data structures using examples of functions not in ( includen to summarizebest case describes an upper bound for all combinations of input it is possibly lower than the worst case 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 the 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 worst case table examples of (nand (nnow let us look at some examples of (nand (ntable (nf(no( ( ) shows the relationship between (nand (nnote that ( the constant values will be ignored because the main purpose ( of the big notation is to analyse the algorithm in general ( fashionso the anomalies that appear for small input sizes are ( simply ignored categories of algorithms according to the big notationwe have five different categories of algorithmsconstant time algorithmrunning time complexity given as ( linear time algorithmrunning time complexity given as (nlogarithmic time algorithmrunning time complexity given as (log npolynomial time algorithmrunning time complexity given as (nkwhere exponential time algorithmrunning time complexity given as ( ntable shows the number of operations that would be performd for various values of table number of operations for different functions of ( (log ( ( log ( ( example show that ( solution by definitionwe have < ( <cg(nsubstituting as (nand as ( )we get < <cn dividing by / < / <cn / < / < now to determine the value of cwe see that / is maximum when = thereforec= to determine the value of < / < < / <