Final answer:
The value of 'a' for this recurrence relation T(n) = T(n/3) + 1 used in the master method is 1, since the problem is divided into only one subproblem of size n/3 each time.
Step-by-step explanation:
The student has presented a recurrence relation T(n) = T(n/3) + 1 and is looking to solve it using the master method. Here, they are asking for the value of a in the context of the master theorem.
The master method is applied to recurrence relations of the form T(n) = aT(n/b) + f(n), where a is the number of subproblems, b is the factor by which the problem size is divided each time, and f(n) represents the non-recursive work being done outside the recursive calls. In the given recurrence relation, since there is no explicit multiplication by a within the recurrence, it implies a is 1, because each recursive call is just the original problem size divided by '3', with only one such subproblem needing to be solved (T(n/3)).