Finding MK Average — LeetCode 1825 Python Solution

HardDesignQueueData StreamOrdered SetHeap (Priority Queue)
Problem
#1825
Reading time
10 min

The problem

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.

Example

Input
["MKAverage", "addElement", "addElement", "calculateMKAverage", "addElement", "calculateMKAverage", "addElement", "addElement", "addElement", "calculateMKAverage"]
Output
[null, null, null, -1, null, 3, null, null, null, 5]
Explanation
MKAverage obj = new MKAverage(3, 1);

Python solution

Python
class MKAverage:
    def __init__(self, m: int, k: int):
        self.m = m
        self.k = k
        self.s = 0
        self.q = deque()
        self.lo = SortedList()
        self.mid = SortedList()
        self.hi = SortedList()

    def addElement(self, num: int) -> None:
        if not self.lo or num <= self.lo[-1]:
            self.lo.add(num)
        elif not self.hi or num >= self.hi[0]:
            self.hi.add(num)
        else:
            self.mid.add(num)
            self.s += num
        self.q.append(num)
        if len(self.q) > self.m:
            x = self.q.popleft()
            if x in self.lo:
                self.lo.remove(x)
            elif x in self.hi:
                self.hi.remove(x)
            else:
                self.mid.remove(x)
                self.s -= x
        while len(self.lo) > self.k:
            x = self.lo.pop()
            self.mid.add(x)
            self.s += x
        while len(self.hi) > self.k:
            x = self.hi.pop(0)
            self.mid.add(x)
            self.s += x
        while len(self.lo) < self.k and self.mid:
            x = self.mid.pop(0)
            self.lo.add(x)
            self.s -= x
        while len(self.hi) < self.k and self.mid:
            x = self.mid.pop()
            self.hi.add(x)
            self.s -= x

    def calculateMKAverage(self) -> int:
        return -1 if len(self.q) < self.m else self.s // (self.m - 2 * self.k)


# Your MKAverage object will be instantiated and called as such:
# obj = MKAverage(m, k)
# obj.addElement(num)
# param_2 = obj.calculateMKAverage()

Complexity

MeasureComplexity
TimeO(n log n)
SpaceO(m) auxiliary

Pattern: Heap / Priority Queue

Keep only the best k elements, or always pull the smallest, in log time. LeetCode 1825. Finding MK Average is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Heap (Priority Queue).

The heap / priority queue guide has the Python template for the pattern and the 163 LeetCode problems that use it.

Related problems

Frequently asked questions

How hard is LeetCode 1825. Finding MK Average?
LeetCode 1825. Finding MK Average is rated Hard on LeetCode.
What is the time complexity of LeetCode 1825. Finding MK Average?
The Python solution on this page runs in O(n log n).
What is the space complexity of LeetCode 1825. Finding MK Average?
The Python solution on this page uses O(m) auxiliary space.
What topics does LeetCode 1825. Finding MK Average cover?
LeetCode 1825. Finding MK Average is tagged Design, Queue, Data Stream, Ordered Set and Heap (Priority Queue) on LeetCode.

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