01.Introduction.md

13. Pattern: Top 'K' Elements

The Top 'K' Elements pattern is a common coding pattern used to solve problems that involve finding the top, smallest, or most/least frequent k elements in an unsorted list. This pattern is particularly useful when dealing with large datasets, as it allows us to solve these problems efficiently without having to sort the entire list.

Understanding the Pattern

The main idea behind this pattern is to maintain a heap of size k while iterating through the list of elements. The type of heap (min-heap or max-heap) depends on the problem at hand. For instance, if we want to find the top k largest elements, we use a min-heap; for the top k smallest elements, we use a max-heap.

PriorityQueue in Java

In Java, the PriorityQueue class is a part of the Java Collections Framework. This class is implemented as a priority heap. A priority heap is a special type of data structure that performs operations based on the priority of the elements. In a PriorityQueue, elements are ordered either in natural order or by a Comparator provided at queue construction time.

Here is a simple example of a PriorityQueue in Java:

import java.util.PriorityQueue;

public class Main {
    public static void main(String[] args) {
        PriorityQueue<Integer> numbers = new PriorityQueue<>();

        // Add items to a Priority Queue (ENQUEUE)
        numbers.add(750);
        numbers.add(500);
        numbers.add(900);
        numbers.add(100);

        // Remove items from the Priority Queue (DEQUEUE)
        while (!numbers.isEmpty()) {
            System.out.println(numbers.remove());
        }
    }
}

In this example, although the elements are added in the order 750, 500, 900, 100, they are polled in the order 100, 500, 750, 900 which is the natural ordering of integers.

Heap Complexities

The time complexity of heap operations is as follows:

• Insertion: The time complexity for inserting an element into a heap is O(log n), where n is the number of elements in the heap.

• Deletion: The time complexity for deleting an element from a heap is also O(log n), as the element to be deleted must first be found in O(log n) time and then removed.

• Peek (or top operation): The time complexity for retrieving the top element from a heap is O(1), as the top element is always present at the root of the heap.

These complexities make heaps an efficient data structure for the Top 'K' Elements pattern. They allow us to insert and delete elements in logarithmic time, which is significantly faster than linear time operations. This efficiency is crucial when dealing with large datasets or real-time data streams.

Conclusion

The Top 'K' Elements pattern is a powerful tool for dealing with large datasets and finding the top k elements. By using a heap data structure, we can solve these problems efficiently and elegantly. Remember, practice is key to mastering this pattern, so try to solve as many problems as you can using this pattern. Happy coding!