with little effortyou should be able to verify that this peculiar combination of operations does in fact produce the correct answernowlooking at the list of operations to compute the factorsand then the additions/subtractions needed to put them together to get the final answerswe see that we need total of seven (arraymultiplications and (arrayadditions/subtractions to do the job this leads to the recurrence ( ( / ( / ) (nth(nlog th( we obtained the close form solution again by applying the master theorem unfortunatelywhile strassen' algorithm does in fact reduce the asymptotic complexity over the standard algorithmthe cost of large number of addition and subtraction operations raises the constant factor involved considerably this means that an extremely large array size is required to make strassen' algorithm practical in actual application random numbers the success of randomized algorithms such as presented in section depend on having access to good random number generator while modern compilers are likely to include random number generator that is good enough for most purposesit is helpful to understand how they workand to even be able to construct your own in case you don' trust the one provided this is easy to do firstlet us consider what random sequence from the following listwhich appears to be sequence of "randomnumbers in factall three happen to be the beginning of some sequence in which one could continue the pattern to generate more values (in case you do not recognize itthe third one is the initial digits of the irrational constant eviewed as series of digitsideally every possible sequence has equal probability of being generated (even the three sequences abovein factdefinitions of randomness generally have features such asone cannot predict the next item the series is unpredictable the series cannot be described more briefly than simply listing it out this is the equidistribution property