Almost sure asymptotics for the random binary search tree
نویسنده
چکیده
Consider the complete rooted binary tree T. We construct a sequence Tn, n = 1, 2, . . . of subtrees of T recursively as follows. T1 consists only of the root. Given Tn, we choose a leaf u uniformly at random from the set of all leaves of Tn and add its two children to the tree to create Tn+1. Thus Tn+1 consists of Tn and the children u1, u2 of u, and contains in total 2n+ 1 nodes, including n+ 1 leaves. We call this sequence of trees (Tn)n≥1 the binary search tree.
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