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Grokking the Coding Interview Patterns

Solution: Finding MK Average

Understand how to implement a data structure that maintains a moving window of integers, partitions them into segments, and calculates the MK Average by excluding extremes. Learn to use deques, sorted lists, and binary search for efficient insertion, deletion, and rebalancing to achieve constant time average calculation.

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Statement

You are given two integers, m and k, and a stream of integers. Your task is to design and implement a data structure that efficiently calculates the MK Average for the stream.

To compute the MK Average, follow these steps:

  1. Stream length check: If the stream contains fewer than m elements, return -1 as the MK Average.

  2. Window selection: Otherwise, copy the last m elements of the stream to a separate container and remove the smallest k elements and the largest k elements from the container.

  3. Average calculation: Calculate the average of the remaining elements (rounded down to the nearest integer).

Implement the MKAverage class

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

  • void addElement(int num): Adds the integer num to the stream.

  • int calculateMKAverage(): Returns the current MK Average for the stream as described above, or -1 if the stream contains fewer than m elements.

Constraints:

  • 3<=3 <= m <=105<= 10^5

  • 1<1 < k*2 ...