exercises given the following sequence of keys ( )trace the indicated algorithm to produce recursive call tree when sorting the values in descending order (amerge sort (bquick sort do the same as in exercise but produce recursive call tree when sorting the values in ascending order show the distribution steps performed by the radix sort when ordering the following list of keys( ( ( "ms""va""ak""la""ca""al""ga""tn""wa""dc analyze the quick sort algorithm to show the worst case time is ( analyze the mergevirtualseq(function and show that it is linear time operation in the worst case analyze the linked list version of the merge sort algorithm to show the worst case time is ( log an important property of sorting algorithms is stability sorting algorithm is stable if it preserves the original order of duplicate keys stability is important when sorting collection that has already been sorted by primary key that will now be sorted by secondary key for examplesuppose we have sequence of student records that have been sorted by name and now we want to sort the sequence by gpa since there can be many duplicate gpaswe want to order any duplicates by name thusif smith and green both have the same gpathen green would be listed before smith if the sorting algorithm used for this second sort is stablethen the proper ordering can be achieved since green would appear before smith in the original sequence (adetermine which of the comparison sorts presented in this and in are stable sorts (bfor any of the algorithms that are not stableprovide sequence containing some duplicate keys that shows the order of the duplicates is not preserved