Quick sort median selection

问题

As we can choose median of 3 element partitioning to implement quick sort. Likewise can we choose median of 5, 7, or 11 element to implement quick sort? If so, then how??

回答1:

You should look into the Median of Medians algorithm. It is a linear time algorithm with the following recurrence...

T(n) ≤ T(n/5) + T(7n/10) + O(n)

... which is O(n). The algorithm details...

1. divide the list into n/5 subsequences of 5 elements each
2. find the median of each list, by brute force. there will be n/5 of these
3. Let m_1,..., m_n/5 be these medians.
4. recursively find the median of these medians. this will be 1 element, the pivot!

... and some pseudo-code...

MedianOfMedians (A[1],...,A[n]) 
begin
    for i=1 to n/5 do {
        let m_i be the median of A[5i − 4], A[5i − 3],..., A[5i];
    }
    pivot = Select(m1,...,m_n/5, n/10); // the pivot
    return pivot
end

References

• http://en.wikipedia.org/wiki/Selection_algorithm#Linear_general_selection_algorithm_-_Median_of_Medians_algorithm
• Median of Medians in Java
• http://www.cs.berkeley.edu/~luca/w4231/fall99/slides/l3.pdf
• http://www.soe.ucsc.edu/classes/cmps102/Spring05/selectAnalysis.pdf
• http://webee.technion.ac.il/courses/044268/w0809_website/recitations/Median.pdf

I hope this helps.
Hristo

来源：https://stackoverflow.com/questions/5605916/quick-sort-median-selection