Finding the k-largest values in a set of data

How can we keep track of the k-largest elements in a set of data?

Implement a class that can maintain the k-largest elements seen so far.

What methods should the class have?

The class should have two methods: count(T x) and kbest().

Answer:

The class KBestCounter implements the interface KBest and is designed to keep track of the k-largest elements seen so far in a set of data.

The KBestCounter class implements the KBest interface, which defines the kbest() method to retrieve the k-largest elements as a sorted list. The implementation utilizes a priority queue (java.util.PriorityQueue) as the underlying data structure. The priority queue is initialized with a comparator that orders elements in ascending order.

The count(T x) method is used to process the next element in the data set. It inserts the element into the priority queue and, if the size of the queue exceeds k, removes the smallest element to maintain the invariant of keeping only the k-largest elements.

The kbest() method retrieves the k-largest elements from the priority queue. It first stores the elements in a temporary list and then clears the priority queue. Finally, it returns the temporary list in descending order, representing the k-largest elements.

By using a priority queue, the KBestCounter class ensures efficient processing and retrieval of the k-largest elements. The time complexity of count(T x) is O(log k) as it involves insertion and removal operations on the priority queue, while kbest() runs in O(k log k) time as it retrieves and sorts the k-largest elements. The priority queue guarantees that only the k-largest elements are stored, and it is restored to its original state after retrieving the k-best elements.