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In a balanced binary tree, you reduce the search space in half each time you check a node. Without getting into the mathematics check Donald Knuth s The Art of Computer Programming, Volume 3: Sorting and Searching (Addison-Wesley 1998) for more information the maximum number of nodes searched is approximately log2n, where n is the number of nodes in the tree. On average, you ll search log2n/2 nodes. In a list of 100 nodes, you ll end up searching 3.32 nodes on average. In a list of 1,000 nodes, you ll end up checking about 5 nodes on average. As you can see, a binary tree provides a significant performance advantage over a linked list. A binary tree that contained just words may not be that interesting, but imagine that these words were names of great political leaders. Each node might contain a leader s name, biographical information, perhaps a pointer to another data structure containing great speeches. The value, name, or word that determines the order of the tree is said to be the key. You don t always search a tree based on the key. Sometimes, you ll want to step through every node in the tree. For example, suppose your tree contained the name and birth date of each of the presidents of the United States. Suppose also that the tree was built using each president s last name as a key. Now suppose you wanted to compose a list of all presidents born in July. In this case, searching the tree alphabetically won t do you any good. You ll have to search every node in the tree. This is where recursion comes in.

Modi ed with permission from Dumitru D, Amato AA Introduction to myopathies and muscle tissue s reaction to injury In Dumitru D, Amato AA, Swartz MJ (eds) Electrodiagnostic Medicine, 2nd edn Philadelphia: Hanley & Belfus, 2002, pp 1233, Fig 26 7

For this exercise, you ll add the interactivity to be able to play the game again once the game ends In order to play the game again, you need to reset all the variables and objects in the game

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Binary trees and recursion were made for each other. To search a tree recursively, the recursing function has to visit the current node, as well as call itself with each of its two child nodes. The child nodes will do the same thing with themselves and their child nodes. Each part of the recursion stops when a terminal node is encountered. Check out this piece of code:

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