1825 - Finding MK Average\.

Hard

You are given two integers, m and k, and a stream of integers. You are tasked to implement a data structure that calculates the MKAverage for the stream.

The MKAverage can be calculated using these steps:

• If the number of the elements in the stream is less than m you should consider the MKAverage to be -1. Otherwise, copy the last m elements of the stream to a separate container.

• Remove the smallest k elements and the largest k elements from the container.

• Calculate the average value for the rest of the elements rounded down to the nearest integer.

Implement the MKAverage class:

• MKAverage(int m, int k) Initializes the MKAverage object with an empty stream and the two integers m and k.

• void addElement(int num) Inserts a new element num into the stream.

• int calculateMKAverage() Calculates and returns the MKAverage for the current stream rounded down to the nearest integer.

Example 1:

Input "MKAverage", "addElement", "addElement", "calculateMKAverage", "addElement", "calculateMKAverage", "addElement", "addElement", "addElement", "calculateMKAverage" [3, 1, 3, 1, [], 10, [], 5, 5, 5, []]

Output: null, null, null, -1, null, 3, null, null, null, 5

Explanation: MKAverage obj = new MKAverage(3, 1); obj.addElement(3); // current elements are 3 obj.addElement(1); // current elements are 3,1 obj.calculateMKAverage(); // return -1, because m = 3 and only 2 elements exist. obj.addElement(10); // current elements are 3,1,10 obj.calculateMKAverage(); // The last 3 elements are 3,1,10. // After removing smallest and largest 1 element the container will be ``[3]. // The average of [3] equals 3/1 = 3, return 3 obj.addElement(5); // current elements are [3,1,10,5] obj.addElement(5); // current elements are [3,1,10,5,5] obj.addElement(5); // current elements are [3,1,10,5,5,5] obj.calculateMKAverage(); // The last 3 elements are [5,5,5]. // After removing smallest and largest 1 element the container will be `[5]. // The average of [5] equals 5/1 = 5, return 5` ``

Constraints:

• <code>3 <= m <= 10⁵</code>

• 1 <= k*2 < m

• <code>1 <= num <= 10⁵</code>

• At most <code>10⁵</code> calls will be made to addElement and calculateMKAverage.