figure randomly generated binary search tree it seems only to be theoretical novelty it has been shown that if we alternateinsertions and deletions ( timesthen the trees will have an expected depth of nafter quarter-million random insert/remove pairsthe tree that was somewhat right-heavy in figure looks decidedly unbalanced (average depth in figure we could try to eliminate the problem by randomly choosing between the smallest element in the right subtree and the largest in the left when replacing the deleted element this apparently eliminates the bias and should keep the trees balancedbut nobody has figure binary search tree after ( insert/remove pairs