Can someOne Please Help me Solve this Algorithm analysis ?

Consider the following problem called the Stable Officemate Problem. Here there are 2n people, each of whom ranks the other 2n - 1 people in order of preference. For example, Addie, Brian, Carlos, and Don might have the following rankings: The goal is to find a stable matching (i.e., n pairs of officemates such that no two people prefer each other to their current officemate). We proved in class that a stable matching always exists for instances of the stable matching problem. Do stable matching's always exist for the stable officemate problem? If so, provide a proof. If not, give a counterexample. Consider the following problem. Does a given input set of n integers {x1, x2, ..., xn}, contain three elements that sum to zero? In the search version of the problem, the correct output is a set of three indices {i, j, k} such that xi + xj + xk = 0 if such a set exists, and "No" otherwise. Show that by sorting the input, you can speed up your algorithm in (b) to obtain an algorithm 2 that runs in O(n^2 log n) time. Show that by using a data structure from CS112, you can speed up your algorithm in (b) to obtain 2 an algorithm that runs in O(n^2) time