Data Structures & Algorithms Multiple Choice Questions on “Treap”.
1. What is the space complexity of a treap algorithm?
a) O(N)
b) O(log N)
c) O(log N)
d) O(N2)
Answer: a
Clarification: The average case and worst case space complexity of a treap is mathematically found to be O(N).
2. A treap is a combination of a tree and a heap.
a) false
b) true
Answer: b
Clarification: A treap is a combination of a tree and a heap. The structure of a treap is determined by the fact that it is heap-ordered.
3. Which is the simplest of all binary search trees?
a) AVL tree
b) Treap
c) Splay tree
d) Binary heap
Answer: b
Clarification: A treap is the simplest of all binary search trees. Each node is given a numeric priority and implementation is non recursive.
4. What is the reason behind the simplicity of a treap?
a) Each node has data and a pointer
b) Each node is colored accordingly
c) It is a binary search tree following heap principles
d) Each node has a fixed priority field
Answer: d
Clarification: A treap is the simplest of all because we don’t have to worry about adjusting the priority of a node.
5. What is the condition for priority of a node in a treap?
a) a node’s priority should be greater than its parent
b) a node’s priority should be at least as large as its parent
c) the priority is randomly assigned and can have any value
d) a node’s priority is always given in decreasing order
Answer: b
Clarification: A node’s priority should satisfy heap order. That is, any node’s priority should be at least as large as its parent.
6. Several other operations like union set difference and intersection can be done in treaps.
a) True
b) False
Answer: a
Clarification: Other than insertion, deletion and search operations, several operations like union, intersection and set difference can be done in treaps.
7. What is the average running time of a treap?
a) O(N)
b) O(N log N)
c) O(log N)
d) O(M log N)
Answer: c
Clarification: The average case and worst case analysis of a treap are mathematically found to be O(log N).
8. Which node has the lowest priority in a treap?
a) root node
b) leaf node
c) null node
d) centre node
Answer: a
Clarification: A root node has the lowest priority in a treap since the node’s priority is based on heap order.
9. What is the priority of a null node?
a) 1
b) 0
c) random number
d) infinity
Answer: d
Clarification: The priority of a null node is set to be infinity in a treap so that during deletion, priority of that particular node is set to infinity, rotated and freed.
10. Who invented treaps?
a) Cecilia and Raimund
b) Arne Andersson
c) Donald Shell
d) Harris and Ross
Answer: a
Clarification: Cecilia and Raimund invented Treaps. Arne Andersson invented AA – Trees. Donald Shell invented shell sort and Harris and Ross formulated maximum flow problem.