Virtual Labs

1. The array 5, 4, 1, 2, 3 is sorted in ascending order. Which option provides the correctly sorted array?

a: 1, 2, 3, 4, 5 Explanation

Explanation

b: 5, 4, 3, 2, 1 Explanation

Explanation

c: 1, 1, 2, 2, 3, 3, 4, 4, 5, 5 Explanation

Explanation

d: Depends on which data structure is used Explanation

Explanation

2. Which of the following statements about logarithms is correct?

\log_2 8 = 3

Explanation

\log_e 2

is the same as

\log_2 e

Explanation

\log_{10} 100

is larger than

\log_2 8

Explanation

\log_3 27

is the same as

\log_9 81

Explanation

3. Which of the following is true about binary trees?

a: Every binary tree is either complete or full Explanation

Explanation

b: Every complete binary tree is also a full binary tree Explanation

Explanation

c: Every full binary tree is also a complete binary tree Explanation

Explanation

d: A perfect binary tree is both complete and full Explanation

Explanation

4. Level of a node is distance from root to that node. For example, level of root is 1 and levels of left and right children of root is 2. The maximum number of nodes on level

i

of a binary tree is:

2^{i-1}

Explanation

2^i

Explanation

2^{i+1}

Explanation

2^{(i+1)/2}

Explanation

5. What is the main purpose of arranging elements into a heap before performing Heap Sort?

a: To make every element equal Explanation

Explanation

b: To establish the heap property so the required extreme element can be selected efficiently Explanation

Explanation

c: To preserve the original order of all elements Explanation

Explanation

d: To convert the array into a linked list Explanation

Explanation

6. In a max-heap, which element is located at the root?

a: The smallest element Explanation

Explanation

b: The median element Explanation

Explanation

c: The largest element Explanation

Explanation

d: An arbitrary element Explanation

Explanation

7. Which statement best describes the time complexity of building a heap from an unsorted array using the bottom-up method?

O(1)

Explanation

O(\log n)

Explanation

O(n)

Explanation

O(n\log n)

Explanation

8. During Heap Sort using a max-heap, what happens after the maximum element is moved to the end of the unsorted portion?

a: The heap size is reduced and the remaining heap is restored Explanation

Explanation

b: The entire array is reversed immediately Explanation

Explanation

c: All elements are inserted into a second array Explanation

Explanation

d: The maximum element is moved back to the root Explanation

Explanation

9. What is the worst-case time complexity of Heap Sort for an array of

n

elements?

O(n)

Explanation

O(n^2)

Explanation

O(\log n)

Explanation

O(n\log n)

Explanation