quickSortHaore<E> function

void quickSortHaore<E>(
  1. List<E> list, {
  2. int? begin,
  3. int? end,
  4. Comparator<E>? compare,
  5. int threshold = 32,
})

Sorts the list of numbers using the quicksort algorithm following Hoare partition scheme with several optimizations.

Parameters

  • list is any list of items to be sorted.
  • To perform partial sorting, you can specify the begin or end.
  • begin is the start index of the range to be sorted.
  • If begin is negative, range starts at the 0
  • If begin is not below the length of the list, range will be empty.
  • end is the final index if the range to be sorted. It is exclusive.
  • If end is above the length of the list, it will be ignored.
  • If end is negative, the absolute value of it will be subtracted from the length of the list to determine where the range ends.
  • If end is not greater than the begin, the range will be empty.
  • compare is a custom compare to order the list elements. If it is null and list items are not Comparable, TypeError is thrown.
  • threshold is the maximum limit for which a range can be sorted using insertion sort.

Optimizations

  1. Using iterative approach to avoid recursion. (function calls are slow)
  2. Keeping stack smaller by tail-call optimization. (reduces memory usage)
  3. Use insertion sort on smaller ranges. (configurable by threshold parameter)
  4. Exclude items equal to the pivot to avoid worst-case performance on list with repeatitive items.
  5. Keeping separate logic for when compare function is provided or not.

Details

Quicksort is a type of divide and conquer algorithm for sorting an array, based on a partitioning routine; the details of this partitioning can vary somewhat, so that quicksort is really a family of closely related algorithms.

Haore partition scheme was proposed by the original developer of quicksort Tony Haore. This scheme selects the item at the middle of the range as pivot, then partitions the list into two parts using two pointers so that all items on the left part is less or equal to the pivot, and all items on the other part is greater or equal to the pivot.

Compared to Lomuto's scheme, this scheme uses less swap operations, which actually helps to speed things up by a lot in dart. You can check the benchmarks for a comparison between these two implementations.

Complexity: Time O(n log n) | Space O(log n)
Worst-case: Time O(n^2) | Space O(log n)

Implementation

void quickSortHaore<E>(
  List<E> list, {
  int? begin,
  int? end,
  Comparator<E>? compare,
  int threshold = 32,
}) {
  int b, e;
  int n = list.length;

  // Find the range given the parameters.
  b = 0;
  e = n;
  if (begin != null && b < begin) {
    b = begin;
  }
  if (end != null && end < e) {
    e = end;
    if (e < 0) e += n;
  }

  // If the range has less than two items, returns immediately.
  if (b + 1 >= e) return;

  // add the range to a stack.
  if (compare == null) {
    quickSortDefault(list, b, e, threshold);
  } else {
    quickSortCustom(list, b, e, threshold, compare);
  }
}