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

Explain expert system, 1. What is an expert system and where are they need...

1. What is an expert system and where are they needed? 2. What are the major issues involved in building an expert system?

Algorithm for inorder traversals, Step-1: For the current node, verify whet...

Step-1: For the current node, verify whether it contain a left child. If it has, then go to step-2 or else go to step-3 Step-2: Repeat step-1 for left child Step-3: Visit (th

Preorder traversal of a binary tree, Preorder traversal of a binary tree ...

Preorder traversal of a binary tree struct NODE { struct NODE *left; int value;     /* can take any data type */ struct NODE *right; };   preorder(struct N

Procedure of analysis of algorithm, Example 1:  Following are Simple sequen...

Example 1:  Following are Simple sequence of statements Statement 1;  Statement 2; ... ... Statement k; The entire time can be found out through adding the times for

Rules for abstract data type-tree, null(nil) = true                     // ...

null(nil) = true                     // nil refer for empty tree null(fork(e, T, T'))= false   //  e : element , T and T are two sub tree leaf(fork(e, nil, nil)) = true leaf(

Explain the memory function method, Explain the Memory Function method ...

Explain the Memory Function method The Memory Function method seeks to combine strengths of the top  down and bottom-up approaches  to  solving  problems  with  overlapping  su

Deletion of an element from the linked list, A LGORITHM (Deletion of an ele...

A LGORITHM (Deletion of an element from the linked list) Step 1  Begin Step 2  if the list is empty, then element cannot be deleted Step 3  else, if the element to be del

Implementation of stack using arrays, A Stack has an ordered list of elemen...

A Stack has an ordered list of elements & an array is also utilized to store ordered list of elements. Therefore, it would be very simple to manage a stack by using an array. Thoug

BINARY SEARCH, GIVE TRACE OF BINARY SEARCH ALGORITHM BY USING A SUITABLE EX...

GIVE TRACE OF BINARY SEARCH ALGORITHM BY USING A SUITABLE EXAMPLE.

Full binary trees, Full Binary Trees: A binary tree of height h that had 2...

Full Binary Trees: A binary tree of height h that had 2h -1 elements is called a Full Binary Tree. Complete Binary Trees: A binary tree whereby if the height is d, and all of

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