amortized analysis of dynamic arrays primitive operations for an append in this sectionwe perform detailed analysis of the running time of operations on dynamic arrays we use the big-omega notation introduced in section to give an asymptotic lower bound on the running time of an algorithm or step within it the strategy of replacing an array with newlarger array might at first seem slowbecause single append operation may require (ntime to performwhere is the current number of elements in the array howevernotice that by doubling the capacity during an array replacementour new array allows us to add new elements before the array must be replaced again in this waythere are many simple append operations for each expensive one (see figure this fact allows us to show that performing series of operations on an initially empty dynamic array is efficient in terms of its total running time using an algorithmic design pattern called amortizationwe can show that performing sequence of such append operations on dynamic array is actually quite efficient to perform an amortized analysiswe use an accounting technique where we view the computer as coin-operated appliance that requires the payment of one cyber-dollar for constant amount of computing time when an operation is executedwe should have enough cyber-dollars available in our current "bank accountto pay for that operation' running time thusthe total amount of cyberdollars spent for any computation will be proportional to the total time spent on that computation the beauty of using this analysis method is that we can overcharge some operations in order to save up cyber-dollars to pay for others current number of elements figure running times of series of append operations on dynamic array