Prepare for Time Complexity of Algorithms Interview with iQwizz | Difficulty Level: Intermediate | Rating: 4.6

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Question 1

Dynamic programming aims to reduce the time complexity of an algorithm by:

Storing the results of overlapping subproblems to avoid redundant computations
Dividing the problem into smaller subproblems and solving them recursively
Employing a divide-and-conquer strategy to break down the problem into smaller instances
Using a greedy approach to always make the locally optimal choice

Question 2

You have an algorithm with a time complexity of O(2^n). If you double the input size, how would you expect the execution time to be affected?

It remains roughly the same.
It increases exponentially.
It doubles.
It increases by a factor of n.

Question 3

You need to choose between two algorithms for your application. Algorithm A has a time complexity of O(n log n) but is known to be difficult to implement efficiently. Algorithm B has a time complexity of O(n^2) but is straightforward to implement and likely to have lower constant factors. Which of the following factors is LEAST important in deciding which algorithm to choose?

The programming language you are using.
The development time and resources available.
The size of the datasets your application will handle.
The acceptable performance limits of your application.

Question 4

What is the time complexity of Dijkstra's algorithm for finding the shortest path in a graph with V vertices and E edges using an adjacency list and a priority queue?

O(V^2)
O(V + E)
O(E log V)
O(V log E)

Question 5

An algorithm processes an input of size 'n' by dividing it in half repeatedly until the size becomes 1. What is the most likely time complexity of this algorithm?

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

Question 6

What does it mean for an algorithm to have a time complexity of Θ(1)?

The algorithm's runtime is unpredictable and varies greatly with different inputs.
The runtime is constant and independent of the input size.
The algorithm is guaranteed to be the fastest possible solution for the problem.
The runtime grows linearly with the input size.

Question 7

You have two algorithms for a task: Algorithm A with Θ(n) complexity and Algorithm B with O(n^2) complexity. Which statement is ALWAYS true?

Algorithm A will be faster than Algorithm B for all input sizes.
Algorithm A and Algorithm B have the same efficiency in terms of time complexity.
Algorithm B might be faster for very small input sizes, but Algorithm A will eventually be faster as input grows.
It's impossible to compare the efficiency of the algorithms without knowing the exact implementation details.

Question 8

What is the time complexity of calculating the nth Fibonacci number using the dynamic programming approach?

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

Question 9

What is the Big-O notation of an algorithm that iterates through an array of size 'n' twice in nested loops?

O(1)
O(n)
O(log n)
O(n^2)

Question 10

Which asymptotic notation provides an upper bound on an algorithm's runtime, but the bound may not be tight?

Big-O (O)
Big Omega (Ω)
Big Theta (Θ)
Little-o (o)

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Question 1

Dynamic programming aims to reduce the time complexity of an algorithm by:

Storing the results of overlapping subproblems to avoid redundant computations
Dividing the problem into smaller subproblems and solving them recursively
Employing a divide-and-conquer strategy to break down the problem into smaller instances
Using a greedy approach to always make the locally optimal choice

Question 2

You have an algorithm with a time complexity of O(2^n). If you double the input size, how would you expect the execution time to be affected?

It remains roughly the same.
It increases exponentially.
It doubles.
It increases by a factor of n.

Question 3

The programming language you are using.
The development time and resources available.
The size of the datasets your application will handle.
The acceptable performance limits of your application.

Question 4

What is the time complexity of Dijkstra's algorithm for finding the shortest path in a graph with V vertices and E edges using an adjacency list and a priority queue?

O(V^2)
O(V + E)
O(E log V)
O(V log E)

Question 5

An algorithm processes an input of size 'n' by dividing it in half repeatedly until the size becomes 1. What is the most likely time complexity of this algorithm?

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

Question 6

What does it mean for an algorithm to have a time complexity of Θ(1)?

The algorithm's runtime is unpredictable and varies greatly with different inputs.
The runtime is constant and independent of the input size.
The algorithm is guaranteed to be the fastest possible solution for the problem.
The runtime grows linearly with the input size.

Question 7

You have two algorithms for a task: Algorithm A with Θ(n) complexity and Algorithm B with O(n^2) complexity. Which statement is ALWAYS true?

Algorithm A will be faster than Algorithm B for all input sizes.
Algorithm A and Algorithm B have the same efficiency in terms of time complexity.
Algorithm B might be faster for very small input sizes, but Algorithm A will eventually be faster as input grows.
It's impossible to compare the efficiency of the algorithms without knowing the exact implementation details.

Question 8

What is the time complexity of calculating the nth Fibonacci number using the dynamic programming approach?

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

Question 9

What is the Big-O notation of an algorithm that iterates through an array of size 'n' twice in nested loops?

O(1)
O(n)
O(log n)
O(n^2)

Question 10

Which asymptotic notation provides an upper bound on an algorithm's runtime, but the bound may not be tight?

Big-O (O)
Big Omega (Ω)
Big Theta (Θ)
Little-o (o)

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