Provide tight asymptotic bounds (i.e. ()) on the worst case running times of the following two procedures.

(a)

1: procedure BackForwardAlg(n) 2: if n 10 then 3: return n 4: if n even then 5: return BackF orwardAlg(n/2) 6: else 7: return BackF orwardAlg(n + 3)

(b) 1: procedure RecursiveAlg(A[1 . . . n]) 2: if n == 1 then 3: return False 4: mid = dn/2e 5: for i = 1 to mid do 6: for j = mid + 1 to n do 7: if A[i] == A[j] then 8: return True 9: return (RecursiveAlg(A[1 . . . mid]) || RecursiveAlg(A[mid + 1 . . . n]))

(c) (2 bonus points) Give a one sentence description of what RecursiveAlg does.