if we calculate the average of this loop ( / )we will observe that it is equal to the number of iterations in the outer loop ( plus divided by in general termsthe inner loop iterates ( )/ times thereforethe efficiency of such code can be given as (nn ( )/ big notation in today' era of massive advancement in computer technologywe are hardly concerned about the efficiency of algorithms ratherwe are more interested in knowing the generic order of the magnitude of the algorithm if we have two different algorithms to solve the same problem where one algorithm executes in iterations and the other in iterationsthe difference between the two algorithms is not much howeverif the first algorithm executes in iterations and the other in iterationsthen it is matter of concern we have seen that the number of statements executed in the program for elements of the data is function of the number of elementsexpressed as (neven if the expression derived for function is complexa dominant factor in the expression is sufficient to determine the order of the magnitude of the result andhencethe efficiency of the algorithm this factor is the big oand is expressed as (nthe big notationwhere stands for 'order of'is concerned with what happens for very large values of for exampleif sorting algorithm performs operations to sort just elementsthen that algorithm would be described as an ( algorithm when expressing complexity using the big notationconstant multipliers are ignored soan ( nalgorithm is equivalent to ( )which is how it should be written if (nand (nare the functions defined on positive integer number nthen (no( ( )that isf of is big- of of if and only if positive constants and existsuch that (nps cg(nit means that for large amounts of dataf(nwill grow no more than constant factor than (nhenceg provides an upper bound note that here is constant which depends on the following factorsthe programming language usedthe quality of the compiler or interpreterthe cpu speedthe size of the main memory and the access time to itthe knowledge of the programmerand the algorithm itselfwhich may require simple but also time-consuming machine instructions we have seen that the big notation provides strict upper bound for (nthis means that the function (ncan do better but not worse than the specified value big notation is simply written as (no( ( )or as (no( ( )heren is the problem size and ( ( ){ ( )positive constants cn such that < (nn hencewe can say that ( ( )comprises set of all the functions (nthat are less than or equal to cg(nfor all values of > if ( > then (no( ( )and (nis an asymptotically tight upper bound for (nexamples of functions in ( includen