An elaborate detailing about the data structure Tree Easy to learn and understand

1. TREE Terminologies
By,
Dr. Gopika S
Department of CS
Kristu Jayanti College , Bengaluru

2. Trees
Tree is a finite set of vertices that has a vertex called
as root and remaining vertices are collection of
subtrees.
Dr. Gopika S , KJC , Bengaluru 2

3. Dr. Gopika S , KJC , Bengaluru 3

4. Dr. Gopika S , KJC , Bengaluru 4

5. 5
Node Degree
• Node degree is the number of children it has
Dr. Gopika S , KJC , Bengaluru

6. 6
Tree Degree
• Tree degree is the maximum of node degrees
tree degree = 3
Dr. Gopika S , KJC , Bengaluru

7. subtree
Tree Terminology
• Root: node without parent (A)
• Siblings: nodes share the same parent
• Internal node: node with at least one
child (A, B, C, F)
• External node (leaf ): node without
children (E, I, J, K, G, H, D)
• Ancestors of a node: parent,
grandparent, grand-grandparent, etc.
• Descendant of a node: child,
grandchild, grand-grandchild, etc.
• Depth of a node: number of ancestors
• Height of a tree: maximum depth of
any node (3)
• Degree of a node: the number of its
children
• Degree of a tree: the maximum
number of its node.
A
B D
C
G H
E F
I J K
Subtree: tree consisting of a
node and its descendants
Dr. Gopika S , KJC , Bengaluru 7

8. • Path: traversal from node to node along the edges that results in
a sequence
• Root: node at the top of the tree
• Parent: any node, except root has exactly one edge running
upward to another node. The node above it is called parent.
• Child: any node may have one or more lines running downward
to other nodes. Nodes below are children.
• Leaf: a node that has no children
• Sub tree: any node can be considered to be the root of a subtree,
which consists of its children and its children's children and so
on.
• Visiting: a node is visited when program control arrives at the
node, usually for processing.
• Traversing: to traverse a tree means to visit all the nodes in some
specified order.
• Levels: the level of a particular node refers to how many
generations the node is from the root. Root is assumed to be
level 0.
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9. • Some Terminology
– node: the item of information plus the branches to each
node.
– degree: the number of subtrees of a node
– degree of a tree: the maximum of the degree of the
nodes in the tree.
– terminal nodes (or leaf): nodes that have degree zero
– nonterminal nodes: nodes that don’t belong to terminal
nodes.
– children: the roots of the subtrees of a node X are the
children of X
– parent: X is the parent of its children.
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10. –siblings: children of the same parent are said to
be siblings.
–Ancestors of a node: all the nodes along the
path from the root to that node.
–The level of a node: defined by letting the root
be at level one. If a node is at level l, then it
children are at level l+1.
–Height (or depth): the maximum level of any
node in the tree
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11. • Example
A is the root node
B is the parent of D and E
C is the sibling of B
D and E are the children of B
D, E, F, G, I are external nodes, or leaves
A, B, C, H are internal nodes
The level of E is 3
The height (depth) of the tree is 4
The degree of node B is 2
The degree of the tree is 3
The ancestors of node I is A, C, H
The descendants of node C is F, G, H, I
A
B C
H
I
D E F G
Level
1
2
3
4
Property: (# edges) = (#nodes) - 1
Dr. Gopika S , KJC , Bengaluru 11

12. Thank you
Dr. Gopika S , KJC , Bengaluru 12