3. (20 points) For each of the following algorithmic descriptions, write the recurrence that characterizes the worst-case time spent by the algorithm. Do not solve the recurrence in closed-form, just write the recurrence itself (a) Given a problem of size n, this algorithm makes 3 recursive calls on problems of size . When the recursive calls finish, the algorithm then spends n time. T(n) (b) Given a problem of size n, this algorithm makes one recursive call on a problem of size n-5, and exccutes 5 ticks when the recursion returns: T(n) = (c) Given a problem of size n, this algorithm first spends n time, then makes 4 recur- and then spends n2 time when the recursive calls sive calls on problems of size finish T(n) (d) Given a problem of size n, this algorithm allocates an array of size n, and then makes 2 recursive calls on problems of size T(n) (e) Given a problem of size n, this algorithm makes one recursive call on a problem of size When the recursive call returns. the algorithm then inserts and removes each of the n items from a min-heap 2 T(n) =