drawn as arrows what is the meaning of downward arrowhow about an upward arrowr- give complete pseudo-code description of the recursive merge-sort algorithm that takes an array as its input and output - show that the running time of the merge-sort algorithm on an -element sequence is (nlogn)even when is not power of - suppose we are given two -element sorted sequences and that should not be viewed as sets (that isa and may contain duplicate entriesdescribe an ( )-time method for computing sequence representing the set (with no duplicatesr- show that ( ( bx ( )for any three sets xaand - suppose we modify the deterministic version of the quick-sort algorithm so thatinstead of selecting the last element in an -element sequence as the pivotwe choose the element at index ln/ what is the running time of this version of quick-sort on sequence that is already sortedr- consider again the modification of the deterministic version of the quicksort algorithm so thatinstead of selecting the last element in an -element sequence as the pivotwe choose the element at index ln/ describe the kind of sequence that would cause this version of quick-sort to run in ( time - show that the best-case running time of quick-sort on sequence of size with distinct elements is (nlognr- describe randomized version of in-place quick-sort in pseudo-code -