II. Since the nodes are numbered from I to n, we can use a onedimensional array to store the nodes. The topmost node in the tree is called the root. This is the best representation for complete and full binary tree representation. The above figure shows how the memory space is wasted in the array representation of queue. 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. IV.

On a 32-bit machine, suppose you have a 32-bit value and two 32-bit pointers per node in the tree. Advantages: I. Linked Representation. 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 There are two types of representation of a binary tree: 1. Binary Tree representation .

In any binary tree linked list representation, there is a number of NULL pointers than actual pointers. 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. III. A binary tree is made of nodes, where each node contains a "left" reference, a "right" reference, and a data element. On the other hand, each node can be connected to arbitrary number of nodes, called children. 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. Every node (excluding a root) in a tree is connected by a directed edge from exactly one other node. A binary tree can be represented using array representation or linked list representation. Array representations of binary trees are very memory-efficient, compared with using pointers. Programming is very easy. In the above figure, a queue of size 10 having 3 elements, is shown. Array representation of a complete binary tree. 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. Array Representation. The numbering scheme used in Figure 5.11 suggests our first representation of a binary tree in memory. 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.

(if the c++ array is used to represent the tree, the zero’th position is left empty.) This node is called a parent. Maximum Number of Nodes in a Binary Tree 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.