Tree Data Structure Achara Sumungkaset Kalasin Rajabhat University

1
Tree Data StructureAchara
SumungkasetKalasin Rajabhat University
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???????????????

• ???????? Tree
• ?????????????????? Tree
• Binary Tree
• Binary Search Tree

3
?????
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
4
?????

• Tree ??????????????????????????????????? (Non
  Linear) ??????????????????? Tree
  ?????????????????????????? (Hierarchical)
  ???????????????? ?????????????????? Tree
  ??????????????????????? Compiler ???? Database
  ??????????????????????????????? ?
  ????????????????????????????????????????

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?????
A
Node
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
Node ??????? ?????? 1 ?????????????????? tree
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?????
A
Root Node
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
Root Node ??????? node ???????????? ???? node
????? node ?????? tree
7
?????
A
ChildNode
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
Child Node ??????? node ??????????
8
???????????????

• ???????? Tree
• Binary Tree
• ?????????????????? Tree
• Binary Search Tree

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Binary Tree

• ?????????????????????????????????????????????
  ?????????? Binary Tree ??? ???????????????????
  (???) ???????????? 2 ???????????? ???????????????
  Binary Tree ??????? ??????????????? ?
  ???????????? 2 ???????? ??????????????????????????
  ???????????? ??????????????????????????

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Binary Tree

• ????????????????????? Binary Tree ????
  ??????????????????????????????????????????????????
  ??????? ??????????????????????????????????????????
  ?????????????? ???????????????????? Binary Tree
  ???? ?????????????????????????????????????????
  ??????????????????????????????????????????????????
  ??? Root ????????????????????????????????????
  ??????????????????????????????????????????????????
  ?????????? ? ??? ?????????????????????????????????
  ???????

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Binary Tree
A
B
E
F
G
L
M
N
O
P
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Binary Tree
A
B
E
F
G
L
M
N
O
P
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Binary Tree
A
A
B
E
F
L
M
N
B
A
F
G
A
B
E
B
E
L
M
F
G
L
M
N
P
O
A
A
B
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Binary Tree
A
B
C
D
E
F
G
H
I
J
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Binary Tree
A
Root
B
C
D
E
F
G
H
I
J
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Binary Tree
A
Leaf
B
C
D
E
F
G
H
I
J
Leaf Node ??? ???????????????????
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Binary Tree
A
Leaf
B
C
D
E
F
G
H
I
J
Leaf Node ??? ???????????????????
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Binary Tree
A
Non-Leaf
B
C
D
E
F
G
H
I
J
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Binary Tree
A
Parent
B
C
D
E
F
G
H
I
J
Parent Node ??????? node ?????????? ???? node
????? node ????????
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Binary Tree
A
Parent
B
C
D
E
F
G
H
I
J
Parent Node ??????? node ?????????? ???? node
????? node ????????
21
Binary Tree
A
Parent
B
C
D
E
F
G
H
I
J
Parent Node ??????? node ?????????? ???? node
????? node ????????
22
Binary Tree
A
Parent
B
C
D
E
F
G
H
I
J
Parent Node ??????? node ?????????? ???? node
????? node ????????
23
Binary Tree
A
Parent
B
C
D
E
F
G
H
I
J
Parent Node ??????? node ?????????? ???? node
????? node ????????
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Binary Tree
A
Brother
B
C
D
E
F
G
H
I
J
Brother Node ??????????????? ???
???????????????????????
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Binary Tree
A
Brother
B
C
D
E
F
G
H
I
J
Brother Node ??????????????? ???
???????????????????????
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Binary Tree
A
Ancestor H
B
C
D
E
F
G
H
I
J
Ancestor Node ???? Node ??????????????
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Binary Tree
A
Ancestor E
B
C
D
E
F
G
H
I
J
Ancestor Node ???? Node ??????????????
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Binary Tree
A
Ancestor E
B
C
D
E
F
G
H
I
J
Ancestor Node ???? Node ??????????????
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Binary Tree
A
Descendant D
B
C
D
E
F
G
H
I
J
Descendant Node ??? ?????????????? x
???????????????????????????????????????? x
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Binary Tree
A
Descendant B
B
C
D
E
F
G
H
I
J
Descendant Node ??? ?????????????? x
???????????????????????????????????????? x
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Binary Tree
A
Descendant A
B
C
D
E
F
G
H
I
J
Descendant Node ??? ?????????????? x
???????????????????????????????????????? x
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Binary Tree
A
Descendant A
B
C
D
E
F
G
H
I
J
Descendant Node ??? ?????????????? x
???????????????????????????????????????? x
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Binary Tree
A
Level
B
C
D
E
F
G
H
I
J
Level ??????? ???????? node
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Binary Tree
A
0
Level
B
C
1
D
E
F
G
2
H
I
J
3
Level ??????? ???????? node
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Binary Tree
A
Height/Depth
B
C
D
E
F
G
H
I
J
Height of tree ??????? ????????????????????
(generation)
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Binary Tree
Complete Binary Tree
A
B
C
D
E
F
G
Complete Binary Tree ??????????????????????????
???????????????? Binary Tree ????????????? ???
???????????????? Leaf Node ??????????????? 2 ????
Leaf Node ?????????????????????????
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Binary Tree
Complete Binary Tree
A
B
C
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Binary Tree
Complete Binary Tree
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???????????????

• ???????? Tree
• Binary Tree
• ?????????????????? Tree
• Binary Search Tree

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Tree Traversal
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Tree Traversal
A
B
C
D
E
F
G
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Tree Traversal

• Preorder
• Inorder
• Postorder

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Tree Traversal

• Preorder Ro L R
• Inorder L Ro R
• Postorder L R Ro

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Tree Traversal

• Preorder

A
B
C
D
E
F
G
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Tree Traversal

• Preorder

A
B
C
D
E
F
G
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Tree Traversal

• Preorder

A
B
C
D
E
F
G
A B D E C F G
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Tree Traversal

• Inorder

A
B
C
D
E
F
G
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Tree Traversal

• Inorder

A
B
C
D
E
F
G
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Tree Traversal

• Inorder

A
B
C
D
E
F
G
D B E A F C G
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Tree Traversal

• Postorder

A
B
C
D
E
F
G
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Tree Traversal

• Postorder

A
B
C
D
E
F
G
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Tree Traversal

• Postorder

A
B
C
D
E
F
G
D E B F G C A
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Tree Traversal
/

• Example

-
2
3
5
9
/ 2 3 5 9
2 3 / 5 - 9
2 3 5 9 - /
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???????????????

• ???????? Tree
• ?????????????????? Tree
• Binary Tree
• Binary Search Tree

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Binary Search Tree

• Binary Search Tree ???????????????? Binary Tree
  ????????????????????????? ???
• ????????????????????????????????????????????
• ( TL lt R )
• ??????????????????????????????????????????????????
  ????? ( R lt TR )

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Binary Search Tree
5
2
8
7
11
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Binary Search Tree
15
5
20
3
12
18
19
10
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Binary Search Tree

• ???????????????? Binary Search Tree
• ????????????? Binary Search Tree

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???????????????? Binary Search Tree

• ??????????????????????????????????
• ??? Binary Search Tree ??????????????
  ?????????????????????????????????? Binary Search
  Tree
• ??? Binary Search Tree ????????????
  ???????????????????????
• 2.1 ?????????????????????????? ???????
  ????????????? ????????
• ?????????????????????????????
• 2.2 ?????????????????????? ?????????????????????
  ????????????
• ??????????????????????????

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???????????????? Binary Search Tree

• ?????????????????????????????? Binary Search
  Tree????????????????? 12 , 9 , 2 , 18 , 23 , 11
  , 14

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????????????? Binary Search Tree

• ??????? 1 ??????????????????????? Leaf Node
  ????????????????
• ???????2 ?????????????????????????????????????????
  ???? ????????????????????????????????
  ??????????????????????????????????????????????????
  ?
• ???????3 ?????????????????????????????????????????
  ? ???????????????????????????? ???????????????????
  ? 3 ???? ???

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????????????? Binary Search Tree

• 3.1 ?????????????????????????????????????????????
  ????????????3.2 ?????????????????????????????????
  ????????????????????????3.3 ?????????????????????
  ?????????????????????????????? ???????????????????
  ??????????????????????????????????????????????????
  ?????????????????????????

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????????????? Binary Search Tree

• ??????????????????? Binary Search Tree??????? 1
  ????????????? 8

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????????????? Binary Search Tree

• ??????? 2 ????????????? 3

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????????????? Binary Search Tree

• ???????3 ????????????? 2

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