Optimal Binary Search Trees
ثبت نشده
چکیده
An optimal binary search tree is a binary search tree for which the nodes are arranged on levels such that the tree cost is minimum. For the purpose of a better presentation of optimal binary search trees, we will consider “extended binary search trees”, which have the keys stored at their internal nodes. Suppose “n” keys k1, k2, ... , k n are stored at the internal nodes of a binary search tree. It is assumed that the keys are given in sorted order, so that k1< k2 < ... < kn. An extended binary search tree is obtained from the binary search tree by adding successor nodes to each of its terminal nodes as indicated in the following figure by squares:
منابع مشابه
Profile and Height of Random Binary Search Trees
The purpose of this article is to survey recent results on distributional properties of random binary search trees. In particular we consider the profile and the height.
متن کاملOn Optimal Binary Search Trees
We present a new linear time heuristic for constructing binary search trees. The analysis of the algorithm, by establishing an upper bound on the cost of the produced binary search trees, permits to derive a limitation on the cost of optimal binary search trees. The obtained upper bound improve on previous results.
متن کاملNew Ways to Construct Binary Search Trees
We give linear-time algorithms for re-ordering and heightrestricting a binary search tree with only a small increase in cost, constructing a nearly optimal binary search tree given the rank by probability of each possible outcome, and height-restricting an optimal binary search tree when the increase in cost is restricted. Whereas most algorithms for constructing good binary search trees need t...
متن کاملP´olya Urn Models and Connections to Random Trees: A Review
This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...
متن کاملSequential Optimization of Binary Search Trees for Multiple Cost Functions
In this paper, we present a methodology to model the optimal binary search tree problem as a directed acyclic graph to extract all possible optimal solutions. We provide a mechanism to find optimal binary search trees relative to different types of cost functions, sequentially. We prove that for a set of n keys our optimization procedure makes O(n) arithmetic operations per cost function such a...
متن کامل