Abstract: A virtual lab is generated for a underlying learning objective defined by a lab instructor. The virtual lab is decomposed into multiple lab steps. Each lab step defines a portion of the underlying learning objective that can be performed independently. Each lab step includes pedagogical information for teaching a learner the portion of the underlying learning objective and information for specifying a portion of the underlying system that will execute the lab step. A first portion of the underlying system is caused to execute a first lab step. This allows the learner to perform the portion of the underlying learning objective defined in the first lab step. An event generated by the learner's performance of the first lab step is received. In response, a specific pedagogical procedure that is dictated by the event is caused to be performed.

Abstract: A computer implemented method for creating a balanced binary tree is provided, in which a list of elements is successively divided into left side and right side groupings. The median of each left side grouping is placed in the tree as a descendent node of the previous median until the list can no longer be divided. The method then involves walking back up the tree to find right-side medians and inserting them as right side descendent nodes into the binary tree. Whenever there is a choice between breaking down a left side grouping and breaking down a right side grouping, the left side grouping takes priority. The method may also be implemented so that right side groupings take priority.