On the Generation of Random Binary Search Trees

We consider the computer generation of random binary search trees with n nodes for the standard random permutation model. The algorithms discussed here output the number of external nodes at each level, but not the shape of the tree. This is important, for example, when one wishes to simulate the height of the binary search tree. Various paradigms are proposed, including depth-first search with pruning, incremental methods in which the tree grows with random-sized jumps, and a tree growing procedure gleaned from birth-and-death processes. The last method takes $O(\log^{4} n)$ expected time.