figure graphical comparison of the growth rates from table big- notation instead of counting the precise number of operations or stepscomputer scientists are more interested in classifying an algorithm based on the order of magnitude as applied to execution time or space requirements this classification approximates the actual number of required steps for execution or the actual storage requirements in terms of variable-sized data sets the term big-owhich is derived from the expression "on the order of,is used to specify an algorithm' classification defining big- assume we have function (nthat represents the approximate number of steps required by an algorithm for an input of size for the second version of our algorithm in the previous sectionthis would be written as (nn nowsuppose there exists function (ndefined for the integers > such that for some constant cand some constant mt ( <cf (nfor all sufficiently large values of > thensuch an algorithm is said to have time-complexity ofor executes on the order off (nrelative to the number of operations it requires in other wordsthere is positive integer and constant (constant of proportionality such that for all >mt ( <cf (nthe