/**
* Sorts the specified range of elements according to the natural ascending order using quicksort.
*
* <p>The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
* McIlroy, “Engineering a Sort Function”, <i>Software: Practice and Experience</i>,
* 23(11), pages 1249−1265, 1993.
*
* @param x the big array to be sorted.
* @param from the index of the first element (inclusive) to be sorted.
* @param to the index of the last element (exclusive) to be sorted.
*/
@SuppressWarnings("unchecked")
public static void quickSort(final boolean[][] x, final long from, final long to) {
final long len = to - from;
// Selection sort on smallest arrays
if (len < SMALL) {
selectionSort(x, from, to);
return;
}
// Choose a partition element, v
long m = from + len / 2; // Small arrays, middle element
if (len > SMALL) {
long l = from;
long n = to - 1;
if (len > MEDIUM) { // Big arrays, pseudomedian of 9
long s = len / 8;
l = med3(x, l, l + s, l + 2 * s);
m = med3(x, m - s, m, m + s);
n = med3(x, n - 2 * s, n - s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
final boolean v = get(x, m);
// Establish Invariant: v* (<v)* (>v)* v*
long a = from, b = a, c = to - 1, d = c;
while (true) {
int comparison;
while (b <= c
&& (comparison = (!(get(x, b)) && (v) ? -1 : ((get(x, b)) == (v) ? 0 : 1))) <= 0) {
if (comparison == 0) swap(x, a++, b);
b++;
}
while (c >= b
&& (comparison = (!(get(x, c)) && (v) ? -1 : ((get(x, c)) == (v) ? 0 : 1))) >= 0) {
if (comparison == 0) swap(x, c, d--);
c--;
}
if (b > c) break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
long s, n = to;
s = Math.min(a - from, b - a);
vecSwap(x, from, b - s, s);
s = Math.min(d - c, n - d - 1);
vecSwap(x, b, n - s, s);
// Recursively sort non-partition-elements
if ((s = b - a) > 1) quickSort(x, from, from + s);
if ((s = d - c) > 1) quickSort(x, n - s, n);
}
