all the nodes of the array list has size pm since the element of at index is not associated with any node of alsos will havein generala number of empty elements that do not refer to existing nodes of in factin the worst casen nthe justification of which is left as an exercise ( - in section we will see class of binary treescalled "heapsfor which thusin spite of the worst-case space usagethere are applications for which the array-list representation of binary tree is space efficient stillfor general binary treesthe exponential worst-case space requirement of this representation is prohibitive table summarizes running times of the methods of binary tree implemented with an array list we do not include any tree update methods here table running times for binary tree implemented with an array list we denote the number of nodes of with nand denotes the size of the space usage is ( )which is ( nin the worst case operation