Problem of the Day
 Solve this equation by moving the numbers:
76 = 24
Problem of the Day
 Solve this equation by moving the numbers:
76 = 24
2
7 = 49
CSC 212 – Data Structures
LECTURE 34:
TREE AND BINARY TREE ADT
Trees
 Represent hierarchical relationships
 Parent-child basis of this abstract data type
 Real-world example: directories & types
csc212/
homeworks/
hard.txt
3K
impossible.txt
2K
programs/
LLQueue.java
10K
DLNode.java
25K
ideas.todo
1M
Tree.java
20K
Trees
 Represent hierarchical relationships
 Parent-child basis of this abstract data type
 Real-world example: organism classification
Mammal
Cat
Lion
Ape
Human
Chimpanzee
Professors
Yankees Fan
Tree Basics
 Yet another Collection
A
 Nodes are Positions
B
 # of elements is its size
 Some things are familiar
 Using Position
E
C
G
F
to hold elements
 Others are very different
 Node class has little overlap
 Cannot discuss next & prev
I
J
K
D
H
Tree Terms
 Defined by relationships
A
 Talk about parents,
siblings,
descendant
 Nodes have no gender
B
E
C
G
F
 Will often mix in terms
like mother, father,
niece, aunt, uncle,
cousin, …
I
J
K
D
H
Tree Terms
 Tree rooted at node A
A
 “Top” or “Start” of tree
 B, C, D are children of A
 A is parent of B, C, D
 B, C, D are siblings
 E, F, G, H are
grandchildren of A
B
E
C
G
F
I
J
K
D
H
Tree Relationships
 Nodes either leaf or interior
A
 Both or neither not options
 A, B, C, F are parents
B
 At least 1 child for each
 Also called “interior nodes” E
 "Leaves" name of others
 Leaf node has no children
C
G
F
I
J
K
D
H
Trees
Recursion
 Trees are recursive structure
A
 Subtree defined by a node
B
E
C
G
F
I
J
K
D
H
Trees
Recursion
 Trees are recursive structure
A
 Subtree defined by a node
 C is root of this subtree
B
E
C
G
F
I
J
K
D
H
Trees
Recursion
 Trees are recursive structure
A
 Subtree defined by a node
 C is root of this subtree
B
C
D
 B root of this subtree
E
G
F
I
J
K
H
Trees
Recursion
 Trees are recursive structure
A
 Subtree defined by a node
 C is root of this subtree
B
C
D
 B root of this subtree
 D root of this subtree
E
G
F
I
J
K
H
Trees
Recursion
 Trees are recursive structure
 Subtree defined by a node
 C is root of this subtree
 B root of this subtree
 D root of this subtree
 Trees are like professors
 Some are tall & thin
Trees
Recursion
 Trees are recursive structure
 Subtree defined by a node
 C is root of this subtree
 B root of this subtree
 D root of this subtree
 Trees are like professors
 Some are tall & thin
 Short & boring a possibility
Trees
Recursion
 Trees are recursive structure
 Subtree defined by a node
 C is root of this subtree
 B root of this subtree
 D root of this subtree
 Trees are like professors
 Some are tall & thin
 Short & boring a possibility
 Others can be empty & useless
Trees vs. Binary Trees
 Both represent parent-child relationships
 Both consist of single "root" node & its descendants
 Nodes can have at most one parent
 Root nodes are orphans -- do not have a parent
 All others, the non-root nodes must have parent
 Children not required for any node in the tree
 No limit to number of children for non-binary nodes
 2 children for node in binary tree is the maximum
Binary Tree
 Extends Tree interface & adds following property
 2 or fewer children per node
 Typically drawing of tree sets childrens' names
 “Left child” is name of child to left of the parent
 Child towards the right is called “Right child”
R
B
D
E
F
I
H
Height and Size of a Tree
 Maximum number of nodes doubles each level
Level 0 – max. 1 node
Height and Size of a Tree
 Maximum number of nodes doubles each level
Level 0 – max. 1 node
Level 1 – max. 2 nodes
Height and Size of a Tree
 Maximum number of nodes doubles each level
Level 0 – max. 1 node
Level 1 – max. 2 nodes
Level 2 – max. 4 nodes
Height and Size of a Tree
 Maximum number of nodes doubles each level
 For a level i in a binary tree
 That level can have 2i nodes
 At most 2(i+1)-1 nodes for tree to that level
Level 0 – max. 1 node
Level 1 – max. 2 nodes
Level 2 – max. 4 nodes
Level 3 – max. 8 nodes
Independent of Implementation
A
B
Z
F
I
Q
M
Binary Tree, Tree, or Other?
Binary Tree, Tree, or Other?
Binary Tree, Tree, or Other?
Binary Tree, Tree, or Other?
Binary Tree, Tree, or Other?
Binary Tree, Tree, or Other?
Binary Tree, Tree, or Other?
A
B
C
D 
Binary Tree, Tree, or Other?
Your Turn
 Get into your groups and complete activity
For Next Lecture
 Read parts of GT 7.2 & 7.3.6 for Monday
 Trees are Iterable, but how would it be done?
 What are the types of traversals & how do they differ?
 When do we do parent first & when do we do our kid?
 Programming Assignment #2 due today
 To get help, do not delay; end of week gets crazy