Prepare for Time Complexity of Algorithms Interview with iQwizz | Difficulty Level: Advance | Rating: 4.1

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Question 1

You need to find the smallest k elements in an unsorted array of size n. What is the most efficient time complexity achievable in the average case?

O(n log n)
O(n^2)
O(n + k log n)
O(k^2)

Question 2

An algorithm performs the following operations: it iterates through an array of size n, and for each element, it performs a binary search on a sorted array of size m. What is the overall time complexity of the algorithm?

O(n log m)
O(m log n)
O(n + log m)
O(n * m)

Question 3

An algorithm processes an input array of size 'n'. It iterates through the array once, performing constant-time operations for each element. Inside the loop, it calls a helper function that has a time complexity of Θ(log n). What is the overall time complexity of this algorithm?

O(n)
O(n^2)
O(n log n)
O(log n)

Question 4

Which of the following statements about best-case, worst-case, and average-case analysis is FALSE?

Worst-case analysis is typically the most important to consider when designing for performance-critical applications.
Average-case analysis attempts to determine the average runtime over all possible inputs.
Worst-case analysis always provides an upper bound on the algorithm's runtime for any input.
Best-case analysis considers the input that results in the algorithm's fastest possible execution.

Question 5

You are comparing two sorting algorithms: Algorithm X with O(n log n) average-case complexity and Algorithm Y with O(n^2) worst-case complexity. In your benchmarks, Algorithm Y consistently outperforms Algorithm X. What is a PLAUSIBLE explanation for this observation?

The input data used in the benchmark always triggers the worst-case scenario for Algorithm X.
The input data, despite being randomly generated, consistently represents a special case where Algorithm Y excels.
The benchmark is flawed and does not accurately measure the execution time of the algorithms.
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.

Question 6

A randomized algorithm has a worst-case running time of O(n^2), but its expected running time is O(n log n). What does this imply about the algorithm's performance?

The algorithm's running time is independent of the input.
The algorithm is unsuitable for practical use due to its unpredictable running time.
On average, the algorithm performs better than its worst-case bound.
The algorithm always runs in O(n log n) time.

Question 7

Which of the following operations generally exhibits O(log n) time complexity in a balanced binary search tree?

Calculating the height of the tree
Finding the minimum element
Inserting a new element
Printing all elements in sorted order

Question 8

Why is time complexity generally considered more important than space complexity in algorithm analysis?

Modern computers have abundant memory, while efficient time utilization often remains a bottleneck.
Space complexity is irrelevant in modern computing.
Time complexity is always more difficult to analyze.
Space complexity cannot be expressed using Big-O notation.

Question 9

Which statement about benchmarking is TRUE?

Benchmarking is only useful for large-scale applications and not for smaller projects.
Benchmarking focuses on measuring the execution time of an algorithm in a controlled environment.
Benchmarking results are always generalizable across different hardware and software environments.
Benchmarking is primarily used for comparing the theoretical time complexity of different algorithms.

Question 10

An algorithm has a time complexity of ω(n). Which of the following statements is definitely false about its running time?

It might have a logarithmic component in its runtime.
It grows at least as fast as a linear function.
It could take constant time in the best case.
It cannot have a constant upper bound.

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Question 1

You need to find the smallest k elements in an unsorted array of size n. What is the most efficient time complexity achievable in the average case?

O(n log n)
O(n^2)
O(n + k log n)
O(k^2)

Question 2

O(n log m)
O(m log n)
O(n + log m)
O(n * m)

Question 3

O(n)
O(n^2)
O(n log n)
O(log n)

Question 4

Which of the following statements about best-case, worst-case, and average-case analysis is FALSE?

Worst-case analysis is typically the most important to consider when designing for performance-critical applications.
Average-case analysis attempts to determine the average runtime over all possible inputs.
Worst-case analysis always provides an upper bound on the algorithm's runtime for any input.
Best-case analysis considers the input that results in the algorithm's fastest possible execution.

Question 5

The input data used in the benchmark always triggers the worst-case scenario for Algorithm X.
The input data, despite being randomly generated, consistently represents a special case where Algorithm Y excels.
The benchmark is flawed and does not accurately measure the execution time of the algorithms.
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.

Question 6

A randomized algorithm has a worst-case running time of O(n^2), but its expected running time is O(n log n). What does this imply about the algorithm's performance?

The algorithm's running time is independent of the input.
The algorithm is unsuitable for practical use due to its unpredictable running time.
On average, the algorithm performs better than its worst-case bound.
The algorithm always runs in O(n log n) time.

Question 7

Which of the following operations generally exhibits O(log n) time complexity in a balanced binary search tree?

Calculating the height of the tree
Finding the minimum element
Inserting a new element
Printing all elements in sorted order

Question 8

Why is time complexity generally considered more important than space complexity in algorithm analysis?

Modern computers have abundant memory, while efficient time utilization often remains a bottleneck.
Space complexity is irrelevant in modern computing.
Time complexity is always more difficult to analyze.
Space complexity cannot be expressed using Big-O notation.

Question 9

Which statement about benchmarking is TRUE?

Benchmarking is only useful for large-scale applications and not for smaller projects.
Benchmarking focuses on measuring the execution time of an algorithm in a controlled environment.
Benchmarking results are always generalizable across different hardware and software environments.
Benchmarking is primarily used for comparing the theoretical time complexity of different algorithms.

Question 10

An algorithm has a time complexity of ω(n). Which of the following statements is definitely false about its running time?

It might have a logarithmic component in its runtime.
It grows at least as fast as a linear function.
It could take constant time in the best case.
It cannot have a constant upper bound.

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