Science in China Series A: Mathematics

, Volume 51, Issue 1, pp 101–114 | Cite as

Limiting theorems for the nodes in binary search trees

  • Liu Jie Email author
  • Su Chun
  • Chen Yu


We consider three random variables X n , Y n and Z n , which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random variables are got, and it is also shown that X n , Y n and Z n are all asymptotically normal as n → ∞ by applying the contraction method.


binary search tree nodes law of large numbers contraction method limiting distribution 


60F05 05C80 


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© Science in China Press 2008

Authors and Affiliations

  1. 1.Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefeiChina

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