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

Pseudocodes, how to write a pseudo code using Kramer''s rule

how to write a pseudo code using Kramer''s rule

Implementation of queue, For a queue a physical analogy is a line at bookin...

For a queue a physical analogy is a line at booking counter. At booking counter, customers go to the rear (end) of the line & customers are attended to several services from the fr

What do you mean by hash clash, What do you mean by hash clash? Hashing...

What do you mean by hash clash? Hashing is not perfect. Occasionally, a collision occurs when two different keys hash into the same hash value and are assigned to the same arra

Evaluation of arithmetic expressions, Stacks are often used in evaluation o...

Stacks are often used in evaluation of arithmetic expressions. An arithmetic expression contains operands & operators. Polish notations are evaluated through stacks. Conversions of

Multidimensional array, Q. The system allocates the memory for any of the m...

Q. The system allocates the memory for any of the multidimensional array from a big single dimensional array. Describe two mapping schemes that help us to store the two dimensi

Insertion into a red-black tree, The insertion procedure in a red-black tre...

The insertion procedure in a red-black tree is similar to a binary search tree i.e., the insertion proceeds in a similar manner but after insertion of nodes x into the tree T, we c

Representing sparse matrix in memory using array, Q. What do you understand...

Q. What do you understand by the term sparse matrix? How sparse matrix is stored in the memory of a computer? Write down the function to find out the transpose of a sparse matrix u

High-level and bubble algorithm , 1. Give both a high-level algorithm and a...

1. Give both a high-level algorithm and an implementation (\bubble diagram") of a Turing machine for the language in Exercise 3.8 (b) on page 160. Use the ' notation to show the co

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