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CS 6515 Bundled Exams with complete solutions.
CS 6515 on-campus Exam 1
CS 6515 Exam 1 | Questions and Answers | 2025 Update | 100% Correct – GT.
CS 6515 Exam 2 | Questions and Answers | 2025 Update | 100% Correct – GT.
CS 6515 Exam 3 | Questions and Answers | 2025 Update | 100% Correct – GT.
Exam (elaborations)
CS 6515 Exam 3 | Questions and Answers | 2025 Update | 100% Correct – GT.
CS 6515 Exam 3 | Questions and Answers | 2025 Update | 100% Correct – GT.
Exam (elaborations)
CS 6515 Exam 2 | Questions and Answers | 2025 Update | 100% Correct – GT.
CS 6515 Exam 2 | Questions and Answers | 2025 Update | 100% Correct – GT.
Exam (elaborations)
CS 6515 Exam 1 | Questions and Answers | 2025 Update | 100% Correct – GT.
CS 6515 Exam 1 | Questions and Answers | 2025 Update | 100% Correct – GT.
Exam (elaborations)
CS6515 - Algorithms- Exam 1 Questions and Answers Already Passed Latest 2025
CS6515 - Algorithms- Exam 1 Questions and Answers Already Passed Latest 2025 
 
Steps to solve a Dynamic Programming Problem - Answers 1. Define the Input and Output. 
 
2. Define entries in table, i.e. T(i) or T(i, j) is... 
 
3. Define a Recurrence relationship - Based on a subproblem to the main problem. (hint: use a prefix of the original input 1 < i < n). 
 
4. Define the Pseudocode. 
 
5. Define the Runtime of the algorithm. Use Time Function notation here => T(n) = T(n/2) + 1......
Exam (elaborations)
CS6515 Exam 1 Questions and Answers Already Passed Latest Update 2025
CS6515 Exam 1 Questions and Answers Already Passed Latest Update 2025 
Binary Search Runtime - Answers O(log n) 
Merge Sort Runtime - Answers O(n log n) 
Naive Multiplication of n-bit Integers Runtime - Answers O(n²) 
Fast Multiplication of n-bit Integers (Using Divide and Conquer) Runtime - Answers O(n^log₂3) ≈ O(n¹.⁵⁹) 
Median Finding Algorithm Runtime - Answers O(n) 
FFT (Fast Fourier Transform) Runtime - Answers O(n log n) 
Gauss's Method for Multiplying Complex Numbers (Number ...
Exam (elaborations)
CS 6515 Exam 2 Questions and Answers Already Passed Latest Update 2025
CS 6515 Exam 2 Questions and Answers Already Passed Latest Update 2025 
Define Euclid's Rule - Answers If x and y are positive integers with x >= y, then gcd(x, y) = gcd( y, x mod y) 
Define Fermat's Little Theorem - Answers If p is prime, then for every 1 <= a < p, a ^(p-1) === 1 (mod p) 
Define Euler's Theorem - Answers For any Z where gcd(Z,N) = 1, then Z ^phi(N) === 1 mod N 
Define Euler's Totient Function - Answers phi(N) is the number of integers between 1...N which ar...
Exam (elaborations)
CS 6515 Exam 3 Questions with Correct Answers Already Passed
CS 6515 Exam 3 Questions with Correct Answers Already Passed 
The Class P - Answers A solution may be found in polynomial time 
The Class NP - Answers A solution may be verified in polynomial time 
NP-Hard - Answers We are yet to find a polynomial time solution 
NP-Complete - Answers Both in NP and at least as hard as NP-Hard problems 
NP Reduction - Steps - Answers 1. Demonstrate that problem B is in the class of NP Problems 
- validate a solution in polynomial time 
 
2. Demonstrate that prob...
Exam (elaborations)
Cs 6515 Exam 1 2025 Updated Actual Exam With Correct Solutions.
Cs 6515 Exam 1 2025 Updated Actual 
Exam With Correct Solutions.
Exam (elaborations)
Cs 6515 Exam 1 Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Cs 6515 Exam 1 Actual Exam Questions With 
Complete Solution Guide (A+ Graded 100% 
Verified) Latest Version 2025!!
Exam (elaborations)
Cs 6515 Exam 1 Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Cs 6515 Exam 1 Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Exam (elaborations)
Cs 6515 Exam Questions And Answers
Steps to solve a Dynamic Programming Problem - 1. Define the Input and Output. 
2. Define entries in table, i.e. T(i) or T(i, j) is... 
3. Define a Recurrence relationship - Based on a subproblem to the main problem. (hint: 
use a prefix of the original input 1 < i < n). 
4. Define the Pseudocode. 
5. Define the Runtime of the algorithm. Use Time Function notation here => T(n) = 
T(n/2) + 1... 
DP: Types of Subproblems (4) - Input = x1, x2, ..., xn 
1) Subproblem = x1, x2, ...,...
Exam (elaborations)
Cs 6515 Exam 2 Questions With Solutions
Basic Properties of Trees - Tree's are undirected, connected and acyclic that connect all 
nodes. 
1. Tree on n vertices has (n-1) edges -> would have a cycle otherwise (more than n-1 
edges means cycle) 
2. In tree exactly one path between every pair of vertices (otherwise it's not connected) - More than 1 path implies cycle - less than 1 path implies not connected 
3. Any connected G(V, E) with |E| = |V| - 1 is a tree 
Kruskal's Algorithm - 1. Sort E by increasing weigt 
Run...
Exam (elaborations)
Cs 6515 Exam 3 Questions With Complete Solution
The Class P - A solution may be found in polynomial time 
 
The Class NP - A solution may be verified in polynomial time 
 
NP-Hard - We are yet to find a polynomial time solution 
 
NP-Complete - Both in NP and at least as hard as NP-Hard problems 
 
NP Reduction - Steps - 1. Demonstrate that problem B is in the class of NP Problems 
- validate a solution in polynomial time 
 
2. Demonstrate that problem B is at least as hard as a problem believed to be NP-Complete. This is done via a reduction...
Exam (elaborations)
Cs 6515 Exam 1 Questions And Answers
Knapsack without repetition - k(0) = 0 
for w = 1 to W: 
 if w_j >w: k(w,j) = k(w, j - 1) 
 else: K(w,j) = max{K(w, j -1),K(w - w_j, j -1) + v_i} 
 
knapsack with repetition - knapsack repeat(w_i....w_n, w_i... w_n, B) 
k(0) = 0 
for i = 1 to n 
 if w_i <= b & k(b) <v_i + K(b-w_i) 
 then k(b) = v_i + K(b-w_i) 
 
Longest Increasing Subsequence - LIS(a_1.... a_n) 
for i = 1 to n 
 L(i) = 1 
 for j = 1 to n -1 
 if a_j < a_i & L(i) < 1 + L(j) 
 L(i) = 1 + L(j) 
max = 1 
for i = 2 to ...
Exam (elaborations)
Cs 6515 Exam 1 Questions With Solution
Binary Search Runtime - O(log n) 
 
Merge Sort Runtime - O(n log n) 
 
Naive Multiplication of n-bit Integers Runtime - O(n²) 
 
Fast Multiplication of n-bit Integers (Using Divide and Conquer) Runtime - O(n^log₂3) ≈ O(n¹.⁵⁹) 
 
Median Finding Algorithm Runtime - O(n) 
 
FFT (Fast Fourier Transform) Runtime - O(n log n) 
 
Gauss's Method for Multiplying Complex Numbers (Number of Multiplications) - 3 multiplications 
 
Euclid's GCD Algorithm Runtime - O(log(min(a, b))) 
 
Strasse...
Exam (elaborations)
Cs 6515 Graph Algorithms Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Cs 6515 Graph Algorithms Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Exam (elaborations)
Cs 6515 Exam 1 Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Cs 6515 Exam 1 Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Exam (elaborations)
Cs 6515 Exam 1 Prep/Comprehensive Guide Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Cs 6515 Exam 1 Prep/Comprehensive Guide Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Exam (elaborations)
Cs 6515 Exam 3 Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!
Cs 6515 Exam 3 Actual Exam Questions With Complete Solution Guide (A+ Graded 100% Verified) Latest Version 2025!!