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

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Question 1

Imagine you're optimizing a QuickSort algorithm for an array of size N. In the worst-case scenario, how does choosing a pivot element randomly impact the time complexity compared to always selecting the first element as the pivot?

Random pivot selection makes the worst-case time complexity unpredictable
Random pivot selection has no impact on the worst-case time complexity, it remains O(N^2)
Random pivot selection changes the worst-case time complexity to O(N log N)
Random pivot selection reduces the worst-case time complexity to O(N)

Question 2

Which notation is most appropriate to describe the best-case time complexity of an algorithm where the input size doesn't affect the running time?

Big-Theta (Θ)
Little-omega (ω)
Big-Omega (Ω)
Big-O (O)

Question 3

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

Question 4

A recursive function has a base case that executes in O(1) time. For each recursive step, it makes 3 recursive calls with input size n/2. What is the overall time complexity of this function?

O(n)
O(n log n)
O(n^2)
O(n^log_2(3))

Question 5

You are designing a system to handle real-time stock market data. Which of the following time complexities would be LEAST desirable for an algorithm processing incoming price updates?

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

Question 6

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 7

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

Question 8

You need to design an algorithm to solve a variation of the knapsack problem with a capacity C and N items. However, you can take multiple copies of the same item. Which algorithmic paradigm best addresses this scenario and provides an efficient solution?

Dynamic Programming with a 2D table
Divide and Conquer
Greedy Algorithm
Depth First Search with Backtracking

Question 9

Consider a nested loop structure where the outer loop runs n times and the inner loop runs from 1 to i, where 'i' is the current iteration of the outer loop. What is the total number of iterations of the inner loop?

n(n+1)/2
n
log n
n^2

Question 10

An algorithm processes an input list of size n. It first performs an O(n log n) sorting operation. Then, for each element in the sorted list, it performs a nested loop iterating over all pairs of elements in the list. What is the overall time complexity of this algorithm?

O(n^3)
O(n^2)
O(n log n)
O(n^2 log n)

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Question 1

Random pivot selection makes the worst-case time complexity unpredictable
Random pivot selection has no impact on the worst-case time complexity, it remains O(N^2)
Random pivot selection changes the worst-case time complexity to O(N log N)
Random pivot selection reduces the worst-case time complexity to O(N)

Question 2

Which notation is most appropriate to describe the best-case time complexity of an algorithm where the input size doesn't affect the running time?

Big-Theta (Θ)
Little-omega (ω)
Big-Omega (Ω)
Big-O (O)

Question 3

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

Question 4

A recursive function has a base case that executes in O(1) time. For each recursive step, it makes 3 recursive calls with input size n/2. What is the overall time complexity of this function?

O(n)
O(n log n)
O(n^2)
O(n^log_2(3))

Question 5

You are designing a system to handle real-time stock market data. Which of the following time complexities would be LEAST desirable for an algorithm processing incoming price updates?

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

Question 6

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 7

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

Question 8

Dynamic Programming with a 2D table
Divide and Conquer
Greedy Algorithm
Depth First Search with Backtracking

Question 9

n(n+1)/2
n
log n
n^2

Question 10

O(n^3)
O(n^2)
O(n log n)
O(n^2 log n)

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