The pointy-haired boss (PHB) of an office in a major technology company would like to throw a party. Based on the performance reviews he has done, the PHB has assigned an integer “fun factor” score, F(x), for each employee, x, in his office. In order for the party to be as crazy as possible, the PHB has one rule: an employee, x, may be invited to the party only if x’s immediate supervisor is not invited. Suppose you are the PHB’s administrative assistant, and it is your job to figure out who to invite, subject to this rule, given the list of F(x) values and the office organizational chart, which is a tree, T, rooted at the PHB, containing the n employees as nodes, so that each employee’s parent in T is the immediate supervisor of that employee. Describe an algorithm for solving this office party problem, by choosing a group of employees to invite to the party such that this group has the largest total fun factor while satisfying the PHB’s rule and also guaranteeing that you are invited, which, of course, means that the PHB is not. What is the running time of your algorithm?