Matakuliah
Tahun
Versi
: T0026/Struktur Data
: 2005
: 1/1
Pertemuan 13
AVL Tree
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat menghasilkan program
modular untuk mengimplementasikan ADT
AVL tree
2
Outline Materi
•
•
•
•
•
Pengertian dan penggunaan AVL tree
Contoh AVL Tree
Inerting data AVL tree
Deleting data AVL tree
Contoh program AVL Tree
3
AVL Tree
•
•
•
•
Introduced by Adelson-Velskii and Landis in 1962
Definition :
– TL and TR are height balanced
– |hL - hR|<=1
 AVL Tree adalah Binary Search Tree yang mempunyai ketentuan :
maksimum perbedaan height antara subtree kiri dan subtree kanan
adalah satu
Balance Factor, BF(T) :
– TallLeft : –1
– TallRight : +1
– Balance : 0
4 kinds of rebalancing :
– LL
: left subtree of the left subtree
– RR
: right subtree of the right subtree
– LR
: right subtree of the left subtree
– RL
: left subtree of the right subtree
4
Operation on AVL Tree
•
INSERT
–
case 1 : BF(T)=0
0
54
54
0
+1
0
30
30
70
70
0
80
Before Insert(80)
–
+1
After Insert(80)
case 2 : BF(T)=+1
Insert in left subtree for BF(T)=+1.
54
0
30
54
+1
-1
30
+1
70
0
80
Before Insert(10)
0
10
0
+1
70
80
After Insert(10)
0
5
Operation on AVL Tree
•
•
•
•
Case 3
Case 4
Case 5
Case 6
: Insert in left subtree for BF(T)=-1
: Insert in right subtree for BF(T)=+1
: Insert in left subtree for BF(T)=+1
: Insert in right subtree for BF(T)=-1
6
Operation on AVL Tree
Single Rotation : LL, RR
54
0
30
+1
54
+1
70
0
80
0
30
+2
54
+2
70
LeftChild
+1
80
88
0
30
0
80
0
Parent
+1
70
0
88
RightChild
7
Operation on AVL Tree
Double Rotation
-1
10
0
5
0
20
30
60
0
40
0
-1
+1
80
50
-1
10
0
90
0
0
5
+1
20
60
-2
+1
80
0
+1
90
40
+1
0
30
50
55
Before Insert(55)
Insert(55)
60
40
20
10
80
90
50
30
55
0
5
-1
10
-1
20
40
0
0
60
0 +1
+1
30 50 80
0
0
55
90
5
R1
R2
8