array-based representation of binary tree an alternative representation of binary tree is based on way of numbering the positions of for every position of let (pbe the integer defined as follows if is the root of then ( if is the left child of position qthen ( ( if is the right child of position qthen ( ( the numbering function is known as level numbering of the positions in binary tree for it numbers the positions on each level of in increasing order from left to right (see figure note well that the level numbering is based on potential positions within the treenot actual positions of given treeso they are not necessarily consecutive for examplein figure ( )there are no nodes with level numbering or because the node with level numbering has no children ( ( figure binary tree level numbering(ageneral scheme(ban example