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

Doubly linked list having n nodes, The time required to delete a node x fro...

The time required to delete a node x from a doubly linked list having n nodes is O (1)

Write a program to create a heap file, Write a program to create a heap fil...

Write a program to create a heap file that holds the records in the file " data_2013 " The source records are variablelength.However, the heap file should hold fixed-length reco

Two - way merge sort, Merge sort is also one of the 'divide & conquer' clas...

Merge sort is also one of the 'divide & conquer' classes of algorithms. The fundamental idea in it is to split the list in a number of sublists, sort each of these sublists & merge

Efficiency of linear search, Efficiency of Linear Search How much numbe...

Efficiency of Linear Search How much number of comparisons is there in this search in searching for a particular element? The number of comparisons based upon where the reco

All pairs shortest paths, N = number of rows of the graph D[i[j] = C[i][...

N = number of rows of the graph D[i[j] = C[i][j] For k from 1 to n Do for i = 1 to n Do for j = 1 to n D[i[j]= minimum( d ij (k-1) ,d ik (k-1) +d kj (k-1)

Sorting, Sort the following array of elements using quick sort: 3, 1, 4, 1,...

Sort the following array of elements using quick sort: 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8.

Data structure, Ask question #Minimum 1Mark each of the following statement...

Ask question #Minimum 1Mark each of the following statements as valid or invalid. If a statement is invalid, explain why. a. current ¼ list; b. temp->link->link ¼ NULL; c. trail->l

Pest control program, PART- Pest Control Program Prepare a Pest Contro...

PART- Pest Control Program Prepare a Pest Control Program for the facility that will address the management of Rodents, Insects and Birds. Your Pest Control Program should

Representation of arrays?, A representation of an array structure is a mapp...

A representation of an array structure is a mapping of the (abstract) array with elements of type T onto the store which is an array with elements of type BYTE. The array could be

Linked list implementation of a dequeue, Double ended queues are implemente...

Double ended queues are implemented along doubly linked lists. A doubly link list can traverse in both of the directions as it contain two pointers namely left pointers and righ

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