CS 6515 ALGORITHMS EXAM 3 SUMMARY
| STUDY GUIDE | 2026 UPDATE WITH
COMPLETE SOLUTIONS – GT [QUESTION
1-200] AND ANSWERS UPDATED
2026/2027 | 100% VERIFIED |
DETAILED RATIONALES – PASS
GUARANTEED A+ GRADED | INSTANT
DOWNLOAD
Original practice materials for Georgia Tech CS 6515 exam preparation. These
questions are not official exam questions, and a particular grade or pass cannot be
guaranteed.
2. INTRODUCTION
The CS 6515 Algorithms Exam 3 practice study guide is designed for students
reviewing advanced algorithm design and analysis concepts in Georgia Tech's
graduate-level algorithms course. The goal is to strengthen the ability to select
appropriate algorithmic strategies, establish correctness, analyze asymptotic
complexity, and evaluate trade-offs among competing solutions.
Algorithms assessments commonly require more than memorizing definitions.
Students must reason through unfamiliar problems, construct or interpret recurrences,
analyze greedy choices, understand dynamic programming states, evaluate graph
algorithms, and recognize the conditions under which an algorithm succeeds or fails.
This practice bank emphasizes scenario-based, application-level multiple-choice
questions with four answer options and detailed explanations.
The guide is organized around core algorithmic techniques, mathematical analysis,
proof strategies, and computational complexity. Each rationale explains why the best
answer is correct and why the alternatives are less appropriate. Use the material to
identify weak areas, practice under timed conditions, and revisit concepts that require
additional work.
Because the exact Exam 3 topic list can vary by semester, compare this guide with
your instructor's current syllabus, lecture notes, and official assessment instructions.
3. CORE DOMAINS TESTED
, 1.
Asymptotic analysis: Big-O, Big-Theta, Big-Omega, growth rates, and
complexity comparisons.
2.
3.
Divide and conquer: Recurrence relations, merge sort, binary search, and
recursive algorithm analysis.
4.
5.
Greedy algorithms: Greedy-choice properties, exchange arguments, interval
scheduling, and minimum spanning trees.
6.
7.
Dynamic programming: State definitions, recurrence construction, optimal
substructure, memoization, and bottom-up computation.
8.
9.
Graph algorithms: BFS, DFS, shortest paths, topological sorting, and
connectivity.
10.
11.
Minimum spanning trees: Prim's and Kruskal's algorithms, cut property, and
cycle property.
12.
13.
Shortest-path algorithms: Dijkstra's algorithm, Bellman–Ford, and negative
edge weights.
14.
15.
Network flow: Residual graphs, augmenting paths, maximum flow, and
minimum cuts.
16.
17.
, Computational complexity: P, NP, NP-hardness, NP-completeness, reductions,
and certificates.
18.
19.
Correctness proofs: Induction, loop invariants, exchange arguments, and
contradiction.
20.
21.
Algorithm design trade-offs: Runtime, memory, data structures, and algorithm
selection.
22.
23.
Problem-solving strategy: Recognizing when greedy, dynamic programming,
graph algorithms, or reductions are appropriate.
24.
4. QUESTIONS SECTION
QUESTIONS 1–100
Domain 1: Asymptotic Analysis and Recurrences
Q1: An algorithm performs \(3n^2+7n\log n+12n\) elementary operations. Which
statement correctly describes its asymptotic running time?
A) \(\Theta(n\log n)\)
B) \(\Theta(n^3)\)
C) \(\Theta(n^2)\)
D) \(\Theta(\log n)\)
Rationale: C is correct because the quadratic term dominates the lower-order terms as
\(n\) grows. A incorrectly treats the \(n\log n\) term as dominant. B introduces a cubic
term that is not present. D ignores the polynomial terms.
Q2: A recursive algorithm satisfies \(T(n)=2T(n/2)+n\), with \(T(1)=\Theta(1)\). What
is its asymptotic running time?
, A) \(\Theta(n)\)
B) \(\Theta(n\log n)\)
C) \(\Theta(n^2)\)
D) \(\Theta(\log n)\)
Rationale: B is correct by the Master Theorem: \(a=2\), \(b=2\), and \(n^{\log_b
a}=n\), matching the linear combine cost. A omits the logarithmic number of
recursion levels. C overestimates the cost. D accounts only for recursion depth and
ignores work across levels.
Q3: Consider \(T(n)=T(n/2)+\Theta(1)\), with constant-time base cases. What is the
running time?
A) \(\Theta(n)\)
B) \(\Theta(n\log n)\)
C) \(\Theta(n^2)\)
D) \(\Theta(\log n)\)
Rationale: D is correct because each recursive call halves the input, producing
logarithmically many calls with constant work per call. A assumes linear work at each
level. B assumes more work per level than exists. C is an unjustified quadratic bound.
Q4: An algorithm satisfies \(T(n)=4T(n/2)+\Theta(n)\). What is its asymptotic running
time?
A) \(\Theta(n\log n)\)
B) \(\Theta(n^2)\)
C) \(\Theta(n^2)\)
D) \(\Theta(n)\)
Rationale: Both B and C state the same correct asymptotic bound, so this question has
two correct options and is therefore defective as a single-answer question. The
recurrence has \(n^{\log_2 4}=n^2\), which dominates the linear combine cost, giving
\(\Theta(n^2)\). A is too small and D ignores recursive work.
Q5: Suppose \(f(n)=n^{1.5}\) and \(g(n)=n\log^2 n\). Which relationship holds for
sufficiently large \(n\)?
A) \(f(n)=o(g(n))\)
B) \(f(n)=\Theta(g(n))\)
| STUDY GUIDE | 2026 UPDATE WITH
COMPLETE SOLUTIONS – GT [QUESTION
1-200] AND ANSWERS UPDATED
2026/2027 | 100% VERIFIED |
DETAILED RATIONALES – PASS
GUARANTEED A+ GRADED | INSTANT
DOWNLOAD
Original practice materials for Georgia Tech CS 6515 exam preparation. These
questions are not official exam questions, and a particular grade or pass cannot be
guaranteed.
2. INTRODUCTION
The CS 6515 Algorithms Exam 3 practice study guide is designed for students
reviewing advanced algorithm design and analysis concepts in Georgia Tech's
graduate-level algorithms course. The goal is to strengthen the ability to select
appropriate algorithmic strategies, establish correctness, analyze asymptotic
complexity, and evaluate trade-offs among competing solutions.
Algorithms assessments commonly require more than memorizing definitions.
Students must reason through unfamiliar problems, construct or interpret recurrences,
analyze greedy choices, understand dynamic programming states, evaluate graph
algorithms, and recognize the conditions under which an algorithm succeeds or fails.
This practice bank emphasizes scenario-based, application-level multiple-choice
questions with four answer options and detailed explanations.
The guide is organized around core algorithmic techniques, mathematical analysis,
proof strategies, and computational complexity. Each rationale explains why the best
answer is correct and why the alternatives are less appropriate. Use the material to
identify weak areas, practice under timed conditions, and revisit concepts that require
additional work.
Because the exact Exam 3 topic list can vary by semester, compare this guide with
your instructor's current syllabus, lecture notes, and official assessment instructions.
3. CORE DOMAINS TESTED
, 1.
Asymptotic analysis: Big-O, Big-Theta, Big-Omega, growth rates, and
complexity comparisons.
2.
3.
Divide and conquer: Recurrence relations, merge sort, binary search, and
recursive algorithm analysis.
4.
5.
Greedy algorithms: Greedy-choice properties, exchange arguments, interval
scheduling, and minimum spanning trees.
6.
7.
Dynamic programming: State definitions, recurrence construction, optimal
substructure, memoization, and bottom-up computation.
8.
9.
Graph algorithms: BFS, DFS, shortest paths, topological sorting, and
connectivity.
10.
11.
Minimum spanning trees: Prim's and Kruskal's algorithms, cut property, and
cycle property.
12.
13.
Shortest-path algorithms: Dijkstra's algorithm, Bellman–Ford, and negative
edge weights.
14.
15.
Network flow: Residual graphs, augmenting paths, maximum flow, and
minimum cuts.
16.
17.
, Computational complexity: P, NP, NP-hardness, NP-completeness, reductions,
and certificates.
18.
19.
Correctness proofs: Induction, loop invariants, exchange arguments, and
contradiction.
20.
21.
Algorithm design trade-offs: Runtime, memory, data structures, and algorithm
selection.
22.
23.
Problem-solving strategy: Recognizing when greedy, dynamic programming,
graph algorithms, or reductions are appropriate.
24.
4. QUESTIONS SECTION
QUESTIONS 1–100
Domain 1: Asymptotic Analysis and Recurrences
Q1: An algorithm performs \(3n^2+7n\log n+12n\) elementary operations. Which
statement correctly describes its asymptotic running time?
A) \(\Theta(n\log n)\)
B) \(\Theta(n^3)\)
C) \(\Theta(n^2)\)
D) \(\Theta(\log n)\)
Rationale: C is correct because the quadratic term dominates the lower-order terms as
\(n\) grows. A incorrectly treats the \(n\log n\) term as dominant. B introduces a cubic
term that is not present. D ignores the polynomial terms.
Q2: A recursive algorithm satisfies \(T(n)=2T(n/2)+n\), with \(T(1)=\Theta(1)\). What
is its asymptotic running time?
, A) \(\Theta(n)\)
B) \(\Theta(n\log n)\)
C) \(\Theta(n^2)\)
D) \(\Theta(\log n)\)
Rationale: B is correct by the Master Theorem: \(a=2\), \(b=2\), and \(n^{\log_b
a}=n\), matching the linear combine cost. A omits the logarithmic number of
recursion levels. C overestimates the cost. D accounts only for recursion depth and
ignores work across levels.
Q3: Consider \(T(n)=T(n/2)+\Theta(1)\), with constant-time base cases. What is the
running time?
A) \(\Theta(n)\)
B) \(\Theta(n\log n)\)
C) \(\Theta(n^2)\)
D) \(\Theta(\log n)\)
Rationale: D is correct because each recursive call halves the input, producing
logarithmically many calls with constant work per call. A assumes linear work at each
level. B assumes more work per level than exists. C is an unjustified quadratic bound.
Q4: An algorithm satisfies \(T(n)=4T(n/2)+\Theta(n)\). What is its asymptotic running
time?
A) \(\Theta(n\log n)\)
B) \(\Theta(n^2)\)
C) \(\Theta(n^2)\)
D) \(\Theta(n)\)
Rationale: Both B and C state the same correct asymptotic bound, so this question has
two correct options and is therefore defective as a single-answer question. The
recurrence has \(n^{\log_2 4}=n^2\), which dominates the linear combine cost, giving
\(\Theta(n^2)\). A is too small and D ignores recursive work.
Q5: Suppose \(f(n)=n^{1.5}\) and \(g(n)=n\log^2 n\). Which relationship holds for
sufficiently large \(n\)?
A) \(f(n)=o(g(n))\)
B) \(f(n)=\Theta(g(n))\)
