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

The threaded binary tree, By changing the NULL lines in a binary tree to th...

By changing the NULL lines in a binary tree to the special links called threads, it is possible to execute traversal, insertion and deletion without using either a stack or recursi

Multiple Queues in a single dimension array, Implement multiple queues in a...

Implement multiple queues in a single dimensional array. Write algorithms for various queue operations for them.

..#title, whate is meant by the term heuristic

whate is meant by the term heuristic

Multikey file organization, what are the applications of multikey file orga...

what are the applications of multikey file organization?

Branch and Bound method, give some examples of least cost branch and bound ...

give some examples of least cost branch and bound method..

What do you understand by tree traversal, What do you understand by tree tr...

What do you understand by tree traversal? The algorithm walks by the tree data structure and performs some computation at everynode in the tree. This process of walking by the

List various problem solving techniques, List various problem solving techn...

List various problem solving techniques. There are two techniques:- 1.  Top down 2.  Bottom- up

Binary search trees, A Binary Search Tree is binary tree which is either em...

A Binary Search Tree is binary tree which is either empty or a node having a key value, left child & right child. By analyzing the above definition, we notice that BST comes int

Prefix and Postfix Expressions, Q.   Draw the expression tree of the infix ...

Q.   Draw the expression tree of the infix expression written below and then  convert it intoPrefix and Postfix expressions. ((a + b) + c * (d + e) + f )* (g + h )

Perform inorder, QUESTION (a) Construct a binary tree for the following...

QUESTION (a) Construct a binary tree for the following numbers assuming that a number greater than the node (starting from the root) goes to the left else it goes to the right.

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