This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Top Tree”.

**1. Which data structure is used to maintain a dynamic forest using a link or cut operation?****A) Top Tree**

B) Array

C) Linked List

D) Stack

Explanation: To maintain a dynamic forest using connect or cut operations, a top tree data structure is used. Top tree is a path-related data structure that is built on an unrooted dynamic binary tree.

**2. If A ꓵ B (A and B are two clusters) is a singleton set then it is a Merge able cluster.****A) True**

B) False

Explanation: Merge able clusters are described as A B is a singleton set where A and B are two clusters and there is only one node that is common to both clusters.

**3. Is Top tree used for maintaining Dynamic set of trees called forest.****A) True**

B) False

Explanation: To maintain a dynamic forest using connect or cut operations, a top tree data structure is used. Top tree is a path-related data structure that is built on an unrooted dynamic binary tree.

**4. What is the time complexity for the initialization of top tree?****A) O (n)**

B) O (n^{2})

C) O (log n)

D) O (n!)

Explanation: Trees, in general, have a lot of weight on their edges. There is also a one-to-one correspondence between the edges and the top trees. As a result, top trees can be created in O (n) time.

**5. How many top trees are there in a tree with single vertex?****A) 0**

B) 1

C) 2

D) 3

Explanation: There are no clusters of trees in the structure of a tree with a single vertex. As a result, in a tree with a single vertex, there are empty top trees. Trees with only one node are known as single node trees.

**6. Which property makes top tree a binary tree?**

A) Nodes as Cluster

B) Leaves as Edges

C) Root is Tree Itself**D) All of the mentioned**

Explanation: If the nodes form a cluster, the leaves act as an edge, and the root of the top tree acts as a tree, it can be called a binary tree. The top tree is then referred to as a binary tree.

**7. Which of the dynamic operations are used in Top Tree data structure implementation?**

A) Link

B) Cut

C) Expose**D) All of the mentioned**

Explanation: Link returns a single tree with vertices that differ from the top trees. The top tree’s edge is removed by cutting. Queries on top trees are implemented using Expose. As a result, all of the options are complex operations.

**8. Which of the following are used as an internal operation in Top tree?****A) Merge**

B) Cut

C) Expose

D) Link

Explanation: Link returns a single tree having different vertices from top trees. Cut removes the edge from the top tree. Expose is used to implement queries on top trees. While merge is an internal operation used to merge two clusters and return as a parent cluster.

**9. What is the time complexity for maintaining a dynamic set of weighted trees?**

A) O (n)

B) O (n^{2})**C) O (log n)**

D) O (n!)

Explanation: The Top tree interface has been used in a variety of applications. One such application that can be implemented in O (log n) time is maintaining a dynamic collection of weighted trees.

**10. Which algorithm is used in the top tree data structure?****A) Divide and Conquer**

B) Greedy

C) Backtracking

D) Branch

Explanation: Top tree is a path-related data structure that is built on an unrooted dynamic binary tree. It enables a divide-and-conquer algorithm.

**11. For how many vertices in a set, is top tree defined for underlying tree?**

A) 3

B) 4

C) 5**D) 2**

Explanation: A top tree is described as a set with no more than two vertices in its underlying tree. External Boundary Vertices are those sets of at least two vertices.

**12. How many edges are present in path cluster?****A) 2**

B) 3

C) 6

D) 1

Explanation: In a path cluster, there are at least two edges. In a data structure, a cluster is identified as a connected subtree with a maximum of two vertices known as Boundary Vertices.

**13. How many edges does a leaf cluster contain?****A) 0**

B) 1

C) 2

D) 3

Explanation: The term “leaf cluster” refers to a cluster that has no edges and only one vertex, the boundary vertex. As a result, there are no edges in a leaf cluster. Point cluster is another name for it.

**14. How many edges are present in Edge cluster?**

A) 0

B) 1

C) 2

D) 4

Explanation: Edge clusters are groups that only have a single edge. As a result, there is just one edge in the edge cluster. In a data structure, a cluster is identified as a connected subtree with a maximum of two vertices known as Boundary Vertices.

A top tree is a data structure for unrooted dynamic trees that is built on a binary tree and is primarily used for path-related operations. Easy divide-and-conquer algorithms are possible. It has since been enhanced to retain different tree properties such as diameter, base, and median in a dynamic manner. Topping is the drastic removal or cutting back of large branches of mature trees. The main branches are reduced to stubs and the tree is sheared like a hedge. Leading, stubbing, and dehorning are all terms used to describe the process of topping.