WGU C949 Data Structures and Algorithms I | Objective Assessment | Version 1
WGU C949 Objective Assessment
Data Structures and Algorithms I
Version 1 | 75 Questions | 2026/2027 Edition
Verified Answers with Comprehensive Rationales
Section 1: Algorithm Analysis and Big-O Notation (Time Complexity, Space Complexity,
and Asymptotic Analysis)
Q1: A software engineer analyzes two algorithms for processing a dataset. Algorithm A executes 3n2 + 5n + 7
operations, and Algorithm B executes 2n log n + 100 operations. Which of the following correctly describes the
asymptotic time complexity of Algorithm A?
A. O(n)
B. O(n log n)
C. O(n2) **[CORRECT]**
D. O(3n2)
Correct Answer: C
Rationale: Big-O notation captures the dominant term while dropping constant coefficients and lower-order terms. In
Algorithm A, the dominant term is 3n2. Dropping the constant 3 and the lower-order terms 5n and 7 yields O(n2). Option A
underestimates the quadratic growth rate. Option B describes linearithmic growth which is slower than quadratic. Option
D is incorrect because Big-O notation never includes constant coefficients such as the leading 3.
Q2: Which of the following statements correctly distinguishes between Big-O, Big-Omega, and Big-Theta
notations?
A. Big-O represents the best-case running time, Big-Omega represents the worst-case, and Big-Theta
represents the average case.
B. Big-O gives an upper bound, Big-Omega gives a lower bound, and Big-Theta gives a tight bound (both
upper and lower). **[CORRECT]**
C. Big-O and Big-Omega are identical notations used interchangeably, while Big-Theta measures space
complexity.
D. Big-O measures best-case, Big-Theta measures worst-case, and Big-Omega measures amortized
complexity.
Correct Answer: B
Rationale: Big-O provides an asymptotic upper bound on growth rate. Big-Omega provides a lower bound, guaranteeing
growth at least as fast as the stated rate. Big-Theta provides a tight bound when upper and lower bounds coincide,
meaning the algorithm grows at exactly that rate asymptotically. Option A incorrectly assigns case types to notations.
Option C is wrong because Big-O and Big-Omega are not interchangeable. Option D confuses the definitions entirely.
Q3: A developer measures execution time for a function that processes arrays of increasing size. For n = 1000 the
function takes 10 ms, for n = 2000 it takes 40 ms, and for n = 4000 it takes 160 ms. What is the most likely time
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, WGU C949 Data Structures and Algorithms I | Objective Assessment | Version 1
complexity?
A. O(n)
B. O(n log n)
C. O(n2) **[CORRECT]**
D. O(2n)
Correct Answer: C
Rationale: When input size doubles from 1000 to 2000, the time quadruples from 10 ms to 40 ms. When it doubles again
from 2000 to 4000, the time again quadruples from 40 ms to 160 ms. This consistent quadrupling upon doubling indicates
quadratic growth O(n2). Linear growth would double the time when input doubles. Linearithmic growth would increase by
slightly more than double. Exponential growth would increase far more dramatically.
Q4: What is the time complexity of the following code segment?
for i in range(n):
for j in range(i, n):
print(i + j)
A. O(n)
B. O(n log n)
C. O(n2) **[CORRECT]**
D. O(n3)
Correct Answer: C
Rationale: The outer loop runs n times. The inner loop runs (n - i) iterations for each i. The total operations are the sum
from i=0 to n-1 of (n - i) = n + (n-1) + ... + 1 = n(n+1)/2, which simplifies to O(n2). Option A underestimates the nested loop
effect. Option B would apply if the inner loop were halving the range. Option D overestimates by assuming three nested
full loops.
Q5: Which of the following correctly orders asymptotic growth rates from slowest to fastest?
A. O(1), O(log n), O(n), O(n log n), O(n2), O(2n), O(n!) **[CORRECT]**
B. O(1), O(n), O(log n), O(n log n), O(n2), O(n!), O(2n)
C. O(log n), O(1), O(n), O(n2), O(n log n), O(2n), O(n!)
D. O(1), O(log n), O(n), O(n2), O(n log n), O(n!), O(2n)
Correct Answer: A
Rationale: The correct ordering from slowest to fastest growth is: O(1) constant, O(log n) logarithmic, O(n) linear, O(n log
n) linearithmic, O(n2) quadratic, O(2n) exponential, O(n!) factorial. Option B incorrectly places O(n) before O(log n) and
swaps O(n!) and O(2n). Option C places O(log n) before O(1) and misorders n2 and n log n. Option D misorders n2 and n log
n and swaps the last two.
Q6: A Python list uses a dynamic array internally. When appending elements one at a time to an initially empty
list, what is the amortized time complexity per insertion?
A. O(1) **[CORRECT]**
B. O(n)
C. O(log n)
D. O(n2)
Correct Answer: A
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Rationale: Amortized analysis spreads the cost of expensive operations over many operations. Python lists double in size
when full. While resizing takes O(n) time, it happens infrequently. Spreading this cost across all n insertions yields O(1)
amortized time per insertion. Most individual insertions are O(1), with occasional O(n) resizes. Option B describes the
worst-case single operation, not the amortized cost. Options C and D do not apply to dynamic array append operations.
Q7: What is the space complexity of an algorithm that creates an auxiliary array of size n and two additional
variables of constant size?
A. O(1)
B. O(log n)
C. O(n) **[CORRECT]**
D. O(n2)
Correct Answer: C
Rationale: Space complexity measures total additional memory relative to input size. The auxiliary array of size n
contributes O(n) space. The two constant-size variables contribute O(1) each, which is dominated by O(n). Therefore total
space complexity is O(n). Option A would only be correct if no array were allocated. Option B has no basis here. Option D
would require a two-dimensional structure proportional to n2.
Q8: Consider the recurrence T(n) = 2T(n/2) + O(n) with T(1) = O(1). Using the Master Theorem, what is the time
complexity?
A. O(n)
B. O(n log n) **[CORRECT]**
C. O(n2)
D. O(log n)
Correct Answer: B
Rationale: Applying the Master Theorem: a=2, b=2, f(n)=O(n). We compute nlog_b(a) = nlog_2(2) = n1 = n. Since f(n) =
Theta(nlog_b(a) * log0(n)), this falls under Case 2, yielding T(n) = O(n log n). Option A would apply if f(n) were O(n1-epsilon).
Option C would require f(n) to be Omega(n1+epsilon). Option D ignores the linear work done at each recursion level.
Q9: An algorithm has best-case O(n), worst-case O(n3), and average-case O(n2). Which Big-O notation is most
appropriate for general description?
A. O(n), because it represents the best possible performance
B. O(n3), because Big-O represents an upper bound on the worst case **[CORRECT]**
C. O(n2), because it represents the average case
D. O(n log n), because it is the median of the three complexities
Correct Answer: B
Rationale: By convention, Big-O without qualification refers to worst-case time complexity, providing an upper bound
guarantee. Therefore O(n3) is the correct general description. The best-case and average-case are useful for context but
are not the standard default. Option D invents a nonexistent median concept. In WGU C949, Big-O without qualification
always means worst-case upper bound.
Q10: Which time complexity indicates an algorithm generally considered infeasible for large inputs (n > 50)?
A. O(n log n)
B. O(n2)
C. O(2n) **[CORRECT]**
D. O(n3)
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WGU C949 Objective Assessment
Data Structures and Algorithms I
Version 1 | 75 Questions | 2026/2027 Edition
Verified Answers with Comprehensive Rationales
Section 1: Algorithm Analysis and Big-O Notation (Time Complexity, Space Complexity,
and Asymptotic Analysis)
Q1: A software engineer analyzes two algorithms for processing a dataset. Algorithm A executes 3n2 + 5n + 7
operations, and Algorithm B executes 2n log n + 100 operations. Which of the following correctly describes the
asymptotic time complexity of Algorithm A?
A. O(n)
B. O(n log n)
C. O(n2) **[CORRECT]**
D. O(3n2)
Correct Answer: C
Rationale: Big-O notation captures the dominant term while dropping constant coefficients and lower-order terms. In
Algorithm A, the dominant term is 3n2. Dropping the constant 3 and the lower-order terms 5n and 7 yields O(n2). Option A
underestimates the quadratic growth rate. Option B describes linearithmic growth which is slower than quadratic. Option
D is incorrect because Big-O notation never includes constant coefficients such as the leading 3.
Q2: Which of the following statements correctly distinguishes between Big-O, Big-Omega, and Big-Theta
notations?
A. Big-O represents the best-case running time, Big-Omega represents the worst-case, and Big-Theta
represents the average case.
B. Big-O gives an upper bound, Big-Omega gives a lower bound, and Big-Theta gives a tight bound (both
upper and lower). **[CORRECT]**
C. Big-O and Big-Omega are identical notations used interchangeably, while Big-Theta measures space
complexity.
D. Big-O measures best-case, Big-Theta measures worst-case, and Big-Omega measures amortized
complexity.
Correct Answer: B
Rationale: Big-O provides an asymptotic upper bound on growth rate. Big-Omega provides a lower bound, guaranteeing
growth at least as fast as the stated rate. Big-Theta provides a tight bound when upper and lower bounds coincide,
meaning the algorithm grows at exactly that rate asymptotically. Option A incorrectly assigns case types to notations.
Option C is wrong because Big-O and Big-Omega are not interchangeable. Option D confuses the definitions entirely.
Q3: A developer measures execution time for a function that processes arrays of increasing size. For n = 1000 the
function takes 10 ms, for n = 2000 it takes 40 ms, and for n = 4000 it takes 160 ms. What is the most likely time
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, WGU C949 Data Structures and Algorithms I | Objective Assessment | Version 1
complexity?
A. O(n)
B. O(n log n)
C. O(n2) **[CORRECT]**
D. O(2n)
Correct Answer: C
Rationale: When input size doubles from 1000 to 2000, the time quadruples from 10 ms to 40 ms. When it doubles again
from 2000 to 4000, the time again quadruples from 40 ms to 160 ms. This consistent quadrupling upon doubling indicates
quadratic growth O(n2). Linear growth would double the time when input doubles. Linearithmic growth would increase by
slightly more than double. Exponential growth would increase far more dramatically.
Q4: What is the time complexity of the following code segment?
for i in range(n):
for j in range(i, n):
print(i + j)
A. O(n)
B. O(n log n)
C. O(n2) **[CORRECT]**
D. O(n3)
Correct Answer: C
Rationale: The outer loop runs n times. The inner loop runs (n - i) iterations for each i. The total operations are the sum
from i=0 to n-1 of (n - i) = n + (n-1) + ... + 1 = n(n+1)/2, which simplifies to O(n2). Option A underestimates the nested loop
effect. Option B would apply if the inner loop were halving the range. Option D overestimates by assuming three nested
full loops.
Q5: Which of the following correctly orders asymptotic growth rates from slowest to fastest?
A. O(1), O(log n), O(n), O(n log n), O(n2), O(2n), O(n!) **[CORRECT]**
B. O(1), O(n), O(log n), O(n log n), O(n2), O(n!), O(2n)
C. O(log n), O(1), O(n), O(n2), O(n log n), O(2n), O(n!)
D. O(1), O(log n), O(n), O(n2), O(n log n), O(n!), O(2n)
Correct Answer: A
Rationale: The correct ordering from slowest to fastest growth is: O(1) constant, O(log n) logarithmic, O(n) linear, O(n log
n) linearithmic, O(n2) quadratic, O(2n) exponential, O(n!) factorial. Option B incorrectly places O(n) before O(log n) and
swaps O(n!) and O(2n). Option C places O(log n) before O(1) and misorders n2 and n log n. Option D misorders n2 and n log
n and swaps the last two.
Q6: A Python list uses a dynamic array internally. When appending elements one at a time to an initially empty
list, what is the amortized time complexity per insertion?
A. O(1) **[CORRECT]**
B. O(n)
C. O(log n)
D. O(n2)
Correct Answer: A
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, WGU C949 Data Structures and Algorithms I | Objective Assessment | Version 1
Rationale: Amortized analysis spreads the cost of expensive operations over many operations. Python lists double in size
when full. While resizing takes O(n) time, it happens infrequently. Spreading this cost across all n insertions yields O(1)
amortized time per insertion. Most individual insertions are O(1), with occasional O(n) resizes. Option B describes the
worst-case single operation, not the amortized cost. Options C and D do not apply to dynamic array append operations.
Q7: What is the space complexity of an algorithm that creates an auxiliary array of size n and two additional
variables of constant size?
A. O(1)
B. O(log n)
C. O(n) **[CORRECT]**
D. O(n2)
Correct Answer: C
Rationale: Space complexity measures total additional memory relative to input size. The auxiliary array of size n
contributes O(n) space. The two constant-size variables contribute O(1) each, which is dominated by O(n). Therefore total
space complexity is O(n). Option A would only be correct if no array were allocated. Option B has no basis here. Option D
would require a two-dimensional structure proportional to n2.
Q8: Consider the recurrence T(n) = 2T(n/2) + O(n) with T(1) = O(1). Using the Master Theorem, what is the time
complexity?
A. O(n)
B. O(n log n) **[CORRECT]**
C. O(n2)
D. O(log n)
Correct Answer: B
Rationale: Applying the Master Theorem: a=2, b=2, f(n)=O(n). We compute nlog_b(a) = nlog_2(2) = n1 = n. Since f(n) =
Theta(nlog_b(a) * log0(n)), this falls under Case 2, yielding T(n) = O(n log n). Option A would apply if f(n) were O(n1-epsilon).
Option C would require f(n) to be Omega(n1+epsilon). Option D ignores the linear work done at each recursion level.
Q9: An algorithm has best-case O(n), worst-case O(n3), and average-case O(n2). Which Big-O notation is most
appropriate for general description?
A. O(n), because it represents the best possible performance
B. O(n3), because Big-O represents an upper bound on the worst case **[CORRECT]**
C. O(n2), because it represents the average case
D. O(n log n), because it is the median of the three complexities
Correct Answer: B
Rationale: By convention, Big-O without qualification refers to worst-case time complexity, providing an upper bound
guarantee. Therefore O(n3) is the correct general description. The best-case and average-case are useful for context but
are not the standard default. Option D invents a nonexistent median concept. In WGU C949, Big-O without qualification
always means worst-case upper bound.
Q10: Which time complexity indicates an algorithm generally considered infeasible for large inputs (n > 50)?
A. O(n log n)
B. O(n2)
C. O(2n) **[CORRECT]**
D. O(n3)
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