Data Structure

1
Data Structure
???????????????
2
Data Structure

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

3
Data Structure and Algorithm?????????????????????
???????

• ?????????????????????????????????

Root Node
Node
Link
?????????????????
????????????????????????
4
Data Structure and Algorithm?????????????????????
???????

• ????????????????????????
• ???????????????????????? (Non Linear)
  ??????????????????????????? ????????????????
  ????????????????????????????????????
• ???????????????????????? ?????????????????????????
  ??????????????? ????????? ????????????????
• ?????????????????? ???????????? (Node)
  ??????????????????????
• ?????????????????????????? (Link)

5
Data Structure and Algorithm?????????????????????
???????

• ????????????????????
• ??????????????????? ?????????? (root node), R
• ???????? ? ???????????? ?????????????????? n
  ????? ?????????????????????????????
  ???????????????????????????????
  ????????????????????????? (Sub tree)

6
Data Structure and Algorithm?????????????????????
???????

• ???????????????
• R ???????????????????
• ???? A,B,C,D
• A ???????????????????
• ???? E, F, G
• F ???????????????????
• ???? J
• B ??????????????????????? H ??? I

R
A
B
C
D
E
F
H
I
G
J
Sub Tree
7
Data Structure and Algorithm?????????????????????
???????

• ???????????????????? ? ?????????
• ????????????????????????????? ????????????????????
  ????????????????
• ???? Father, Son, Grandson
• ?????????????????????? Mother, Child, Grandchild
• ???????????? (Level)
• ?????????????????????????????????????????????????
  ??????
• ??????????????????????????? 1 (??????????????????
  ???????????? 0)
• ???????????????????????????????? ???? 3 1
  (???? 3 0) ???????

8
Data Structure and Algorithm?????????????????????
???????

• ????????????
• R ?????????? ????? 1
• A,B,C,D ???????????? 2
• E,F,G,H,I ???????????? 3
• J ???????????? 4

R
A
B
C
D
E
F
H
I
G
J
9
Data Structure and Algorithm?????????????????????
???????

• ???????????? (Level Degree)
• ?????????????????????????????
• A ??????? ???? 3
• B ??????? ???? 2
• F ??????????? 1
• C,D,E,G,H,I,J ??????????? 0

R
A
B
C
D
E
F
H
I
G
J
10
Data Structure and Algorithm?????????????????????
???????

• ????????????? (Leaf Node)
• ????????????????????? 0
• ????????????????????????? 0 ?????????????????
  (interior/branch node)
• A,B,F ?????????????
• C,D,E,G,H,I,J ??????????

R
A
B
C
D
E
F
H
I
G
J
11
Data Structure and Algorithm?????????????????????
???????

• Predecessor, Successor
• ??????????????????????/????
• Predecessor (Ancestor) ???????????????
• Successor (Descendant) ?????????????????
• R,A ???? Predecessor ??? E,F,G,J
• E,G ????? Successor
• J ???? Successor ??? F
• F ???? Predecessor ??? J

R
A
B
C
D
E
F
H
I
G
J
12
Data Structure and Algorithm?????????????????????
???????

• Immediate Successor ???? Son ???? Child ??????? i
• ???????????????????????? i ?????????????? i
  ??????????
• Immediate Predecessor ???? Father ???? Mother
  ??????? i
• ???????????????????????? i ?????????????????? i
  ??????????
• E,F,G ??? Son/Child ??? A
• J ???? Son/Child ??? F
• F ???? Father/Mother ??? J

R
A
B
C
D
E
F
H
I
G
J
13
Data Structure and Algorithm?????????????????????
???????

• ??? (Forest)
• ??? ?????????????? ???????????????????????????????
  ??????????????? ?????????????????????????????????
  ??????????????????? ?????????????
• ???? ???????????????????????????????? ?
  ?????????????????????????

A
B
C
D
E
F
H
I
K
L
G
M
J
14
Data Structure and Algorithm?????????????????????
???????

• ????????????????? (Ordered Tree)
• ???????????????????????????????????????? ????
  ????, ?????????, ????????
• ???????????????????? (Unordered Tree)
• ?????????????????????????????????????????
  ???????????????? ?????????????????

A
B
?????? A ??? B ??????????????????????????????????
??????? ????????????????????? ???????????????
15
Data Structure and Algorithm?????????????????????
???????

• ??????????????????????????????????
• ???????????????????? ??????????????????????
  ???????????????? ?
• ???????????????? Son ????? ????????? 5 son ??? k
  5 ????????? 3 son
• ??? K 3 ??????????????????????????????????????
  ??????????
• ???????????????????? k ??????????????????????????
  ????????????????

???????
Son,1
Son,2
Son,3
Son, k
16
Data Structure and Algorithm?????????????????????
???????

• ??????????????????????????????????
• ?????????????????????????????????????? ???? B
  ????? 4
• ???????????? 9 ???? (A-I) ???????????????????????
  ???????????????????
• 5 ?????????? 9 ???? ??????????????????
  ???????????????? ? ??????????

???????
A
B
C
Son,1
Son,2
Son,3
Son,4
D
E
F
G
H
I
17
Data Structure and Algorithm?????????????????????
???????
A

• ??????????????????????????????????

B
C
D
E
F
G
H
I
1 2 3 4 5
6 7 8 9
A B C D E F G H I
2 4 8 - 9 - - - -
3 5 - - - - - - -
- 6 - - - - - - -
- 7 - - - - - - -
INFO SON,1 SON,2 SON,3 SON,4
18
Data Structure and Algorithm?????????????????????
???????

• ??????????????????????????????????
• ?????????????????????????????? ???????????????????
  ???????????????????
• ??????????????????????????? ??????????????????????
  
• ???????????????????? K ?????????? n ????
  ????????????????????????
• ??????? n ???? ??????????????? kn ????
• ???????????????????????? n-1 ????
  (?????????????????????????????????????)
• ????????????????????????????? kn (n 1)
• kn n 1
• n(k 1) 1
• 9(4 -1) 1 28 ?????????????

19
Data Structure and Algorithm?????????????????????
???????

• ??????????????????????????? (Binary Tree)
• ???????????? ???????????????????????????????? 2
  ????? ??????????????????? ????????????????????????
  ?????
• ?????????????????? ???????? left subtree
• ????????????????? ???????? right subtree
• ?????????????????? ??? ???????????????????????????
  ???????? ???????????????

20
Data Structure and Algorithm?????????????????????
???????

• ???????????????????????????
• ???????????????????? ?????????????????????????????
  ??? 2
• ?????????????????????????????? ???????????????????
  ?? ????????????????????
• ?????????????????????????? Father
• ???????????????????? LSon, ???????????????????
  RSon

Father
LSon
RSon
21
Data Structure and Algorithm?????????????????????
???????

• ???????????????????????????

Binary Tree
Non Binary Tree
22
Data Structure and Algorithm?????????????????????
???????

• ?????????????????????????????????????
• ???????????????????????????? ?????????????????????
  
• ?????????? ??? ?????? ????????????????????????????
  ?
• ??? n ????????????????????, l ???????????????
  (level )
• n 2l 1
• ???????? ???????????????????? 23 1 7 ????

23
Data Structure and Algorithm?????????????????????
???????

• ???????????????????????????????????
• ??????????????????? Son ????? ????????????????????
  ????????? 2
• ??????????????????????????????????????????
• ?. ???????????????????????????????
• ?. ????????????????????????????????????????????
• ??????????????
• 1. ??????????????????????????????????????????????
  ???????
• Leftmost son, next sibling
  (????????????????)
• 2. ??????????????????????? 45?
  ?????????????????????????

24
Data Structure and Algorithm?????????????????????
???????

• ??????????????????????????????????????
• ????????????? B ???? leftmostson ??????? C ????
  next-sibling ??? B ?????? D ???? next-sibling ???
  C
• ????????????? ????????????????????? 45?

A
A
A
?????????? 2
B
C
D
B
C
D
B
C
?????????? 1
D
25
Data Structure and Algorithm?????????????????????
???????

• ???????????????????????????????
• ?????? 2 ??????
• ?. ????????????????????????
• ?. ????????????????????????????
  ????????????????????????
• ????????????????????????

Data
Data
????
LLink
RLink
LSon
RSon
26
Data Structure and Algorithm?????????????????????
???????

• ????????????????????????
• LLink ???? LSon ??????????????????????????????????
  ????????
• RLink ???? RSon ??????????????????????????????????
  ???????
• T ????????????????????????? ?????? T
  ???????????????????????????????
• ??? T ?????????????????? ??? T
  ?????????????????

Data
Data
????
LLink
RLink
LSon
RSon
27
Data Structure and Algorithm?????????????????????
???????

• ????????????????????????

T
A
A
B
X
B
X
0
0
C
D
C
D
0
0
0
E
Link ???????????????? ??????????? 0
??????????????????????????????????????????
T ??????????????????????????????????????
E
0
0
28
Data Structure and Algorithm?????????????????????
???????

• ????????????????????????????
• (???????????????????? Sequential Access)
• ???????????????????????????????? 1
  ????????????????????
• ?????????????????????????????????????????? (Full
  Binary Tree)
• ?????????????????????????????????????????????? 1
  ????
• ??????????????????????????????????????????????????
  ?? Full Binary Tree
• ????????????????????????? 2l - 1

29
Data Structure and Algorithm?????????????????????
???????

• ????????????????????????????

A
1
2
3
B
X
4
5
6
7
C
D
E
8
9
10
11
12
13
14
15
1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
A B X C D - - E - - - - - - -
30
Data Structure and Algorithm?????????????????????
???????

• ????????????????????????????
• ??????????????? ???(Father) ?????? ? (Lson, Rson)
• ????????????? Father (i) ??? i 5 (??? D)
• ?????????? (absolute value) ??? i/2 father
  ???????????????? 2
• ?????????? Lson (i) (??? B)
• ?????????? 2i Lson ???????????????? 4
• ?????????? Rson (i) (??? C)
• ?????????? 2i 1 Rson ???????????????? 5(D)

31
Tree Type

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

parent
Left Son
Right Son
32
Tree Type

• Binary Search Tree
• ?????????????????????????? parent ???? child
  ?????????? 2
• ???? child ??????? parent ?????????????
• ???? child ?????? parent ????????????

33
Binary Search Tree

• Representations
• ??????????????????????????????????????????????????
  

typedef struct node int n_int node
left node right tree_node
Left Son pointer
Right Son pointer
34
BST Operation

• Insert
• ?????????????????? leaf ????????
• ??????????????????????????????? root
• ????????????????? ??????????????????????????????
  (?????????????? null)

D B F A C E G
D
B
F
G
E
A
C
35
BST Operation

• Insert
• ??????????????? Tree (1)

B A D C G F E
B
A
D
C
G
F
E
36
BST Operation

• Insert
• ??????????????? Tree (2)

A B C D E F G
A
B
C
D
E
F
G
37
BST Operation

• Delete
• ?? 3 ?????????????????
• ?? leaf
• ??????????? child ?????????
• ??????????? child ???????

D
2
3
B
F
1
A
E
C
38
BST Operation

• Delete Leaf Node
• ??????????????????????????????????????????????????
  ? null
• ?????? leaf
• ???????? root ?????????????????? tree ????

D
NULL
B
F
A
E
C
39
BST Operation

• Delete 1 child node
• ????????????????????????????????????????????????
  child
• ??????
• ??????? root ????????????????????? root ????

D
B
F
A
E
C
40
BST Operation

• Delete 2 child node
• ????????????????????????????????????????????????
• ????????????? ??????????????????

D
B
F
A
E
C
??????????????????????????????????????
?????????????
41
BST Operation

• Delete 2 child node ??????????????????????
• ??????????????????????????????????????????????????
  ?
• ?????????????????????????????????
• ??????????????????

D
A
B
F
E
A
C
42
BST Operation

• Delete 2 child node ?????????????????????? (2)

F
C
D
H
J
B
E
A
C
43
BST Operation

• Delete 2 child node ???????????????????
• ????????????????????????????????????????????????
• ??????????????????????????????
• ???????????????

D
C
B
F
E
A
C
44
BST Operation

• Delete 2 child node ??????????????????? (2)

F
E
D
H
B
F
G
A
C
45
BST Operation

• Searching
• ??????????????????????????????????????? root
• ???????? tree ??????????? insert
  ???????????????????
• ????? return ??? ???????? leaf ???????????????????
  ????????????? tree

root
D
search E
F
B
A
E
C
G
46
BST Operation

• Searching
• ??????????? search ??? tree ??????????????????????
  linear

A
B
C
D
E
F
G
search E
D
Linear 5 comp. Tree 3 comp.
F
B
A
E
C
G
47
BST Operation

• Searching
• ?????????????????????

Data Time Comparison Time Comparison
Data Linked List Tree
A 1 3
B 2 2
C 3 3
D 4 1
E 5 3
F 6 2
G 7 3
Total 28 17
Average 28/7 4 17/7 2.43
48
BST Traversal

• Traverse Binary Search Tree
• Inorder
• Preorder
• Postorder
• Reverse Inorder
• Reverse Preorder
• Reverse Postorder

49
BST Traversal

• Traverse Binary Search Tree
• ????????? tree ???? 3 ????
• R ? root
• TL ? left subtree
• TR ? right subtree
• ????? traverse subtree
• ???????????

R
TL
TR
50
BST Traversal

• Traverse Binary Search Tree
• Inorder ? TLRTR
• Preorder ? RTLTR
• Postorder ? TLTRR
• Reverse Inorder ? TRRTL
• Reverse Preorder ? RTRTL
• Reverse Postorder ? TRTLR

51
BST Traversal

• Inorder Traversal

TLRTR
TL
R
TL
TR
A B C
E F G
TR
R
D
D
A B C D E F G
52
BST Traversal

• Preorder Traversal

RTLTR
TL
R
TL
TR
B A C
F E G
TR
R
D
D
D B A C F E G
53
BST Traversal

• Postorder Traversal

TLTRR
TL
R
TL
TR
A C B
E G F
TR
R
D
D
A C B E G F D
54
BST Traversal

• Reverse Inorder

TRRTL
TL
R
TL
TR
C B A
G F E
TR
R
D
D
G F E D C B A
55
BST Traversal

• Reverse Preorder

RTRTL
TL
R
TL
TR
B C A
F G E
TR
R
D
D
D F G E B C A
56
BST Traversal

• Reverse Postorder

TRTLR
TL
R
TL
TR
C A B
G E F
TR
R
D
D
G E F C A B D
57
?????????????