induction and loop invariants exercises java datastructures net the seven functions used in this book in this sectionwe briefly discuss the seven most important functions used in the analysis of algorithms we will use only these seven simple functions for almost all the analysis we do in this book in facta section that uses function other than one of these seven will be marked with star to indicate that it is optional in addition to these seven fundamental functionsappendix contains list of other useful mathematical facts that apply in the context of data structure and algorithm analysis the constant function the simplest function we can think of is the constant function this is the functionf(ncfor some fixed constant csuch as or that isfor any argument nthe constant function (nassigns the value in other wordsit doesn' matter what the value of isf (nwill always be equal to the constant value since we are most interested in integer functionsthe most fundamental constant function is ( and this is the typical constant function we use in this book note that any other constant functionf(nccan be written as constant times (nthat is, (ncg(nin this case as simple as it isthe constant function is useful in algorithm analysisbecause it characterizes the number of steps needed to do basic operation on computerlike adding two numbersassigning value to some variableor comparing two numbers