| 234-Tree Analysis |
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| | Time
for insert or get is proportional to trees height |
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| | Let N
be the number of nodes, n be the number of items, and h |
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| be
the height |
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| | Define
h so that a tree consisting of a single node is height 0 |
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| | Its easy to see 1+2+4+
+2h £ N £
1+4+16+
+4h |
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| | Its
also easy to see N £ n £ 3N |
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| | Using the above, we have n ³ 1+2+4+
+2h =
2h+1-1 |
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| | Rewriting,
we have h £ log(n+1) - 1 or h = O(log n) |
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| | Thus,
Dictionary operations on 234-trees take time O(log n) in |
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| the
worst case |
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| CS409 - Spring
2000 |
| 10 |