient than running a standard max-flow algorithm). Show and prove the efficiency
of your algorithm.
[+1% Extra Credit] How was your semester? Anything we could have done that would have made it easier,
better, or more fun (while still having you learn things)? [This exact question WILL be on the survey.]