## Find Median from Data Stream

07/17/2016 Heap Design

## Question

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)
findMedian() -> 1.5
findMedian() -> 2


## Solution

Result: Accepted Time: 180 ms

Here should be some explanations.

class MedianFinder {
public:
priority_queue<int,vector<int>,less<int>> low;
priority_queue<int,vector<int>,greater<int>> up;
// Adds a number into the data structure.
void addNum(int num) {
if(!low.size() || low.top() >= num)
low.push(num);
else
up.push(num);
}
void balance()
{
while(low.size() > up.size())
up.push(low.top()),low.pop();
while(up.size() > low.size())
low.push(up.top()),up.pop();
}
// Returns the median of current data stream
double findMedian() {
balance();
if(low.size() == up.size())
return 0.5*(low.top()+up.top());
else if(low.size() > up.size())
return low.top();
return up.top();
}
MedianFinder(){}
};

// Your MedianFinder object will be instantiated and called as such:
// MedianFinder mf;

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$