Home/ Questions/Q 4254634
In Process

The Archive Base Latest Questions

Editorial Team
  • 0
Asked: 2026-05-21T05:06:39+00:00

As we can choose median of 3 element partitioning to implement quick sort. Likewise

  • 0

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??

Share

Leave an answer

You must login to add an answer.

Need An Account,

1 Answer

  1. Editorial Team

    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

    I hope this helps.
    Hristo

    • 0