AK: Change pivot selection of dual_pivot_quick_sort

Picking the first and last elements as pivots makes it so that
a sorted array is the worst-case input for the algorithm.

This change instead picks pivots at approximately 1/3 and 2/3 in
the array. This results in desired performance for sorted arrays.

Of course this only changes which inputs result in worst-case
performance, but hopefully those inputs occur less frequently than
already sorted arrays.

AK/QuickSort.h

@@ -18,13 +18,24 @@ namespace AK {
 template<typename Collection, typename LessThan>
 void dual_pivot_quick_sort(Collection& col, int start, int end, LessThan less_than)
 {
- if (start >= end) {
+ int size = end - start + 1;
+ if (size <= 1) {
  return;
  }
 
- int left_pointer, right_pointer;
- if (!less_than(col[start], col[end])) {
- swap(col[start], col[end]);
+ if (size > 3) {
+ int third = size / 3;
+ if (less_than(col[start + third], col[end - third])) {
+ swap(col[start + third], col[start]);
+ swap(col[end - third], col[end]);
+ } else {
+ swap(col[start + third], col[end]);
+ swap(col[end - third], col[start]);
+ }
+ } else {
+ if (!less_than(col[start], col[end])) {
+ swap(col[start], col[end]);
+ }
  }
 
  int j = start + 1;
@@ -57,8 +68,8 @@ void dual_pivot_quick_sort(Collection& col, int start, int end, LessThan less_th
  swap(col[start], col[j]);
  swap(col[end], col[g]);
 
- left_pointer = j;
- right_pointer = g;
+ int left_pointer = j;
+ int right_pointer = g;
 
  dual_pivot_quick_sort(col, start, left_pointer - 1, less_than);
  dual_pivot_quick_sort(col, left_pointer + 1, right_pointer - 1, less_than);