An array A[1...n] is said to have a majority element if more than half of its entries are the same. Given an array, the task is to design an efficient algorithm to tell whether the array has a majority element, and, if so, to find that element. The elements of the array are not necessarily from some ordered domain like the integers, and so there can be no comparisons of the form: is A[i] > A[J]? (Think of the array elements as jpeg files, say.) However you can answer questions of the form: is A[i] = A[J]? in constant time. Show how to solve this problem in O(n log n) time. Can you give a linear-time algorithm? Pair up the elements of A arbitrarily, to get n/2 pairs. Look at each pair: if the two elements are different, discard both of them; if they are the same, keep just one of them. Show that after this procedure there are at most n/2 elements left, and that they have a majority element if and only if A does