Data Structures and Algorithms in Java
Data Structures and Algorithms in Java
6th Edition
ISBN: 9781119278023
Author: Michael T. Goodrich; Roberto Tamassia; Michael H. Goldwasser
Publisher: Wiley Global Education US
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Chapter 8, Problem 1R

Explanation of Solution

a.

Root node:

  • Root node means highest node in the tree structure, and has no parent.
  • According to the Figure 8.3, the root node is “/user/rt/courses/”, because it is the highest node in the tree structure.

Explanation of Solution

b.

Internal node:

  • Internal node means any node of a tree which has child nodes. It is lso known as an inner node, or branch node.
  • According to the Figure 8.3, the internal nodes are “/user/rt/courses/”, “cs016/”, “cs252/”, “homeworks/”, “programs/”, “projects/”, “papers/”, and “demos/” because, they are the internal nodes in the given Tree.

Explanation of Solution

c.

Descendant node:

  • Descendant node of a node is any node in the path from that node to the leaf node. The immediate descendant of a node is the “child” node.
  • According to the Figure 8.3, the descendant node of “cs016/” contains  are “grades”, “homeworks/”, “programs/”, “hw1”, “hw2”, “hw3”, “pr1”, “pr2”, and “pr3”.
  • Therefore, the total number of descendant node of “cs016/” contains 9.

Explanation of Solution

d.

Ancestor node:

  • An ancestor node of a node is any node in the path from that node to the root node. The immediate ancestor of a node is the “parent” node.
  • According to the Figure 8.3, the ancestor node of “cs016/” is “/user/rt/courses/”.
  • Therefore, the total number of ancestor node of “cs016/” contains 1.

Explanation of Solution

e.

Siblings of node:

  • Sibling of nodes is nodes on the same hierarchical level under the same parent node.
  • According to the Figure 8.3, the siblings of node “homeworks/” are “grades/” and “programs/”.

Explanation of Solution

f.

Subtree:

  • Subtree of the node is defined as a tree which is a child of a node.
  • According to the Figure 8.3, the subtree rooted at node “projects/” are “papers/”, and “demos/”.

Explanation of Solution

g.

Depth of node:

  • The depth of a node is the number of edges from the node to the tree’s root node.
  • According to the Figure 8.3, the depth of node “papers/” are 2 they are “buylow” and “sellhigh”.

Explanation of Solution

h.

Height of a tree:

  • The height of a node is the number of edges on the longest path from the node to the leaf.
  • According to the Figure 8.3, the height of a tree is 4.

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