Midterm (DSA) Practice

What does it mean that the lower-bound on the worst-case time complexity for comparison-based sorting is Omega (n log(n))?

A) It means that the worst-case of a comparison-based sorting algorithm is at most n log(n).

B) It means that the worst-case of a comparison-based sorting algorithm is at least n log(n).

C) It means that using comparison-based sorting we cannot sort slower than in n log(n).

D) It means that using comparison-based sorting we cannot sort faster than in n log(n).

Omdraaien

We consider bucket sort.
What is the worst-case running time of bucket sort?

A) It is in Theta (n), because the for-loops are not nested.

B) It is in Theta (n^2), because we may call insertion sort, which is quadratic, on an input of size n, namely if (floor of nA[i]) is the same for all indices i.

C) It is in Theta (n^2), because worst-case sorting is always in n^2.

D) It is in Theta (n^3), because we may call insertion sort which is quadratic n times.

Omdraaien

Which of the following is(are) in increasing rate of growth?

A) n log(n), n^2, 2^7, n!

B) 3n, 2^3, n log(n), n^3

C) 2^7, n log(n), n^2, n!

D) n log(n), n^2, n^7, 2^n

E) n^2, n^3, n log(n), 2^n

Omdraaien

In the recurrence tree for merge sort

A) The height is n and the work per layer is the linear work to merge

B) The height is log(n) and the work per layer is the linear work to split.

C) The height is n and the work per layer is the linear work to split.

D) The height is log(n) and the work per layer is the linear work to merge.

Omdraaien

We consider a decision tree for a comparison-based sorting tree for sorting an array of size n. The smallest possible depth of a leaf is

A) n

B) n log(n)

C) n!

D) log(n)

Omdraaien

We apply heapsort to an array where all n elements are the same. What is its performance in this case?

A) n because we can build a max-heap in linear time

B) n log(n) because we execute n times MaxHeapify

C) n log(n) because half of the nodes are already max-heaps

D) n because we perform n times a constant amount of steps

Omdraaien

Which of the following statements are true? 1) Swapping two elements of an array can be done in constant time. 2) The smallest key of a max-heap is at the leftmost leaf. 3) All algorithms for turning an array into a max-heap are in Omega (n log(n)). 4) For all comparison-based sorting algorithms the worst-case time complexity is in Omega (n log(n)).

Omdraaien

We consider two statements. Statement A is: 2^(n+1) is in O(2^n). Statement B is: 2^(2n) is in O(2^n). Which of the following holds?

Omdraaien