data structures using limitations of big notation there are certain limitations with the big notation of expressing the complexity of algorithms these limitations are as followsmany algorithms are simply too hard to analyse mathematically there may not be sufficient information to calculate the behaviour of the algorithm in the average case big analysis only tells us how the algorithm grows with the size of the problemnot how efficient it isas it does not consider the programming effort it ignores important constants for exampleif one algorithm takes ( time to execute and the other takes ( time to executethen as per big oboth algorithm have equal time complexity in real-time systemsthis may be serious consideration omega notation (othe omega notation provides tight lower bound for (nthis means that the function can never do better than the specified value but it may do worse notation is simply written asf(no( ( ))where is the problem size and ( ( ){ ( )positive constants such that hencewe can say that ( ( )comprises set of all the functions (nthat are greater than or equal to cg(nfor all values of > if cg(non >nothen (no( ( )and (nis an asymptotically tight lower bound for (nexamples of functions in ( includen examples of functions not in ( includenn to summarizebest case describes lower bound for all combinations of input this implies that the function can never get any better than the specified value for examplewhen sorting an array the best case is when the array is already correctly sorted worst case describes lower bound for worst case input combinations it is possibly greater than best case for examplewhen sorting an array the worst case is when the array is sorted in reverse order if we simply write oit means same as best case example show that ( solution by the definitionwe can write <cg( < ( <cn < dividing by / <cn / < / / < < / nowlim + / naetherefore < < hencec now to determine the value of < < / - < < /