comparative analysis suppose two algorithms solving the same problem are availablean algorithm awhich has running time of ( )and an algorithm bwhich has running time of ( which algorithm is betterwe know that is ( )which implies that algorithm is asymptotically better than algorithm balthough for small value of nb may have lower running time than we can use the big-oh notation to order classes of functions by asymptotic growth rate our seven functions are ordered by increasing growth rate in the following sequencethat isif function (nprecedes function (nin the sequencethen (nis ( ( )) log nnn log nn we illustrate the growth rates of the seven functions in table (see also figure from section log log table selected values of fundamental functions in algorithm analysis we further illustrate the importance of the asymptotic viewpoint in table this table explores the maximum size allowed for an input instance that is processed by an algorithm in second minuteand hour it shows the importance of good algorithm designbecause an asymptotically slow algorithm is beaten in the long run by an asymptotically faster algorithmeven if the constant factor for the asymptotically faster algorithm is worse running time (ms maximum problem size ( second minute hour , , , , , , table maximum size of problem that can be solved in second minuteand hourfor various running times measured in microseconds