Binary tree and binarytree parts, Data Structure & Algorithms

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Q. What do you understand by the term Binary Tree? What is the maximum number of nodes which are possible in a Binary Tree of depth d. Explain the terms given below with respect to the Binary trees
1)Strictly Binary Tree       
2) Complete Binary Tree
3) Almost Complete Binary Tree                                                               

Ans:

A binary tree is a tree in which no nodes can posses' more than two children.

Figure drawn below shows us that the binary tree consists of the root and two subtrees, Tl and Tr, both of which could possibly be empty.

1962_Binary Tree.png

 

The highest numbers of nodes a binary tree of depth d can have is 2 d+1-1.

(i)      Strictly Binary Tree:- If every non leaf node in binary tree has neither the left tree nor the right tree empty subtrees , then the tree is known as a strictly binary tree.

(ii)     Complete Binary Tree:- The complete binary tree of depth d is that strictly binary tree whose all the leaves are at level D.

(iii)     Almost  Complete  Binary  Tree:- The  binary tree  of  depth  d  is  an  almost complete binary tree if and only if:
1.Any node end at level less than d-1 has two children.
2. for any node nd in the tree with

(iv)    a right descendant at the level d, nd should have a left child and every descendant of the nd is either a leaf at level d or has two children.


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