(fsum for ( = <=ni*= for ( = <=nj++sum++(gassume that array contains valuesrandom takes constant timeand sort takes log steps for ( = <ni++for ( = <nj++ [idsutil random( )sort( )(hassume array contains random permutation of the values from to sum for ( = <ni++for ( = [ ]!=ij++sum++(isum if (even( )for ( = <ni++sum++else sum sum show that big-theta notation (thdefines an equivalence relation on the set of functions give the best lower bound that you can for the following code fragmentas function of the initial value of while ( if (odd( ) else do you think that the upper bound is likely to be the same as the answer you gave for the lower bound does every algorithm have th running-time equationin other wordsare the upper and lower bounds for the running time (on any specified class of inputsalways the same does every problem for which there exists some algorithm have th runningtime equationin other wordsfor every problemand for any specified class of inputsis there some algorithm whose upper bound is equal to the problem' lower bound