AVL Tree – - WordPress.com
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AVL Tree – A BST where height of two subtrees differs at most one. Permitted balance factors for any node are 0,1 and -1. Balance factor of any node can be computed by subtracting the height of right subtree from height of left subtree. • Insertion, deletion and searching can be performed in O(logn). • Height <= 1.44 * (log n) where is n is number of nodes
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Transcript of AVL Tree – - WordPress.com
AVL Tree –
A BST where height of two subtrees differs at most one. Permitted balance factors for any node are 0,1 and -1. Balance factor of any node can be computed by subtracting the height of right subtree from height of left subtree.
• Insertion, deletion and searching can be performed in O(logn).• Height <= 1.44 * (log n) where is n is number of nodes
AVL Tree Example:
• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree
14
1711
7 53
4
AVL Tree Example:
• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree
14
177
4 5311
13
AVL Tree Example:
• Now insert 12
14
177
4 5311
13
12
AVL Tree Example:
• Now insert 12
14
177
4 5311
12
13
AVL Tree Example:
• Now the AVL tree is balanced.
14
177
4 5312
1311
AVL Tree Example:
• Now insert 8
14
177
4 5312
1311
8
AVL Tree Example:
• Now insert 8
14
177
4 5311
128
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
128
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
174
7
12
13
• 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
1510
13
20
24
1510
15, 20, 24, 10, 13, 7, 30, 36, 25
7
13
20
2415
10
7
30
3613
20
3015
10
7
3624
13
20
3015
10
7
3624
15, 20, 24, 10, 13, 7, 30, 36, 25
25
13
20
30
15
10
7
36
24
2513
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
