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

Algorithm to merge two sorted arrays with third array, Q. Write down an alg...

Q. Write down an algorithm to merge the two sorted arrays into the third array. Do  not perform the sort function in the third array.                           Ans: void m

Data type, Q. Define the terms data type and abstract data type. Comment up...

Q. Define the terms data type and abstract data type. Comment upon the significance of both these.   Ans: We determine the total amount of memory to reserve by determining

Last in first out method, This method is the reverse of FIFO and assumes th...

This method is the reverse of FIFO and assumes that each issue of stock is made from latest items received in the enterprises .Thus if the last lot to be received is not sufficient

Applications of b-trees, A database is a collection of data organized in a ...

A database is a collection of data organized in a manner that facilitates updation, retrieval and management of the data. Searching an unindexed database having n keys will have a

Search on a heap file, Consider the file " search_2013 ". This is a text fi...

Consider the file " search_2013 ". This is a text file containingsearch key values; each entry is a particular ID (in the schema given above). You are tosimulate searching over a h

State the example of pre- and post-conditions, State the example of pre- an...

State the example of pre- and post-conditions Suppose that function f(x) should have a non-zero argument and return a positive value. We can document these pre- and post-condit

In order post order, illlustraate the construction of tree of a binary tree...

illlustraate the construction of tree of a binary tree given its in order and post order transversal

Binary search, Explain binary search with an example

Explain binary search with an example

State the symbols of abstract data type operation, Symbols of ADT oepration...

Symbols of ADT oeprations All Symbol ADT operations are implemented in Symbol class, except toSymbol(), which is implemented in classes (like String) which can generate a Symb

LINKED LIST, HOW LINKED LIST HEADER WORKS? HOW TO INSERT AND DELETE ELEMENT...

HOW LINKED LIST HEADER WORKS? HOW TO INSERT AND DELETE ELEMENTS IN LINKED LIST?

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