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

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Question 1

Consider a social network graph with V users and E friendships. You want to find the shortest path between two users (A and B) in terms of friendship connections. What is the time complexity of the most efficient algorithm for this scenario in the worst-case?

O(E log V) using Dijkstra's Algorithm with a binary heap
O(V + E) using Breadth First Search
O(V!) using brute-force depth-first search
O(V^2) using Floyd-Warshall Algorithm

Question 2

When optimizing code for better time complexity, which approach will NOT always lead to improved real-world performance?

Reducing the number of operations within loops.
Caching frequently accessed data to avoid recomputation.
Using a more complex data structure with better time complexity for certain operations.
Replacing an O(n^2) algorithm with an O(n log n) algorithm.

Question 3

You are tasked with optimizing a critical function in a real-time trading system. Your theoretical analysis suggests Algorithm A (O(log n)) is superior to Algorithm B (O(n)). However, benchmarking reveals Algorithm B performs better for your typical data size. What is the MOST likely reason for this discrepancy?

Theoretical analysis is unreliable and cannot predict real-world performance.
Algorithm A's hidden constant factors are significantly larger than Algorithm B's, making it slower for smaller input sizes.
Benchmarking is flawed and does not accurately represent the real-world scenario.
The trading system's hardware is optimized for linear-time algorithms like Algorithm B.

Question 4

Consider a dynamic array implementation where resizing to double the capacity takes O(n) time. If we perform 'n' insertions sequentially, what is the amortized time complexity per insertion?

O(n)
O(log n)
O(1)
O(n log n)

Question 5

You need to choose an algorithm for a real-time system with strict timing constraints. Algorithm X has a time complexity of O(n log n) in the worst case and Θ(1) in the best case. Algorithm Y has a time complexity of Θ(n) in all cases. Which algorithm is a safer choice and why?

Neither algorithm is suitable for a real-time system.
Algorithm X, because its best-case complexity is excellent.
Algorithm Y, because its time complexity is consistent and predictable.
Both algorithms are equally suitable for a real-time system.

Question 6

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.
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.
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.

Question 7

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

Question 8

Consider an algorithm that iterates through a sorted array of size n. In the best-case scenario, the algorithm finds the desired element in the first comparison. What is the time complexity of this algorithm in the best case?

O(log n)
O(n)
O(n log n)
O(1)

Question 9

Which statement about benchmarking is TRUE?

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

Question 10

You are designing a data structure that supports two operations: 'insert' and 'find median'. 'Insert' adds an element in O(log n) time. Which of the following allows the 'find median' operation to also be achieved in O(log n) time?

A self-balancing binary search tree
A standard binary search tree
A sorted array
A hash table

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Question 1

O(E log V) using Dijkstra's Algorithm with a binary heap
O(V + E) using Breadth First Search
O(V!) using brute-force depth-first search
O(V^2) using Floyd-Warshall Algorithm

Question 2

When optimizing code for better time complexity, which approach will NOT always lead to improved real-world performance?

Reducing the number of operations within loops.
Caching frequently accessed data to avoid recomputation.
Using a more complex data structure with better time complexity for certain operations.
Replacing an O(n^2) algorithm with an O(n log n) algorithm.

Question 3

Theoretical analysis is unreliable and cannot predict real-world performance.
Algorithm A's hidden constant factors are significantly larger than Algorithm B's, making it slower for smaller input sizes.
Benchmarking is flawed and does not accurately represent the real-world scenario.
The trading system's hardware is optimized for linear-time algorithms like Algorithm B.

Question 4

Consider a dynamic array implementation where resizing to double the capacity takes O(n) time. If we perform 'n' insertions sequentially, what is the amortized time complexity per insertion?

O(n)
O(log n)
O(1)
O(n log n)

Question 5

Neither algorithm is suitable for a real-time system.
Algorithm X, because its best-case complexity is excellent.
Algorithm Y, because its time complexity is consistent and predictable.
Both algorithms are equally suitable for a real-time system.

Question 6

The input data used in the benchmark always triggers the worst-case scenario for Algorithm X.
Algorithm Y is inherently more efficient than Algorithm X for all input sizes and distributions.
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.

Question 7

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

Question 8

O(log n)
O(n)
O(n log n)
O(1)

Question 9

Which statement about benchmarking is TRUE?

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

Question 10

A self-balancing binary search tree
A standard binary search tree
A sorted array
A hash table

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