Answer to Question #120782 in Discrete Mathematics for Roshanthi

Question

1. Discuss two examples on binary trees both quantitatively and qualitatively.

Answer 1

BINARY TREE :Each node can have atmost two children.maximum number of nodes possible at any level i is 2ⁱ. Binary tree play a vital role in a software application.one of the most application of binary

tree is searching algorithm.

Binary tree is a special data structure used for data storage purpose. Binary tree are used to represent a nonlinear data structure.

First example Quantitative binary tree

complete binary tree: A binary tree is a complete binary tree if all levels are completely filled (except possibly the last level and the last level has nodes as left as possible.

Maximum nodes =2^h+1 -1

Minimum nodes =2^h

maximum height=log n

second Example Qualitative binary tree

FULL BINARY TREE: Each node have either 0 or 2 children.Each node will contain exactly two children

except leaf node

number of leaf nodes= number of internal node +1.

maximum nodes=2^h+1 -1

minimum nodes=2^h +1

maximum height =(n-1)/2

Array especially suited for full binary tree