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

State in brief about assertion, State  in brief about assertion Asser...

State  in brief about assertion Assertion: A statement which should be true at a designated point in a program.

Define midsquare method, Midsquare Method :- this operates in 2 steps. In t...

Midsquare Method :- this operates in 2 steps. In the first step the square of the key value K is taken. In the 2nd step, the hash value is obtained by deleting digits from ends of

Undirected graph and adjacency matrix, Q. Consider the specification writte...

Q. Consider the specification written below of a graph G V(G ) = {1,2,3,4} E(G ) = {(1,2), (1,3), (3,3), (3,4), (4,1)} (i)        Draw the undirected graph. (

State the painter algorithm, Painter's Algorithm As the name suggests, ...

Painter's Algorithm As the name suggests, the algorithm follows the standard practice of a painter, who  would paint the background (such as a backdrop) first, then the major d

A tree having ''m'' nodes has (m-1) branches. prove., Q. Prove the hypothes...

Q. Prove the hypothesis that "A tree having 'm' nodes has exactly (m-1) branches".      Ans: A tree having m number of nodes has exactly (m-1) branches Proof: A root

Determine the critical path and the expected completion, The information in...

The information in the table below is available for a large fund-raising project. a. Determine the critical path and the expected completion time of the project. b. Plot the total

Cache simulator, how to design a cache simulator with 4-way set associative...

how to design a cache simulator with 4-way set associative cache

Explain in detail about the ruby arrays, Explain in detail about the Ruby a...

Explain in detail about the Ruby arrays Ruby arrays have many interesting and powerful methods. Besides indexing operations which go well beyond those discussed above, arrays h

Create a binary tree , Create a class "box" that will contain a random inte...

Create a class "box" that will contain a random integer value v such that O

Create algorithm for similarities between documents, Here is a diagram show...

Here is a diagram showing similarities between documents; this is an actual set of physics lab assignments from a large university. Each node (square) in the graph is a doc

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