11 Questions
a tree with n vertices has n-1 edges prove it with basis steps and inductive step
What is the purpose of topological sort?
To obtain a linear ordering of the vertices in a directed graph or tree.
Name three applications of trees in computer science.
Data structures, algorithms, and computer graphics.
What is a binary tree and how many children can a node have?
A binary tree is a tree where each node has at most two children.
What type of trees are used in database management systems and file systems?
Binary search trees.
How do binary trees contribute to computer vision?
They are used for image processing and feature extraction.
What is a tree in the context of discrete mathematics?
An undirected graph that is connected and acyclic, with a root vertex and internal vertices.
What are the main traversal techniques for trees?
Depth-First Search (DFS) and Breadth-First Search (BFS).
What is the root-to-leaf path in a tree?
The edge connecting a vertex to its parent.
What is the depth of a tree?
The sum of the lengths of the root-to-leaf paths.
What are the types of vertices in a tree?
Root, internal, and leaves.
This quiz covers the proof of why a tree with n vertices has n-1 edges using basis and inductive steps. It examines the basis step to establish the initial condition and the inductive step to show that if the proposition holds for some vertex, it holds for the next vertex as well.
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