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

Algorithms, write short note on algorithms

write short note on algorithms

Random searching, write aprogram for random -search to implement if a[i]=x;...

write aprogram for random -search to implement if a[i]=x;then terminate other wise continue the search by picking new randon inex into a

Implementation of circular queues, One of the main problems with the linear...

One of the main problems with the linear queue is the lack of appropriate utilization of space. Assume that the queue can store 100 elements & the complete queue is full. Thus, it

Acyclic graph, Tree is a widely used data structure employed for representi...

Tree is a widely used data structure employed for representing several problems. We studied tree like a special case of acyclic graph. Though, rooted trees are most prominent of al

Linked list implementation of any circular queue, Link list representation ...

Link list representation of a circular queue is more efficient as it employs space more competently, of course with the added cost of storing the pointers. Program 7 gives the link

Sorting, Retrieval of information is made simpler when it is stored into so...

Retrieval of information is made simpler when it is stored into some predefined order. Therefore, Sorting is a very important computer application activity. Several sorting algorit

Data structure arrays, In this unit, we learned the data structure arrays f...

In this unit, we learned the data structure arrays from the application point of view and representation point of view. Two applications that are representation of a sparse matrix

Algorithm, Example of worse case of time

Example of worse case of time

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