3. (20 points) For each of the following algorithmic descriptions, write the recurrence that characterizes the worst-case time spent by the algorithm. Then solve the recurrence in closed-form using the Master method or analysis of your choice. Show your work for credit. (a) (6 points) Given a problem of size n, this algorithm makes 32 recursive calls on problems of size When the recursive calls finish, the algorithm then spends n time. Recurrence. T(n)= Closed-form solution: T(n) = e- --) (b) (6 points) Given a problem of size n, this algorithm makes one recursive call on a problem of size n- 1, and executes 5 ticks when the recursion returns: Recurrence. T(n)= Closed-form solution: T(n) 6( (c) (8 points) Given a problem of size n, this algorithm allocates an array of size n, and then makes 2 recursive calls on problems of size Recurrence: T(n) Closed-form solution: T(n) =6(