Post on 06-Sep-2018
AVL Tree Example:
• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree
14
17 11
7 53
4
ΕΠΛ 231 – Δομές Δεδομένων και Αλγόριθμοι
Φροντιστήριο 7
1. Ξεκινώντας με ένα άδειο AVL-δένδρο να εφαρμόσετε διαδοχικά εισαγωγή των στοιχείων
2, 1, 4, 5, 9, 3, 6, 7, 16, 0 δείχνοντας το αποτέλεσμα της κάθε μιας από τις εισαγωγές.
AVL Tree Example:
• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree
14
17 7
4 53 11
13
AVL Tree Example:
• Now insert 12
14
17 7
4 53 11
13
12
AVL Tree Example:
• Now insert 12
14
17 7
4 53 11
12
13
AVL Tree Example:
• Now the AVL tree is balanced.
14
17 7
4 53 12
13 11
AVL Tree Example:
• Now insert 8
14
17 7
4 53 12
13 11
8
AVL Tree Example:
• Now insert 8
14
17 7
4 53 11
12 8
13
AVL Tree Example:
• Now the AVL tree is balanced.
14
17
7
4
53
11
12
8 13
AVL Tree Example:
• Now remove 53
14
17
7
4
53
11
12
8 13
AVL Tree Example:
• Now remove 53, unbalanced
14
17
7
4
11
12
8 13
AVL Tree Example:
• Balanced! Remove 11
14
17
7
4
11
12 8
13
AVL Tree Example:
• Remove 11, replace it with the largest in its left branch
14
17
7
4
8
12
13
AVL Tree Example:
• Remove 8, unbalanced
14
17
4
7
12
13
AVL Tree Example:
• Remove 8, unbalanced
14
17
4
7
12
13
AVL Tree Example:
• Balanced!!
14
17 4
7
12
13
In Class Exercises
• Build an AVL tree with the following values:
15, 20, 24, 10, 13, 7, 30, 36, 25
15
15, 20, 24, 10, 13, 7, 30, 36, 25
20
24
15
20
24
10
13
15
20
24
13
10
13
20
24
15 10
13
20
24
15 10
15, 20, 24, 10, 13, 7, 30, 36, 25
7
13
20
24 15
10
7
30
36 13
20
30 15
10
7
36 24
13
20
30 15
10
7
36 24
15, 20, 24, 10, 13, 7, 30, 36, 25
25
13
20
30
15
10
7
36
24
25 13
24
36
20
10
7
25
30
15
Remove 24 and 20 from the AVL tree.
13
24
36
20
10
7
25
30
15
13
20
36
15
10
7
25
30
13
15
36
10
7
25
30
13
30
36
10
7
25
15
Question 2 (a) Insert the following sequence of elements into an AVL tree, starting with an empty
tree: 10, 20, 15, 25, 30, 16, 18, 19.
(b) Delete 30 in the AVL tree that you got.
Solution: (a) Red dashed line signifies first part of double rotate action.
(b).
10
25 15
30
20
18
16 19 10
25
15
20
18
16
19 10 25
15 20
18
16 19
20
10
15
15
10
20
10 20
15
25
30
10 25
15
30 20
16
10
25
15
30
20
16 10
25 15
30
20
16
18
19
10
25 15
30
20
18
16 19