| Analysis of Random BST |
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| • | Only
the number of items and their order is important |
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| – | Can
restrict our attention to BSTs containing items {1,…, n} |
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| • | We
assume that each item is equally likely to appear |
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| as
the root |
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| • | Define
H(n) º expected height of BST of size n |
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| • | If
item i is the root then expected height is |
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| 1 + max { H(i-1), H(n-i) } |
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| We
average this over all possible i |
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| • | Can
solve the resulting recurrence (by induction) |
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| H(n) = O(log n) |
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| CS409 - Spring
2000 |
| 5 |