windowed_median.cpp File Reference

An implementation of a median calculation of a sliding window along a data stream. More...

#include <cassert>
#include <cstdlib>
#include <ctime>
#include <list>
#include <set>
#include <vector>

Include dependency graph for windowed_median.cpp:

Go to the source code of this file.

Classes
class	probability::windowed_median::WindowedMedian
	A class to calculate the median of a leading sliding window at the back of a stream of integer values. More...

Namespaces
namespace	probability
	Probability algorithms.
namespace	windowed_median
	Functions for the Windowed Median algorithm implementation.

Typedefs
using	probability::windowed_median::Window = std::list<int>
using	probability::windowed_median::size_type = Window::size_type

Functions
static void	test (const std::vector< int > &vals, int windowSize)
	Self-test implementations.
int	main ()
	Main function.

Detailed Description

An implementation of a median calculation of a sliding window along a data stream.

Given a stream of integers, the algorithm calculates the median of a fixed size window at the back of the stream. The leading time complexity of this algorithm is O(log(N), and it is inspired by the known algorithm to [find median from (infinite) data stream](https://www.tutorialcup.com/interview/algorithm/find-median-from-data-stream.htm), with the proper modifications to account for the finite window size for which the median is requested

Algorithm

The sliding window is managed by a list, which guarantees O(1) for both pushing and popping. Each new value is pushed to the window back, while a value from the front of the window is popped. In addition, the algorithm manages a multi-value binary search tree (BST), implemented by std::multiset. For each new value that is inserted into the window, it is also inserted to the BST. When a value is popped from the window, it is also erased from the BST. Both insertion and erasion to/from the BST are O(logN) in time, with N the size of the window. Finally, the algorithm keeps a pointer to the root of the BST, and updates its position whenever values are inserted or erased to/from BST. The root of the tree is the median! Hence, median retrieval is always O(1)

Time complexity: O(logN). Space complexity: O(N). N - size of window

Author

Yaniv Hollander

Definition in file windowed_median.cpp.

Typedef Documentation

size_type

using probability::windowed_median::size_type = Window::size_type

Definition at line 49 of file windowed_median.cpp.

Window

using probability::windowed_median::Window = std::list<int>

Definition at line 48 of file windowed_median.cpp.

Function Documentation

main()

int main

(

void

)

Main function.

Returns

0 on exit

A few fixed test cases

Array of sorted values; odd window size

Array of sorted values - decreasing; odd window size

Even window size

Array with repeating values

Array with same values except one

Array that includes repeating values including negatives

Array with large values - sum of few pairs exceeds MAX_INT. Window size is even - testing calculation of average median between two middle values

Random test cases

Array size in the range [5, 20]

Window size in the range [3, 10]

Random array values (positive/negative)

Testing randomized test

Definition at line 196 of file windowed_median.cpp.

           {
    test({1, 2, 3, 4, 5, 6, 7, 8, 9},
         3);  
    test({9, 8, 7, 6, 5, 4, 3, 2, 1},
         3);  
    test({9, 8, 7, 6, 5, 4, 5, 6}, 4);     
    test({3, 3, 3, 3, 3, 3, 3, 3, 3}, 3);  
    test({3, 3, 3, 3, 7, 3, 3, 3, 3}, 3);  
    test({4, 3, 3, -5, -5, 1, 3, 4, 5},
         5);  

    test({470211272, 101027544, 1457850878, 1458777923, 2007237709, 823564440,
          1115438165, 1784484492, 74243042, 114807987},
         6);

    std::srand(static_cast<unsigned int>(std::time(nullptr)));
    std::vector<int> vals;
    for (int i = 8; i < 100; i++) {
        const auto n =
            1 + std::rand() /
                    ((RAND_MAX + 5u) / 20);  
        auto windowSize =
            1 + std::rand() / ((RAND_MAX + 3u) /
                               10);  
        vals.clear();
        vals.reserve(n);
        for (int i = 0; i < n; i++) {
            vals.push_back(
                rand() - RAND_MAX);  
        }
        test(vals, windowSize);  
    }
    return 0;
}

test()

void test ( const std::vector< int > & vals, int windowSize )

static

Self-test implementations.

Parameters

vals	Stream of values
windowSize	Size of sliding window

Comparing medians: efficient function vs. Naive one

Definition at line 182 of file windowed_median.cpp.

                                                             {
    probability::windowed_median::WindowedMedian windowedMedian(windowSize);
    for (const auto val : vals) {
        windowedMedian.insert(val);

        assert(windowedMedian.getMedian() == windowedMedian.getMedianNaive());
    }
}