5/13/25, 8:45 PM CS6515 - Algorithms- Exam 1 (2025/2026) ACTUAL EXAM COMPREHENSIVE QUESTIONS AND VERIFIED ACCURATE SOLUTI…
CS6515 - Algorithms- Exam 1 (2025/2026)
ACTUAL EXAM COMPREHENSIVE QUESTIONS
AND VERIFIED ACCURATE SOLUTION (DETAILED
& ELABORATED) |GET IT 100% ACCURATE!! 2025
TEST!!
Save
Terms in this set (92)
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
Steps to solve a Dynamic subproblem to the main problem. (hint: use a prefix of
Programming Problem 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...
https://quizlet.com/1043516702/cs6515-algorithms-exam-1-20252026-actual-exam-comprehensive-questions-and-verified-accurate-solution-detailed-… 1/14
, 5/13/25, 8:45 PM CS6515 - Algorithms- Exam 1 (2025/2026) ACTUAL EXAM COMPREHENSIVE QUESTIONS AND VERIFIED ACCURATE SOLUTI…
Input = x1, x2, ..., xn
1) Subproblem = x1, x2, ..., xi ; O(n)
2) Subproblem = xi, xi+1, ..., xj ; O(n^2)
DP: Types of Subproblems Input = x1, x2, ..., xn; y1, y2, ..., ym
(4) 1) Subproblem = x1, x2, ..., xi; y1, y2, ..., yj ; O(mn)
Input = Rooted Binary Tree
1) Subproblem = Smaller rooted binary tree inside the
Input.
Given r = common ratio and a = first term in series
=> a + ar + ar^2 + ar^3 + ... + ar^(n-1)
DC: Geometric Series
=> a * [(1 - r^n) / (1-r)]
Given d = common difference and a = first term in
series => a + (a + d) + (a + 2d) + ... + (a + (n-1)d
DC: Arithmetic Series
Sum = n/2 [2a + (n-1)d]
If T(n) = aT([n/b]) + O(n^d) for constants a>0, b>1, d>=0:
T(n) = {
DC: Solving Recurrences -
O(n^d) if d > logb(a)
Master Theorem
O((n^d)logn) if d = logb(a)
O(n^(logb(a))) if d < logb(a)
}
(1, 2PIj/n) for j = 0, 1, ..., n-1
Nth roots of Unity
*Around the Unit Circle!
https://quizlet.com/1043516702/cs6515-algorithms-exam-1-20252026-actual-exam-comprehensive-questions-and-verified-accurate-solution-detailed-… 2/14
CS6515 - Algorithms- Exam 1 (2025/2026)
ACTUAL EXAM COMPREHENSIVE QUESTIONS
AND VERIFIED ACCURATE SOLUTION (DETAILED
& ELABORATED) |GET IT 100% ACCURATE!! 2025
TEST!!
Save
Terms in this set (92)
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
Steps to solve a Dynamic subproblem to the main problem. (hint: use a prefix of
Programming Problem 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...
https://quizlet.com/1043516702/cs6515-algorithms-exam-1-20252026-actual-exam-comprehensive-questions-and-verified-accurate-solution-detailed-… 1/14
, 5/13/25, 8:45 PM CS6515 - Algorithms- Exam 1 (2025/2026) ACTUAL EXAM COMPREHENSIVE QUESTIONS AND VERIFIED ACCURATE SOLUTI…
Input = x1, x2, ..., xn
1) Subproblem = x1, x2, ..., xi ; O(n)
2) Subproblem = xi, xi+1, ..., xj ; O(n^2)
DP: Types of Subproblems Input = x1, x2, ..., xn; y1, y2, ..., ym
(4) 1) Subproblem = x1, x2, ..., xi; y1, y2, ..., yj ; O(mn)
Input = Rooted Binary Tree
1) Subproblem = Smaller rooted binary tree inside the
Input.
Given r = common ratio and a = first term in series
=> a + ar + ar^2 + ar^3 + ... + ar^(n-1)
DC: Geometric Series
=> a * [(1 - r^n) / (1-r)]
Given d = common difference and a = first term in
series => a + (a + d) + (a + 2d) + ... + (a + (n-1)d
DC: Arithmetic Series
Sum = n/2 [2a + (n-1)d]
If T(n) = aT([n/b]) + O(n^d) for constants a>0, b>1, d>=0:
T(n) = {
DC: Solving Recurrences -
O(n^d) if d > logb(a)
Master Theorem
O((n^d)logn) if d = logb(a)
O(n^(logb(a))) if d < logb(a)
}
(1, 2PIj/n) for j = 0, 1, ..., n-1
Nth roots of Unity
*Around the Unit Circle!
https://quizlet.com/1043516702/cs6515-algorithms-exam-1-20252026-actual-exam-comprehensive-questions-and-verified-accurate-solution-detailed-… 2/14
