Abstract
The purpose of this paper is to settle two conjectures by Flajolet, Gourdon and Martinez (1996). We confirm that in a random binary tree on n nodes, the expected number of different subtrees grows indeed as Θ ( n log n ) . Secondly, if K is the largest integer such that all possible shapes of subtrees of cardinality less than or equal to K occur in a random binary search tree, then we show that K ~ log n log log n in probability.
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