extendable array with initial length one the total time to perform series of push operations in sstarting from being empty is (njustificationlet us assume that one cyber-dollar is enough to pay for the execution of each push operation in sexcluding the time spent for growing the array alsolet us assume that growing the array from size to size requires cyber-dollars for the time spent copying the elements we shall charge each push operation three cyber-dollars thuswe overcharge each push operation that does not cause an overflow by two cyber-dollars think of the two cyber-dollars profited in an insertion that does not grow the array as being "storedat the element inserted an overflow occurs when the array list has elementsfor some integer > and the size of the array used by the array list representing is thusdoubling the size of the array will require cyber-dollars fortunatelythese cyber-dollars can be found at the elements stored in cells - through (see figure note that the previous overflow occurred when the number of elements became larger than - for the first timeand thus the cyber-dollars stored in cells - through were not previously spent thereforewe have valid amortization scheme in which each operation is charged three cyber-dollars and all the computing time is paid for that iswe can pay for the execution of push operations using cyber-dollars in other wordsthe amortized running time of each push operation is ( )hencethe total running time of push operations is (nfigure illustration of series of push operations on an array list(aan -cell array is fullwith two cyber-dollars "storedat cells through (ba push operation causes an overflow and doubling of capacity copying the eight old elements to the new array is paid for by the cyber-dollars already stored in the table inserting the new element is paid for by one of the cyber-dollars charged to the push operationand the two cyber-dollars profited are stored at cell