We analyze weighted depths of nodes with given labels, the last inserted node, nodes ordered as visited by the depth first search process, the weighted path length and the weighted Wiener index in a random binary search tree. We establish three regimes of nodes depending on whether the second...
摘要: Let Hn be the height of a random binary search tree on n nodes. We show that there exist constants α = 4.311… and β = 1.953… such that E(Hn) = αln n − βln ln n + O(1), We also show that Var(Hn) = O(1).关键词:...
相对简单很多67但是考虑到要计算AVL,只好重编一个二叉排序树89*/10#include<iostream>11#include<fstream>12#include<string>13#include<iomanip>14usingnamespacestd;1516typedefstructBinary_Tree_Node17{18stringdata;19Binary_Tree_Node *left_child,*right_child;20}BTN;2122classBinary_Sort_Tree23...
p-order statistics a Gaussian limit law. Forp = 1 this gives the well-known result that the depth of a randomlyselected node in a random binary search tree converges in law to theNormal distribution.1. Introduction.in random search trees, respectively, random recursive trees were studied.It ...
Under certain conditions, sums of functions of subtrees of a random binary search tree are asymptotically normal. We show how Stein's method can be applied to study these random trees, and survey methods for obtaining limit laws for such functions of subtrees. DOI: 10.1142/9789812567673_0016 ...
A random hyperplane search tree is a binary space partition tree obtained by recursive application of random hyperplane splits. We investigate the structural distributions of such random trees with a particular focus on the growth with d. A blessing of dimensionality arises--as d increases, random...
We prove convergence in distribution for the profile (the number of nodes at each level), normalized by its mean, of random recursive trees when the limit ratio α of the level and the logarithm of tree size lies in [0,e). Convergence of all moments is shown to hold only for α∈ [...
This work is a generalization of our earlier results for the random binary search tree in Holmgren (2010), which is one specific case of split trees. Other important examples of split trees include m-ary search trees, quad trees, medians of (2k + 1)-trees, simplex trees, tries, and ...
the expected height of the hyperplane tree is not worse than that of the k-d tree or the ordinary one-dimensional random binary search tree, and that, for any fixed d ≥ 3, the expected height improves over that of the standard random binary search tree by an asymptotic factor strictly ...
Roberts, M.I.: Almost sure asymptotics for the random binary search tree. arXiv:1002.3896 [math.PR] (2010) Ruelle, D.: A mathematical reformulation of Derrida’s REM and GREM. Commun. Math. Phys. 108, 225–239 (1987) Article MathSciNet ADS MATH Google Scholar Ruzmaikina, A., ...