Restructuring binary search trees revisited

Binary search trees are a fundamental data structure. There are two complexity metrics commonly associated with them: the maximum number of comparisons made during a search and the expected number of comparisons made during a search. Minimizing these metrics, separately or together, has been extensively studied. The difficulty of doing this depends on how much information is given. There are 2n+ 1 possible outcomes of a search in a binary search tree on n keys: the search target could be less than the smallest key; for each key, the search target could equal that key; for each consecutive pair of keys, the search target could be strictly between them; or the search target could be greater than the largest key. For a fixed probability distribution P over these outcomes, the cost of a binary search tree is the expected number of comparisons made during a search. In this paper we show how, given one binary search tree T , we can construct another binary search tree