Self-Balancing Trees Search: Difference between revisions
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== Parameters == | == Parameters == | ||
n: size of tree | $n$: size of tree | ||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Hopcroft 2-3 Tree ( Self-Balancing Trees Search)|Hopcroft 2-3 Tree]] || 1970 || $O( | | [[Hopcroft 2-3 Tree ( Self-Balancing Trees Search)|Hopcroft 2-3 Tree]] || 1970 || $O(\log n)$ || $O({1})$ || Exact || Deterministic || | ||
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| [[Guibas, Sedgewick Red-Black Tree ( Self-Balancing Trees Search)|Guibas, Sedgewick Red-Black Tree]] || 1972 || $O( | | [[Guibas, Sedgewick Red-Black Tree ( Self-Balancing Trees Search)|Guibas, Sedgewick Red-Black Tree]] || 1972 || $O(\log n)$ || $O({1})$ || Exact || Deterministic || [https://ieeexplore-ieee-org.ezproxy.canberra.edu.au/document/4567957 Time] | ||
|- | |- | ||
| [[AVL Tree ( Self-Balancing Trees Search)|AVL Tree]] || 1962 || $O(logn)$ || $O({1})$ || Exact || Deterministic || | | [[AVL Tree ( Self-Balancing Trees Search)|AVL Tree]] || 1962 || $O(logn)$ || $O({1})$ || Exact || Deterministic || | ||
Revision as of 08:24, 10 April 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 | $O(\log n)$ | $O({1})$ | Exact | Deterministic | |
| Guibas, Sedgewick Red-Black Tree | 1972 | $O(\log n)$ | $O({1})$ | 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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Time-Space Tradeoff
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