find-median-from-data-stream.py

# Time:  O(nlogn) for total n addNums, O(logn) per addNum, O(1) per findMedian.
# Space: O(n), total space

# Median is the middle value in an ordered integer list. 
# If the size of the list is even, there is no middle value. 
# So the median is the mean of the two middle value.
#
# Examples: 
# [2,3,4] , the median is 3
#
# [2,3], the median is (2 + 3) / 2 = 2.5
#
# Design a data structure that supports the following two operations:
#
# void addNum(int num) - Add a integer number from the data stream to the data structure.
# double findMedian() - Return the median of all elements so far.
# For example:
#
# add(1)
# add(2)
# findMedian() -> 1.5
# add(3) 
# findMedian() -> 2

# Heap solution.
from heapq import heappush, heappop

class MedianFinder:
    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.__max_heap = []
        self.__min_heap = []

    def addNum(self, num):
        """
        Adds a num into the data structure.
        :type num: int
        :rtype: void
        """
        # Balance smaller half and larger half.
        if not self.__max_heap or num > -self.__max_heap[0]:
            heappush(self.__min_heap, num)
            if len(self.__min_heap) > len(self.__max_heap) + 1:
                heappush(self.__max_heap, -heappop(self.__min_heap))
        else:
            heappush(self.__max_heap, -num)
            if len(self.__max_heap) > len(self.__min_heap):
                heappush(self.__min_heap, -heappop(self.__max_heap))

    def findMedian(self):
        """
        Returns the median of current data stream
        :rtype: float
        """
        return (-self.__max_heap[0] + self.__min_heap[0]) / 2.0 \
               if len(self.__min_heap) == len(self.__max_heap) \
               else self.__min_heap[0]

# Your MedianFinder object will be instantiated and called as such:
# mf = MedianFinder()
# mf.addNum(1)
# mf.findMedian()