## Sliding Median

### June 29, 2012

We saw the streaming median problem in a recent exercise. Today we look at a slight variant on that problem, the sliding median, which slides a window of width *k* over an input stream, reporting the median of each successive window.

The streaming median required us to keep the entire input stream in memory. But for the sliding median, we keep only the most recent *k* items. We keep two data structures. A cyclical queue keeps the most recent input items, in the order in which they are input. An ordered map keeps the input items in sorted order. After reading the first *k* items, each time we read an item we output the current median, delete the oldest item in the cyclical queue from the ordered map, insert the new item into both the ordered map and the cyclical queue, and go on to the next item.

Your task is to write a program that implements the sliding median calculation. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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[...] today’s Programming Praxis exercise, our goal is to determine the median values of a sliding window over a [...]

My Haskell solution (see http://bonsaicode.wordpress.com/2012/06/29/programming-praxis-sliding-median/ for a version with comments):

Fairly basic python implementation.

It uses a sorted list for the ordered map.

templated c++ implementation.

SlidingMedian class uses three data structures:

1) List which maintains the order of values as they arrive

2) Two STL sets, which are implemented as balanced binary search trees. One set stores all values less than or equal to the median, the other set stores values greater than or equal to the median.

Insert and median retrieval is therefore O(log n).

Of course, anyone that is actually paying attention would have used:

in place of