Discrete random variates with finite support using differential search trees

Differential search trees can be used for selection with replacement and for a form of selection without replacement. We show that they can be extended to many different types of selection, both with and without replacement. In addition, virtually every aspect of a differential search tree can be modified dynamically. We provide algorithms for making these modifications. Virtually all differential search tree algorithms are straightforward and easy to implement, especially with our preferred implementation, which is both simple and efficient. Differential search tree operations are virtually all logarithmic with the exception of building the tree and dynamically adding leaves to the tree, which are both linear.