worksheet 17: Tree Introduction Name:
An Active Learning Approach to Data Structures using C 1
Worksheet 17: Tree Introduction
Trees are the third most used data structure in computer science, after arrays
(including vectors and other array variations) and linked lists. They are
ubiquitous, found everywhere in computer algorithms.
A tree consists of a collection of nodes connected by directed arcs. A tree has a
single root node. A node that points to other nodes is termed the parent of those
nodes while the nodes pointed to are the children. Every node except the root
has exactly one parent. Nodes with no children are termed leaf nodes, while
nodes with children are termed interior nodes. Identify the root, children of the
root, and leaf nodes in the following tree.
There is a single unique path
from the root to any node;
that is, arcs don’t join
together. A path’s length is
equal to the number of arcs
traversed. A node’s height is
equal to the maximum path
length from that node to a left
node. A leaf node has height
0. The height of a tree is the
height of the root. A nodes
depth is equal to the path
length from root to that node.
The root has depth 0. Identify
the height of the root in the
tree shown at right, and the
node with largest depth.
Explain why the following are not legal trees.
