5. For each subprogram below, derive (in detail as shown in lect23_01_18-1.pdf: page 11, inserted page with cost/timestable, and [CLRS22] Chapter pages 29 - 31) the worst case running time first, provide its asymptotic tight bound (big-Theta estimate), and answer specific questions. (a) What does the code fragment compute? procedure P1 (integer n; array A[1..n] of integer); S:=A[1]; for i:=2 to n step 2 loop - Increments of 2 S:=S+A[i]; end loop; return S; P11; end P11 (b) What does the code fragment compute? Give a computationally equivalent algorithm P_2 with a linear worst-case running time. procedure P_2 (integer n; array A[0..n1] of integer); S:=0fori:=0ton1loopS:=S+A[0];forj:=1toiloopS:=S+A[j]; end loop; end loop; return S; end P11; procedure P3 (integer n ); for i:=1 to n loop x:=n2, while x>0 loop x:=x2i; end loop; end loop; end P33