AVL Trees (Adelson – Velskii – Landis) AVL tree: 20 30 187 1625 5 1719.
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AVL Trees (Adelson – Velskii – Landis) AVL tree: 20 30 18 7 16 25 5 17 19
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Transcript of AVL Trees (Adelson – Velskii – Landis) AVL tree: 20 30 187 1625 5 1719.
AVL Trees(Adelson – Velskii – Landis)
AVL tree:20
30187
16 25
5 17 19
AVL Trees
Not AVL tree:
27
20
30187
16 25
5 17 19
AVL Tree Rotations
Single rotations: insert 14, 15, 16, 13, 12, 11, 10
14
15
• First insert 14 and 15:
• Now insert 16.
AVL Tree Rotations
Single rotations:
14
15
• Inserting 16 causes AVL violation:
• Need to rotate.
16
AVL Tree Rotations
Single rotations:
14
15
• Inserting 16 causes AVL violation:
• Need to rotate.
16
AVL Tree Rotations
Single rotations:
14
15
• Rotation type:
16
AVL Tree Rotations
Single rotations:
14
15
• Rotation restores AVL balance:
16
AVL Tree Rotations
Single rotations:
14
15
16
• Now insert 13 and 12:
13
12
• AVL violation - need to rotate.
AVL Tree Rotations
Single rotations:
• Rotation type:
14
15
16
13
12
AVL Tree Rotations
Single rotations:
13
15
16
• Now insert 11.
12 14
AVL Tree Rotations
Single rotations:
13
15
16
• AVL violation – need to rotate
12 14
11
AVL Tree Rotations
Single rotations:
• Rotation type:
13
15
16
12 14
11
AVL Tree Rotations
Single rotations:
13
15
16
12
1411
• Now insert 10.
AVL Tree Rotations
Single rotations:
13
15
16
12
1411
10
• AVL violation – need to rotate
AVL Tree Rotations
Single rotations:
13
15
16
12
1411
10
• Rotation type:
AVL Tree Rotations
Single rotations:
13
15
16
11
1410 12
• AVL balance restored.
AVL Tree Rotations
Double rotations: insert 1, 2, 3, 4, 5, 7, 6, 9, 8
• First insert 1 and 2:13
15
16
11
1410 12
AVL Tree RotationsDouble rotations:
13
15
16
11
1410
• AVL violation - rotate
1
2
12
AVL Tree RotationsDouble rotations:
13
15
16
11
1410
• Rotation type:
1
2
12
AVL Tree Rotations
Double rotations:
• Now insert 3.
• AVL balance restored:
1 10
13
15
16
11
142 12
AVL Tree Rotations
Double rotations:
• AVL violation – rotate:
1 10
13
15
16
11
142 12
3
AVL Tree Rotations
Double rotations:
• Rotation type:
1 10
13
15
16
11
142 12
3
AVL Tree Rotations
Double rotations:
• AVL balance restored:
1 3
13
15
16
10
142 11
12
• Now insert 4.
AVL Tree Rotations
Double rotations:
• AVL violation - rotate
1 3
13
15
16
10
142 11
12
4
AVL Tree Rotations
Double rotations:
• Rotation type:
1 3
13
15
16
10
142 11
12
4
AVL Tree Rotations
Double rotations:
10
13
15
2
111 3
4 12 14 16
• Now insert 5.
AVL Tree Rotations
Double rotations:
10
13
15
2
111 3
4 12 14 16
• AVL violation – rotate.
5
AVL Tree RotationsSingle rotations:
10
13
15
2
111 3
4 12 14 16
5
• Rotation type:
AVL Tree RotationsSingle rotations:
10
13
15
2
111 4
5 12 14 163
• AVL balance restored:
• Now insert 7.
AVL Tree RotationsSingle rotations:
10
13
15
2
111 4
5 12 14 163
• AVL violation – rotate.
7
AVL Tree RotationsSingle rotations:
10
13
15
2
111 4
5 12 14 163
7
• Rotation type:
AVL Tree RotationsDouble rotations:
10
13
15
4
112 5
7 12 14 1631
• AVL balance restored.
• Now insert 6.
AVL Tree RotationsDouble rotations:
10
13
15
4
112 5
7 12 14 1631
• AVL violation - rotate.
6
AVL Tree RotationsDouble rotations:
10
13
15
4
112 5
7 12 14 1631
• Rotation type:
6
AVL Tree RotationsDouble rotations:
10
13
15
4
112 6
712 14 16
31
• AVL balance restored.
• Now insert 9 and 8.
5
AVL Tree RotationsDouble rotations:
10
13
15
4
112 6
712 14 16
31
• AVL violation - rotate.
9
8
5
AVL Tree RotationsDouble rotations:
10
13
15
4
112 6
712 14 16
31
• Rotation type:
9
8
5
AVL Tree RotationsFinal tree:
10
13
15
4
112 6
812 14 16
31
• Tree is almost perfectly balanced
5
97
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