Question

This part involves finding a new algorithm by yourself. You do NOT have to implement it with C++. You may just state the algorithm in pseudo-code. The problem is as follows: You have an integer array of n elements. You want to return true if there is a set of more than n/2 elements in the array with the same value, false otherwise. Notice that if the array is sorted (that is you are allowed to use a sorting algorithm), the solution becomes easy: Just go over the sorted array by keeping track of the number of elements of the same value. However, for this part, you are NOT allowed to use a sorting algorithm. The only operation you can perform is to compare the values of two elements of the array, which tells you if they are equal or not. Let us call this operation equality testing. Give an algorithm using O(n log n) equality testing operations. You should use the divide-and-conquer paradigm discussed in the lectures. For partial credit, give an algorithm using O(n^2 ) equality testing operations (which is in fact very easy).