-Trees concepts and preliminaries -Tree implementation -Tree traversal ADT: Abstract Data Type

1. CS221A – Data Structures &
Algorithms
Trees

2. Agenda
 Trees Concepts and Preliminaries
 Tree Implementation
 TreeTraversal

3. Trees
 An ADT that can store data hierarchically.With a parent
child relationship.
 Widely-used data structure that emulates a hierarchical
tree structure with a set of linked nodes.
 It is a connected graph where each node has a set of zero
or more children nodes, and at most one parent node.

4. Trees
 Node is a structure which may contain a value, a
condition, or represent a separate data structure (which
could be a tree of its own).
 Each node in a tree has zero or more child nodes, which are
below it in the tree (by convention, trees grow down, not up as
they do in nature).
 A node that has a child is called the child's parent node (or
ancestor node, or superior).
 A node has at most one parent.
 Nodes that do not have any children are called leaf nodes.
They are also referred to as terminal nodes.

5. Trees
 A simple unordered tree;
 the node labeled 7 has
two children, labeled 2
and 6, one parent, labeled
2.The root node, at the
top, has no parent.

6. Trees
 The topmost node in a
tree is called the root
node.
 The root node will not have
parents.
 It is the node at which
operations on the tree
commonly begin (although
some algorithms begin with
the leaf nodes and work up
ending at the root).
 All other nodes can be
reached from it by following
links or edges.
Root NodeLinks or edges

7. Trees
 The height of a node is
the length of the longest
downward path to a leaf
from that node.
 The height of the root is
the height of the tree.
0
1
2
Height of the
Tree : 3
00
1
2
0

8. Trees
 The depth of a node is
the length of the path to
its root (i.e., its root path).
 An internal node or
inner node is any node of
a tree that has child nodes
and is thus not a leaf node.
 Stepping through the items
of a tree, by means of the
connections between
parents and children, is
called walking the tree
or TreeTraversal.
3
1
2
33
1
2
0
2
Inner Node

9. Trees
 Tree is a collection of N
nodes, one of which is the
root and N - 1 edges.
 N = 9
 E = 8

10. Trees Implementation

11. Tree Implementation

12. Trees Implementation
 Each Node Maintains Data and a pointer to each of its
child nodes.
 As Number of Children per Node is an unknown , we
keep the children of each node in a linked list of tree
nodes.

13. Tree Implementation
 typedef struct TreeNode *PtrToNode;
 struct TreeNode
 {
 ElementType Element;
 PtrToNode FirstChild;
 PtrToNode NextSibling;
 }

14. Tree Implementation
 voidTraverse(Tree t)
 {
 printf (tElement);
 if (tFirstChild != Null)
 Traverse(tFirstChild);
 if (tNextSibling !=Null)
 Traverse(tNextSibling);
 }