229 lines
3.0 KiB
Markdown
229 lines
3.0 KiB
Markdown
### Q1
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Explain why we need to maintain a binary search tree in balance such as an AVL tree.
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```
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Only a balanced tree can guarantee search performance of O(logN).
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and, AVL tree’s theoretical search performance is 1.44 log2N. (see lecture notes)
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```
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### Q2
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Build a binary search tree with the following integers being inserted in the order from
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left to right: 72, 48, 35, 80, 60, 85, 75, 21, 9, 28
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```
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72
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/ \
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/ \
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/ \
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/ \
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48 80
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/ \ / \
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/ \ / \
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35 60 75 85
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/
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21
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/ \
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9 28
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```
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### Q3
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With the integers in Q2, show the steps of building an AVL tree. Indicate also the
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balance value of each node and the rotations so required to maintain the tree in
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balance.
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```
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insert 72
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72
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insert 48
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72
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/
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48
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insert 35
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72
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/
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48
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35
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=>Right rotate at 72
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48
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/ \
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35 72
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insert 80
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48
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/ \
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35 72
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\
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80
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insert 60
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48
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35 72
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60 80
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insert 85
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48
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35 72
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/ \
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60 80
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\
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85
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=> Left rotate at 48
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72
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/ \
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/ \
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48 80
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/ \ \
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/ \ 85
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35 60
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insert 75
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72
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48 80
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/ \ / \
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35 60 75 85
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insert 21
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72
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48 80
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35 60 75 85
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/
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21
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insert 9
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72
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48 80
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35 60 75 85
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/
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21
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/
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9
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=> Right rotate at 35
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72
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48 80
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21 60 75 85
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9 35
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insert 28
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72
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/ \
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48 80
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21 60 75 85
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/ \
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9 35
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/
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28
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=> double rotate: left rotate at 21
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72
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48 80
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35 60 75 85
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/
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21
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9 28
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=> double rotate: right ritate at 48
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72
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35 80
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21 48 75 85
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/ \ \
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9 28 60
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```
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### Q4
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Show the steps of deleting the following nodes from the AVL tree in Q3. Indicate also the balance value of each node and the rotations so required to maintain the tree in balance.
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60, 48
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```
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delete 60
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72
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35 80
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21 48 75 85
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/ \
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9 28
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delete 48
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72
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35 80
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/ / \
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21 / \
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/ \ 75 85
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9 28
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=> rotate at 35
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72
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/ \
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/ \
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21 80
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/ \ / \
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9 35 / \
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/ 75 85
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28
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``` |