Self-Balancing Trees Search: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Self-Balancing Trees Search - Time.png|1000px]] | [[File:Self-Balancing Trees Search - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Self-Balancing Trees Search - Space.png|1000px]] | [[File:Self-Balancing Trees Search - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Self-Balancing Trees Search - Pareto Frontier.png|1000px]] | [[File:Self-Balancing Trees Search - Pareto Frontier.png|1000px]] | ||
Revision as of 13:05, 15 February 2023
Description
Search for a given element within a self-balancing tree.
Parameters
n: size of tree
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Hopcroft 2-3 Tree | 1970 | $O(logn)$ | $O({1})$ | Exact | Deterministic | |
| Guibas, Sedgewick Red-Black Tree | 1972 | $O(logn)$ | $O({1})$ | Exact | Deterministic | Time |
| AVL Tree | 1962 | $O(logn)$ | $O({1})$ | Exact | Deterministic | |
| Tarjan Splay Tree | 1985 | $O(n)$ | $O({1})$ | Exact | Deterministic | |
| Bayer, McCreight B-Tree | 1970 | $O(b*log(n)$/log(b))? | $O({1})$ | Exact | Deterministic | |
| Scapegoat Tree | 1989 | $O(nlogn)$ | $O({1})$? | Exact | Deterministic | Time |
| Treap | 1989 | $O(n)$ | $O({1})$? | Exact | Randomized | Time |
| Tango Tree | 2004 | $O((k+{1})$log(log(n))) | Exact | Deterministic | Time |
Time Complexity Graph
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Space Complexity Graph
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Pareto Frontier Improvements Graph
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