295. Find Median from Data Stream
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 is3[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:
addNum(1)
addNum(2)
findMedian() -> 1.5
addNum(3)
findMedian() -> 2
Solution: MinHeap & MaxHeap
import heapq
class MaxHeap:
def __init__(self):
self.q = []
def __len__(self):
return len(self.q)
def add(self, num):
heapq.heappush(self.q, -num)
def pop(self):
return -heapq.heappop(self.q)
def top(self):
return -self.q[0]
class MinHeap:
def __init__(self):
self.q = []
def __len__(self):
return len(self.q)
def add(self, num):
heapq.heappush(self.q, num)
def pop(self):
return heapq.heappop(self.q)
def top(self):
return self.q[0]
class MedianFinder(object):
def __init__(self):
"""
initialize your data structure here.
"""
self.left = MaxHeap()
self.right = MinHeap()
def addNum(self, num):
"""
:type num: int
:rtype: void
"""
if len(self.left) > 0 and num <= self.left.top():
self.left.add(num)
if len(self.left) > len(self.right) + 1:
self.right.add(self.left.pop())
else:
self.right.add(num)
if len(self.right) > len(self.left) + 1:
self.left.add(self.right.pop())
def findMedian(self):
"""
:rtype: float
"""
if len(self.left) == len(self.right):
return (self.left.top() + self.right.top()) / 2.0
if len(self.left) > len(self.right):
return self.left.top() / 1.0
return self.right.top() / 1.0
Lessons:
- Use max-heap for left side, use min-heap for right side.