Question

Write a recurrence relation describing the worst case running time of each of the following algorithms, and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution by using substitution or a recursion tree. You may NOT use the Master Theorem. Simplify your answers, expressing them in a form such as O(nk) or (nklog n) whenever possible. If the algorithm takes exponential time, then just give an exponential lower bound using the 2 notation. function func7(A, n) /* A = array of n integers */ 1. if n < 20 then return (A[1]); 2. i = 10; 3. while (i<n-7) do 4. A[i+ A[i] - A[n - i); 5. in 4*i; 6. endwhile 7. x +func7(A, n-3); 8. return (30); function func8(A,n) /* A = array of n integers */ 1. if n < 20 then return (A[1]); 2. 20; 3. i n -5; 4. while (i > 10) do 5. Ali - A[i] + A[i+ 3); 6. + 2+ func8(A, i); 7. it i-2; 8. endfor 9. return (2);

Answer 1

funco (An) Recurrence Relation T(n)= T(n-3 using Tree method Height of Tree T(m) - eng(n) Tin-3) — log(n-3) Tin-6) - log (n-6) 71,-9) -- log in-9) - TG)= [legent by (n-3) + log (n-6) + lng (0-9) +---) z times T(m) = ( eogn + legn+ eigen tegn) & times T(m) = 2 login [To= o(ningen) funco (a.n) Recurrence Relation TI) = 777(-5)+n T(0) = 10-5)+n Uedselrecensen substitution T()= ( T(n-10)+ n-5 ) +n Tly) = (2)+(-10)+ nn-s) + T(*)= (2)*(n-15)+ () (6-10) + 2 (0-5)+n | TG= O(no) ,