Thus, a perfect binary tree will have the maximum number of nodes for all alternative binary trees of the same height and it will be $2^{h+1}-1$ which we are going to prove next. IV. Array Representation. In any binary tree linked list representation, there is a number of NULL pointers than actual pointers. In the above figure, a queue of size 10 having 3 elements, is shown. Array representation of a complete binary tree. Since the nodes are numbered from I to n, we can use a onedimensional array to store the nodes. This node is called a parent.

A binary tree can be represented using array representation or linked list representation.
A binary tree is made of nodes, where each node contains a "left" reference, a "right" reference, and a data element. The numbering scheme used in Figure 5.11 suggests our first representation of a binary tree in memory. Maximum Number of Nodes in a Binary Tree Programming is very easy. Every node (excluding a root) in a tree is connected by a directed edge from exactly one other node. On the other hand, each node can be connected to arbitrary number of nodes, called children. There are two types of representation of a binary tree: 1. This is the best representation for complete and full binary tree representation. Array representations of binary trees are very memory-efficient, compared with using pointers.

II. The topmost node in the tree is called the root. Perfect Binary Tree → In a perfect binary tree, each leaf is at the same level and all the interior nodes have two children. This representation is very easy to understand. If a node is present at index: i. Node’s left child will be present at index: 2 * i. Node’s right child will be present at index: ( 2 * i ) + 1 Advantages: I. The above figure shows how the memory space is wasted in the array representation of queue. (if the c++ array is used to represent the tree, the zero’th position is left empty.) On a 32-bit machine, suppose you have a 32-bit value and two 32-bit pointers per node in the tree.

It has two type : Array representation * The nodes of tree can stored in array * Can be accessed in sequence one after another * Element counting start from 0 to (n-1) It declaration as follows : int array [n]; Array representation of tree : Array representation of tree 0 1 2 TREE [0] X TREE [1] Y TREE [2] Z X Y Z.

In this representation, the binary tree is stored in the memory, in the form of a linked list where the number of nodes are stored at non-contiguous memory locations and linked together by inheriting parent child relationship like a tree.

The value of the front variable is 5, therefore, we can not reinsert the values in the place of already deleted element before the position of front. When a binary tree is represented using linked list representation, the reference part of the node which doesn't have a child is filled with a NULL pointer. Binary Tree representation . Linked Representation. III.