ACK! Sorting to find a median is criminal.
"Introduction to Algorithms" by Thomas H. Cormen, Charles E. Leiserson,
Ronald L. Rivest
ISBN: 0262031418
explains the better algorithm very well.
Here is a freely available C++ template (written by me) for a bunch of
statistics (everything *but* the selection problem):
ftp://cap.connx.com/pub/tournament_software/STATS.HPP
It uses this template for improved summation accuracy:
ftp://cap.connx.com/pub/tournament_software/Kahan.Hpp
Here is an outline for selection. I wrote it in C++, but a rewrite to C
is trivial:
// Quickselect: find Kth smallest of first N items in array A
// recursive routine finds Kth smallest in A[Low..High]
// Etype: must have copy constructor, oeprator=, and operator<
// Nonrecursive driver is omitted.
template < class Etype >
void
QuickSelect (Etype A[], int Low, int High, int k)
{ if (Low + Cutoff > High) InsertionSort (&A[Low], High - Low + 1); else {
// Sort Low, Middle, High int Middle = (Low + High) / 2;
if (A[Middle] < A[Low]) Swap (A[Low], A[Middle]); if (A[High] < A[Low]) Swap (A[Low],
A[High]); if (A[High] < A[Middle]) Swap (A[Middle], A[High]);
// Place pivot at Position High-1 Etype Pivot = A[Middle]; Swap (A[Middle], A[High - 1]);
// Begin partitioning int i, j; for (i = Low, j = High - 1;;) { while (A[++i] < Pivot);
while (Pivot < A[--j]); if (i < j) Swap (A[i], A[j]); else break;
}
// Restore pivot Swap (A[i], A[High - 1]);
// Recurse: only this part changes if (k < i) QuickSelect (A, Low, i - 1, k); else if (k > i)
QuickSelect (A, i + 1, High, k); }
}
template < class Etype >
void
QuickSelect (Etype A[], int N, int k)
{ QuickSelect (A, 0, N - 1, k - 1);
}
If you want to use this stuff to improve statistics with vacuum, be my
guest.
