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

Queue, algorithm for insertion in a queue using pointers

algorithm for insertion in a queue using pointers

What is a height balanced tree, What is a height balanced tree? Height Ba...

What is a height balanced tree? Height Balanced Tree (AVL Tree) An AVL tree is a binary search tree in which the height of the left and right subtree of the root vary by at most

Sparse matrix, How sparse matrix stored in the memory of a computer?

How sparse matrix stored in the memory of a computer?

Asymptotic analysis, Asymptotic Analysis Asymptotic analysis is dependi...

Asymptotic Analysis Asymptotic analysis is depending on the idea that as the problem size grows, the complexity can be defined as a simple proportionality to some known functio

A linear list of elements in which deletion can be done, A linear list of e...

A linear list of elements in which deletion can be done from one end (front) and insertion can take place only at the other end (rear) is called as a   Queue.

Test whether a binary tree is a binary search tree, Q. Write down an algori...

Q. Write down an algorithm to test whether a Binary Tree is a Binary Search Tree.              A n s . The algorithm to check whether a Binary tree is as Binary Search

Define different types of sparse matrix, Q1. Define a sparse matrix. Explai...

Q1. Define a sparse matrix. Explain different types of sparse matrices? Evaluate the method to calculate address of any element a jk of a matrix stored in memory. Q2. A linear

Help with Assignment, Need help with Data Structures assignment requiring C...

Need help with Data Structures assignment requiring C++ program

Memory allocation strategies, Q. Explain the various memory allocation stra...

Q. Explain the various memory allocation strategies.                                                            Ans. M e m ory Allocation Strategies are given as follow

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