Question

1. In a heap, the upper bound on the number of leaves is: (A) O(n)
(B) O(1) (C) O(logn) (D) O(nlogn)
2. In a heap, the distance from the root to the furthest leaf is:
(A) θ(nlogn) (B) θ(logn)
(C) θ(1) (D) θ(n)
3. In a heap, let df be the distance of the furthest leaf from the root and let dc be the analogous distance of the closest leaf. What is df − dc, at most?
(A) 1 (C) 2
(B) θ(logn) (D) 0
4. What is the most number of nodes in a heap with a single child?
(A) 0 (D) Θ(logn)
(B) Θ(n) (C) 2
(E) 1
5. What is the fewest number of nodes in a heap with a single child?
(A) 0 (C) one per level (B) 1 (D) 2
6. T or F: There can be two or more nodes in a heap with exactly one child.
7. T or F: A heap can have no nodes with exactly one child.
8. T or F: All heaps are perfect trees.
9. T or F: No heaps are perfect trees.
10. T or F: All heaps are complete trees.
11. T or F: No heaps are complete trees.
12. T or F: A binary tree with one node must be a heap.
13. T or F: A binary tree with two nodes and with the root having the smallest value must be a min-heap.
14. T or F: If a node in a heap is a right child and has two children, then its sibling must also have two children.
15. T or F: If a node in a heap is a right child and has one child, then its sibling must also have one child.

Answer 1

$\small \color{blue}Answer:\;\;$

1)  (A) O(n)
2)  (B) θ(logn)
3)  (B) θ(logn)
4)  (E) 1

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