Proper Binary Trees, Their Nodes, Internal Nodes Versus Leaves & More! (Maths for Computer Science)

Описание: In this lecture we introduce binary trees, proper binary trees, with examples. Then, we prove using counting arguments the number of nodes a proper binary tree has, and as a consequence a direct relationship between the internal nodes and leaves in such a tree.

Time Stamps:
0:00 Lecture Begins
1:19 Binary Tree definition
6:43 Proper Binary Tree definition
10:18 Proof using counting arguments that the number of nodes in a proper binary tree is twice the number of internal nodes plus one.
28:21 Proof as a result that the number of internal nodes in a proper binary tree is one less than the number of its leaves.
34:40 Closing

Note: To elaborate on the point I made about proving properties and designing algorithms for proper binary trees. Having zero or two children every time makes cases easier to work with, the recursive nature of the tree is simpler (never having to deal with the case when there is one child), and often algorithms for proper binary trees can be modified so as to operate with binary trees.


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