4. What is the maximal number of swap operations performed during the process of selecting consecutive minima during the execution of the heap-sort algorithm? In your count skip the swap operations performed during the process of creating the initial heap. Assume that the input array has size n. (i) Express your answer in the form of a sum. (ii) Remove the symbol of summation and analyze the order of growth. Hint: Make use of the formula: 1*21 +2*22 +3*23 ++N*2N =(N-1)*2N+1+2. procedure pushdown(first, last: integer); var r: integer; begin r := first; while r <= last div 2 do if last = 2*r then begin if A[r].key > A[2*r].key then swap(A[r],A[2*r]); r := last end else if A[r].key > A[2*r].key and A[2*r].key <= A[2*r+1].key then begin swap(A[r],A[2*r]); r := 2*r end else if A[r].key > A[2*r+1].key and A[2*r+1].key < A[2*r].key then begin swap(A[r],A[2*r+1]); r := 2*r+1 end else r := last end; { pushdown } procedure heapsort; var i: integer; begin for i := n div 2 downto 1 do pushdown(i,n); for i := n downto 2 do begin swap(A[1],A[i]); pushdown(1,i-1) end end; { heapsort }