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Randomly balanced binary trees


A procedure to attach a new element to a binary tree at a predefined level is introduced; this insertion algorithm is performed in timeO (ln n), maintains all the properties of binary trees and can be seen as a generalization of the well known rotation technique. If the elements are inserted in the tree according to suitable distribution functions of the levels, the tree can be kept «balanced» even if the elements arrive in their proper order. Empirical evidence is given that the average searching time is of orderO (ln n) in this latter case. Finally, a brief comparison with existing methods is presented.

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Sprugnoli, R. Randomly balanced binary trees. Calcolo 17, 99–117 (1980).

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  • Binary Tree
  • Balance Tree
  • Binary Search Tree
  • Extra Space
  • Proper Order