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A binary tree is a special tree where each non-leaf node can have atmost two child nodes. Most important types of trees which are used to model yes/no, on/off, higher/lower, i.e., binary decisions are binary trees.
Recursive Definition: A binary tree is either empty or a node that has left and right sub-trees that are binary trees. Empty trees are represented as boxes (but we will almost always omit the boxes).
In a formal way, we can described binary tree as a finite set of nodes which is either empty or partitioned in to sets of T0, Tl, Tr , where T0 is the root and Tl and Tr are left and right binary trees, respectively.
Properties of a binary tree are following
N = 20 + 21 + 22 + .......+ 2d = 2d+1 - 1
A set s is conveniently shown in a computer store by its characteristic function C(s). This is an array of logical numbers whose ith element has the meaning "i is present in s". As
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