WGU C949 DATA STRUCTURES AND ALGORITHMS OBJECTIVE
ASSESSMENT (OA) 150 QUESTIONS AND CORRECT ANSWERS
(VERIFIED ANSWERS) PLUS RATIONALES 2026 Q&A | INSTANT
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Algorithm Analysis & Big-O (Q1–20)
1. When analyzing the time complexity of an algorithm that processes each element
of an input list exactly once using a single loop, which of the following Big-O
notations best describes the worst-case runtime as a function of input size n?
A. O(1), because the algorithm always performs a constant number of operations regardless
of input
B. O(n), because the number of operations grows linearly with the number of input
elements
C. O(n²), because nested loops are always required to process every element in a list
D. O(log n), because the algorithm reduces the problem size by half on each iteration
Single pass over n elements yields linear time complexity.
2. Which of the following best describes the primary purpose of using Big-O notation
when comparing two different algorithms that solve the same problem?
A. To measure the exact runtime in seconds on a specific machine for a single input size
B. To describe how runtime or space requirements grow as input size increases,
abstracting away hardware
C. To determine which algorithm uses the most memory regardless of execution time or
input size
D. To guarantee that one algorithm will always be faster than another for every possible
input
Big-O captures growth rates, not absolute times.
,3. When evaluating the worst-case time complexity of a nested loop structure where
the outer loop runs n times and the inner loop runs up to n times for each outer
iteration, which of the following notations best describes the overall complexity?
A. O(n), because only the outer loop contributes significantly to total runtime
B. O(n²), because the total number of inner operations is proportional to n × n
C. O(log n), because the inner loop reduces the problem size on each iteration
D. O(1), because nested loops always execute in constant time regardless of input
Nested loops each up to n give quadratic time.
4. Which of the following best describes the difference between best-case,
worst-case, and average-case time complexity for a given algorithm?
A. Best-case is always equal to worst-case, and average-case is irrelevant for algorithm
analysis
B. Best-case, worst-case, and average-case describe runtime under different input
scenarios and distributions
C. Worst-case is only used for recursive algorithms, while best-case applies only to iterative
ones
D. Average-case is always the same as worst-case for all sorting and searching algorithms
Different cases reflect different input conditions.
5. When analyzing a binary search algorithm on a sorted array of size n, which of the
following best describes the worst-case time complexity and the reason for that
classification?
A. O(n), because binary search must examine every element in the worst case
B. O(log n), because the search space is halved on each comparison
C. O(n log n), because binary search combines linear and logarithmic behavior
D. O(1), because binary search always finds the target in a single step
Halving the search space each step yields logarithmic time.
6. Which of the following best describes the time complexity of accessing an element
by index in a standard array implementation, assuming the index is within bounds?
,A. O(n), because the array must be scanned from the beginning to find the correct element
B. O(1), because arrays support direct random access via index arithmetic
C. O(log n), because a binary search is required to locate the element by index
D. O(n²), because two-dimensional indexing always requires quadratic time
Array indexing is constant time.
7. When comparing two algorithms with time complexities O(n) and O(n log n), which
of the following statements best describes their relative performance for very large
input sizes?
A. O(n log n) will always be faster than O(n) for all input sizes and scenarios
B. O(n) will grow more slowly than O(n log n), so it will generally be faster for large n
C. Both algorithms will have identical performance for large n because constants dominate
D. O(n log n) becomes O(1) for large n, making it faster than any linear algorithm
n grows more slowly than n log n as n → ∞.
8. Which of the following best describes the space complexity of an in-place sorting
algorithm that sorts an array using only a constant amount of extra memory beyond
the input array?
A. O(n), because the algorithm must store a copy of the entire input
B. O(1), because only a fixed number of extra variables are used regardless of input
size
C. O(log n), because recursion always requires logarithmic stack space
D. O(n²), because in-place algorithms require quadratic auxiliary storage
In-place with constant extra space is O(1) auxiliary.
9. When analyzing the time complexity of a recursive algorithm that makes two
recursive calls on inputs of size n−1 and performs constant work outside the calls,
which of the following best describes the growth rate of the number of calls?
A. O(n), because each level of recursion reduces the input size by one
B. O(2ⁿ), because the recursion tree roughly doubles the number of calls at each level
, C. O(log n), because the depth of recursion is logarithmic in the input size
D. O(n²), because two recursive calls always produce quadratic behavior
Two calls per level with depth n yields exponential growth.
10. Which of the following best describes the primary reason why constant factors
and lower-order terms are typically ignored when expressing time complexity using
Big-O notation?
A. Constants and lower-order terms are always zero for all practical algorithms and input
sizes
B. Big-O focuses on dominant growth rates for large inputs, where constants become
less significant
C. Constants and lower-order terms are impossible to calculate accurately for recursive
algorithms
D. Ignoring constants guarantees that the algorithm will run faster on all hardware platforms
Big-O abstracts away constants to emphasize asymptotic growth.
11. When analyzing an algorithm that uses a single loop to iterate over an array and,
inside that loop, performs a binary search on the same array, which of the following
best describes the overall worst-case time complexity?
A. O(n), because the outer loop dominates and the binary search is negligible
B. O(n log n), because each of the n iterations performs a logarithmic-time search
C. O(log n), because binary search is more efficient than linear iteration
D. O(n²), because any nested operation automatically results in quadratic time
n iterations × O(log n) per iteration = O(n log n).
12. Which of the following best describes the time complexity of inserting an element
at the end of a dynamic array (such as ArrayList or vector) when the array has
available capacity and does not need to resize?
A. O(n), because all existing elements must be shifted to make room for the new element
B. O(1), because the element can be placed directly into the next free slot
ASSESSMENT (OA) 150 QUESTIONS AND CORRECT ANSWERS
(VERIFIED ANSWERS) PLUS RATIONALES 2026 Q&A | INSTANT
DOWNLOAD PDF
Algorithm Analysis & Big-O (Q1–20)
1. When analyzing the time complexity of an algorithm that processes each element
of an input list exactly once using a single loop, which of the following Big-O
notations best describes the worst-case runtime as a function of input size n?
A. O(1), because the algorithm always performs a constant number of operations regardless
of input
B. O(n), because the number of operations grows linearly with the number of input
elements
C. O(n²), because nested loops are always required to process every element in a list
D. O(log n), because the algorithm reduces the problem size by half on each iteration
Single pass over n elements yields linear time complexity.
2. Which of the following best describes the primary purpose of using Big-O notation
when comparing two different algorithms that solve the same problem?
A. To measure the exact runtime in seconds on a specific machine for a single input size
B. To describe how runtime or space requirements grow as input size increases,
abstracting away hardware
C. To determine which algorithm uses the most memory regardless of execution time or
input size
D. To guarantee that one algorithm will always be faster than another for every possible
input
Big-O captures growth rates, not absolute times.
,3. When evaluating the worst-case time complexity of a nested loop structure where
the outer loop runs n times and the inner loop runs up to n times for each outer
iteration, which of the following notations best describes the overall complexity?
A. O(n), because only the outer loop contributes significantly to total runtime
B. O(n²), because the total number of inner operations is proportional to n × n
C. O(log n), because the inner loop reduces the problem size on each iteration
D. O(1), because nested loops always execute in constant time regardless of input
Nested loops each up to n give quadratic time.
4. Which of the following best describes the difference between best-case,
worst-case, and average-case time complexity for a given algorithm?
A. Best-case is always equal to worst-case, and average-case is irrelevant for algorithm
analysis
B. Best-case, worst-case, and average-case describe runtime under different input
scenarios and distributions
C. Worst-case is only used for recursive algorithms, while best-case applies only to iterative
ones
D. Average-case is always the same as worst-case for all sorting and searching algorithms
Different cases reflect different input conditions.
5. When analyzing a binary search algorithm on a sorted array of size n, which of the
following best describes the worst-case time complexity and the reason for that
classification?
A. O(n), because binary search must examine every element in the worst case
B. O(log n), because the search space is halved on each comparison
C. O(n log n), because binary search combines linear and logarithmic behavior
D. O(1), because binary search always finds the target in a single step
Halving the search space each step yields logarithmic time.
6. Which of the following best describes the time complexity of accessing an element
by index in a standard array implementation, assuming the index is within bounds?
,A. O(n), because the array must be scanned from the beginning to find the correct element
B. O(1), because arrays support direct random access via index arithmetic
C. O(log n), because a binary search is required to locate the element by index
D. O(n²), because two-dimensional indexing always requires quadratic time
Array indexing is constant time.
7. When comparing two algorithms with time complexities O(n) and O(n log n), which
of the following statements best describes their relative performance for very large
input sizes?
A. O(n log n) will always be faster than O(n) for all input sizes and scenarios
B. O(n) will grow more slowly than O(n log n), so it will generally be faster for large n
C. Both algorithms will have identical performance for large n because constants dominate
D. O(n log n) becomes O(1) for large n, making it faster than any linear algorithm
n grows more slowly than n log n as n → ∞.
8. Which of the following best describes the space complexity of an in-place sorting
algorithm that sorts an array using only a constant amount of extra memory beyond
the input array?
A. O(n), because the algorithm must store a copy of the entire input
B. O(1), because only a fixed number of extra variables are used regardless of input
size
C. O(log n), because recursion always requires logarithmic stack space
D. O(n²), because in-place algorithms require quadratic auxiliary storage
In-place with constant extra space is O(1) auxiliary.
9. When analyzing the time complexity of a recursive algorithm that makes two
recursive calls on inputs of size n−1 and performs constant work outside the calls,
which of the following best describes the growth rate of the number of calls?
A. O(n), because each level of recursion reduces the input size by one
B. O(2ⁿ), because the recursion tree roughly doubles the number of calls at each level
, C. O(log n), because the depth of recursion is logarithmic in the input size
D. O(n²), because two recursive calls always produce quadratic behavior
Two calls per level with depth n yields exponential growth.
10. Which of the following best describes the primary reason why constant factors
and lower-order terms are typically ignored when expressing time complexity using
Big-O notation?
A. Constants and lower-order terms are always zero for all practical algorithms and input
sizes
B. Big-O focuses on dominant growth rates for large inputs, where constants become
less significant
C. Constants and lower-order terms are impossible to calculate accurately for recursive
algorithms
D. Ignoring constants guarantees that the algorithm will run faster on all hardware platforms
Big-O abstracts away constants to emphasize asymptotic growth.
11. When analyzing an algorithm that uses a single loop to iterate over an array and,
inside that loop, performs a binary search on the same array, which of the following
best describes the overall worst-case time complexity?
A. O(n), because the outer loop dominates and the binary search is negligible
B. O(n log n), because each of the n iterations performs a logarithmic-time search
C. O(log n), because binary search is more efficient than linear iteration
D. O(n²), because any nested operation automatically results in quadratic time
n iterations × O(log n) per iteration = O(n log n).
12. Which of the following best describes the time complexity of inserting an element
at the end of a dynamic array (such as ArrayList or vector) when the array has
available capacity and does not need to resize?
A. O(n), because all existing elements must be shifted to make room for the new element
B. O(1), because the element can be placed directly into the next free slot
