Consider the voting problem from Exercise C-11.13, but now suppose a candidate wins only if he or she gets a majority of the votes cast. Design and analyze a fast algorithm for determining the winner if there is one.

Data from in Exercise C-11.13

Suppose we are given an n-element sequence S such that each element in S represents a different vote for president, where each vote is given as an integer representing a particular candidate. Design an O(nlog n)- time algorithm to see who wins the election S represents, assuming the candidate with the most votes wins (even if there are O(n) candidates).