## Array-based representation of a binary tree, Data Structure & Algorithms

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Assume a complete binary tree T with n nodes where each node has an item (value). Label the nodes of the complete binary tree T from top to bottom & from left to right 0, 1, ..., n-1. Relate with T the array A where the ith   entry of A is the item in the node labeled i of T, i = 0, 1, ..., n-1. Table illustrates the array representation of a Binary tree of Figure Given the index i of a node, we can efficiently & easily compute the index of its parent and left & right children:

Index of Parent: (i - 1)/2, Index of Left Child: 2i + 1, Index of Right Child: 2i + 2.

 Node # Item Left child Right child 0 A 1 2 1 B 3 4 2 C -1 -1 3 D 5 6 4 E 7 8 5 G -1 -1 6 H -1 -1 7 I -1 -1 8 J -1 -1 9 ? ? ?

Table: Array Representation of a Binary Tree

First column illustrates index of node, second column contain the item stored into the node & third & fourth columns mention the positions of left & right children

(-1 shows that there is no child to that specific node.)

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