Tree 1

1
??????Tree (1)

• ?????????????? ?????????
• ???????????????????????????????????????

2
????????????

• ???????????????????????? (Introduction)
• ????????????????????? ????????? (terminology)
• ??????????????? (binary tree)
• ?????????????????????? (complete binary tree)
• (nearly complete binary tree)
• ??????????????????????????????????

3
root
node
branch
?????????????????????????????????
4
????????????????????????

• ???? ???????????????????????????????????????
  (Non-Linear Data Structure)
• ???????????????????????????? (??????????)
• ????????????????????????????????? ??? (Root)
• ??????????????????????????????????????? ????
  (Node)
• ??????????????????????????????????????????? ????
  (Branch) ???? ????? (Link)
• ????????????????? ???????????? (subtree)
• ??????????? root ??? subtree ????????????

5
R ???? root ??? subtree A,B,C,D A ???? root ???
subtree E,F,G F ???? root ??? subtree J C ????
subtree ???????? root C
6
????????????????????? ?????????

• ?????? (tree) ??????????
• 1.node ??????????????
• 2.branch ????????? node ???????????

node A, B, C branch AB, AC
7

• root ??????? node ?????? tree

root A ????????? B , C

• Degree ??????? ????? subtree ?????????????? Node
  ?????

node A ?? degree ??????? 2 node B ?? degree
??????? 0 node C ?? degree ??????? 0
8

• leaf ??????? node ????????????????? 0

root A leaf D , E , C

• internal node , branch node ??????? node
  ????????? root ??? leaf

branch node B
9

• parent ??????? node ????????????????? 0 (node
  ????? subtree )

parent A , B

• child ??????? node ??????? subtree ??? tree ????

child B , C , D , E
10

• level ????????????????? root ????? node ?????

• height ???? depth ??? tree ??????? level ??????
  ??? leaf ??????? 1

depth 2 1 3
11

• sibling ???????????????? parent ???????

sibling ??? B ??? C sibling ??? D ??? E ??? F
12
parents children leaves internal nodes depth
degree(A) degree(B) degree(H) degree(C) degree(E)
A, B, F
3
B, E, F, C, D, G, H, I
2
E, C, D, G, H, I
0
B, F
0
3
0
13
Exercise 1
A

• - node ??????? parent
• - node ??????? child
• - level ??? tree
• - height ??? tree
• - degree ????????????
• - parent ????????????
• - children ????????????
• - sibling ????????????

C
B
H
G
D
F
E
L
I
K
J
L
1.??? tree ???????? ???? - node ??????? root -
node ??????? leaf - node ??????? internal node
14
??????????????? (binary tree)

• ??????? tree ???????? node ??????? subtree lt 2
  ( ????? node ?? degree lt 2 )

15
Empty ???? Null Tree
16
???????????????????????????

• ?????????????????????????? (hight) ???????? node
  ?? binary tree
• ???????? h ?????????????? binary tree
• n ????????? node ?? binary tree
• ???????????????? (h) ????????????????? node
  (n)????????????????????????????????????? binary
  tree ???????
• ?????????????? node (n) ??????????????????? (h)
  ????????????????????????????????????? binary tree
  ???????

17

• ??????????????????? binary tree 3

nmax 7
nmin 3
???????? nmax 2h 1 nmin h
18

• ?????????????????? node ??? binary tree 5

hmax 5
hmin 3
???????? hmin log2n 1 hmax n
19
?????????????????????? (complete binary tree)

• ??? binary tree ????? node ??????? level (???
  node ????????? leaf ?? child ?????????????????????
  ?)

nearly complete binary tree

• ??? binary tree ????? node ??????? level ??????
  level ??????? ??? node ?? level
  ?????????????????????????????

20
(No Transcript)
21
??????????????????????????????????

• binary tree ????????????????????????? 2 ??? ???
• ??????????????????????
• ??????????? 3 ????????????????????
• ??????????? 1 ?????????????????????????????
• ?????????????? pointer

22
???????????????????? 3 ????????????????????

• ?????????????????????????????????? 3 ??? ???
• data ????????????????? node
• left ?????????????? node ?????????????????
• right ?????????????? node ????????????????
• ??? node ??????? node ??? ?????????? -1 (???
  NULL)
• ???????????? root ?????????????? node ????? tree

23
????????
???????????????????
general binary tree
data
left
right
root
A
A
2
3
1
1
2
B
6
4
B
C
C
7
-1
3
E
8
5
4
H
-1
-1
5
D
E
F
D
-1
-1
6
F
-1
-1
7
G
H
G
-1
-1
8
24
???????????????????? 1 ???????????????????????????
??

• ???????????????????? complete binary tree
• ?????????????????????????? node ??????? level 0 ,
  1 , , k ????????
• ??????? level ?????????????? node
  ???????????????????????????????? ????????
• ?????????????????????? tree ?????????????????
  ???? complete binary tree

25
????????
general binary tree
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
???????????????????
26

• ???????????????????????? tree ??? ???????? ??????
• ??? binary tree ???????????????? h
  ?????????????????????????? 2h 1 ????????????
• parent ??????? i ??? ???????????????? i/2 ??? i
  ?????????? 1
• left child ??????? i ??? ???????????????? 2i
• right child ??????? i ??? ???????????????? 2i 1

27
?????????????? pointer

• ??????????????????????????????????
  ??????????????????????????????????????????????????
  
• ?????????????? node ??? tree ??????????????
• data ????????????????? node
• Lptr ???? address ??? node ?????????????????
• Rptr ???? address ??? node ????????????????

28
????????
29
???????

• ??? binary tree ??????????????????????????????????
  ???????? 1 ??????????????????????????????????
  ??????????????????????? 1024 ????????????????
  ??????????????????
• 1. binary tree ??????????????????
• 2. ?????? ? ??????????????? 837 ???? parent node
  ???????? ? ?????????????????

30
???????

• 3. ?????? ? ??????????????? 422
  ??????????????????? ? ?????????????
• 4. ?????????????????????????????????????????
  ????????? ????????????
• 5. ???????????????????????????????????????????????
  ????????? ????????? ????????????