astrous consequences on program' space or time performance unusual data distributions can also be used to advantageas shown in section in summaryfor real-time applications we are likely to prefer worst-case analysis of an algorithm otherwisewe often desire an average-case analysis if we know enough about the distribution of our input to compute the average case if notthen we must resort to worst-case analysis faster computeror faster algorithmimagine that you have problem to solveand you know of an algorithm whose running time is proportional to unfortunatelythe resulting program takes ten times too long to run if you replace your current computer with new one that is ten times fasterwill the algorithm become acceptableif the problem size remains the samethen perhaps the faster computer will allow you to get your work done quickly enough even with an algorithm having high growth rate but funny thing happens to most people who get faster computer they don' run the same problem faster they run bigger problemsay that on your old computer you were content to sort , records because that could be done by the computer during your lunch break on your new computer you might hope to sort , records in the same time you won' be back from lunch any soonerso you are better off solving larger problem and because the new machine is ten times fasteryou would like to sort ten times as many records if your algorithm' growth rate is linear ( if the equation that describes the running time on input size is (ncn for some constant )then , records on the new machine will be sorted in the same time as , records on the old machine if the algorithm' growth rate is greater than cnsuch as then you will not be able to do problem ten times the size in the same amount of time on machine that is ten times faster how much larger problem can be solved in given amount of time by faster computerassume that the new machine is ten times faster than the old say that the old machine could solve problem of size in an hour what is the largest problem that the new machine can solve in one hourfigure shows how large problem can be solved on the two machines for the five running-time functions from figure this table illustrates many important points the first two equations are both linearonly the value of the constant factor has changed in both casesthe machine that is ten times faster gives an increase in problem size by factor of ten in other wordswhile the value of the constant does affect the absolute size of the problem that can be solved in fixed amount of timeit does not affect the improvement in