Refer to following Exercise for the definition of a full binary tree.Exercise : In Example 3.22, we gave a recursive definition of a binary tree. Suppose we modify this definition by deleting part B1, so that an empty tree is not a binary tree. A tree satisfying this revised definition is called a full binary tree. now please answer the following solutionspile.com

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Refer to following Exercise for the definition of a full binary tree.

Exercise : In Example 3.22, we gave a recursive definition of a binary tree. Suppose we modify this definition by deleting part B1, so that an empty tree is not a binary tree. A tree satisfying this revised definition is called a full binary tree.

$Consider the recursive definition of full binary tree as, $ B_{1} \cdot $ The empty tree is a binary tree. $ B_{2} $. A s$

now please answer the following questions:

(a) Use structural induction to prove that a full binary tree has an odd number of nodes.

(b) Prove that a full binary tree has an even number of edges.

Consider the recursive definition of full binary tree as,

B_{1} ?

The empty tree is a binary tree.

B_{2}

. A single vertex is a binary tree and in this case, the vertex is the root of the tree.

R

. If

T_{1}

and

T_{2}

are binary trees with roots

r_{1}

and

r_{2}

respectively, then the following tree is a binary tree with root

r

. Modify the definition by deleting part

^{B_{1}}

, that is an empty tree is not a binary tree. A tree that satisfies the modified definition is called a full binary tree. (a) An example of a full binary tree with five nodes and root

r

is shown below.

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