Median in a stream

Hard

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Average time to solve is 50m

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Problem statement

Given that integers are read from a data stream. Your task is to find the median of the elements read so far.

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 floor of the average of the two middle values.

For example :

[2,3,4] - median is 3.
[2,3] - median is floor((2+3)/2) = 2.

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line of input contains a single integer T, representing the number of test cases or queries to be run. 

Then the T test cases follow.
The first line of each test case contains the number of elements, N, in the input data stream.

The second line of each test case contains N space separated elements of the input data stream.

Output Format:

For each test case, print the median of the elements after each incoming element. Each median value is separated by a single space.

The output of each test case is printed in a separate line.

Note :

You do not need to print anything, just return the vector of medians after each element is read from the stream.

Constraints :

1 <= T <= 10
1 <= N <= 10^4
0 <= data <= 10^8
Where T is the number of test cases, N is the number of elements in the data stream.

Time Limit : 1 sec

Sample Input 1:

Sample Output 1:

1 1 2
9 9 
4

Explanation for Sample Input 1:

For test case 1 
After reading first element of stream , Median of [1] is 1 
After reading second element of stream, Median of [1, 2]  = floor((1+2)/2)  = 1
After reading third element of stream, Median of [1,2,3] = 2
So the output will be 1 1 2.

Sample Input 2:

Sample Output 2:

5 4 5
3 5

Explanation for Sample Input 2:

For test case 1 
After reading first element of stream, Median of [5] is 5
After reading second element of stream, Median of [5, 3]  = floor((5+3)/2)  = 4
After reading third element of stream, Median of [5,3,8] = 5 , it is the middle value of the sorted array
So the output will be 5 4 5.

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