Degree of node, Data Structure & Algorithms

Assignment Help:

Q. The degree of a node is defined as the number of children it has. Shear show that in any binary tree, the total number of leaves is one more than the number of nodes of degree 2

Ans:

Let n be the total number of nodes of degree 2 in a binary tree T. We have to  show that the number of leaves in T is n+1. Let us prove it by induction technique.

For n=1, the result is certain that the leaves are two i.e. 1+1.

Let the formulae be true for n=k, i.e. if there are n nodes of degree 2 in T then T has k+1 leaves of it.

If we add the two children to one of the leaf node then, the number nodes with degree two will be k+1 and number of leaf node will be (k+1)-1+2 = (k+1)+1. Hence we can conclude by induction method that if a binary tree t has n nodes of degree 2 It then it has n+1 leaves.

 


Related Discussions:- Degree of node

Find the complexity of an algorithm, Q.1 What is an algorithm? What are the...

Q.1 What is an algorithm? What are the characteristics of a good algorithm? Q.2 How do you find the complexity of an algorithm? What is the relation between the time and space c

Design a framework of a genetic algorithm, You have to design a framework o...

You have to design a framework of a Genetic Algorithm (GA) with basic functionality. The basic functionality includes representation, recombination operators, tness function and se

Non-recursive implementation of preorder traversal, For preorder traversal,...

For preorder traversal, in the worst case, the stack will rise to size n/2, where n refer to number of nodes in the tree. Another method of traversing binary tree non-recursively t

Logical database design, 1. For the ER diagram you created in assignment, t...

1. For the ER diagram you created in assignment, the artefact of the conceptual database design, map the ER model into the relational model according to how it was designed in the

Context sensitive f1 help on a field, In what ways we can get the context s...

In what ways we can get the context sensitive F1 help on a field?' Data element documentation. Data element additional text in screen painter. Using the process on help r

Flow chart, that will determine the volume of the sphere or the volume of c...

that will determine the volume of the sphere or the volume of cone or volume of pyramid depending on the choice of the user

Progrrame, how to write a code for for a company , for calculate the salary...

how to write a code for for a company , for calculate the salary pay

Disadvantages of the lifo costing method, The disadvantages or limitations ...

The disadvantages or limitations of the last in first out costing method are: The election of last in first out for income tax purposes is binding for all subsequent yea

Algorithm for linear search, Here,  m represents the unordered array of ele...

Here,  m represents the unordered array of elements n  represents number of elements in the array and el  represents the value to be searched in the list Sep 1: [Initialize]

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd