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Add quickselect (#1654)

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* sort: extract partition from quicksort

Extract the partition logic from quicksort into a macro. This allows to
reuse the partition logic for, e.g., the quickselect algorithm.

* sort: implement quickselect

implement Hoare's selection algorithm (quickselect) on the basis of the
already implemented quicksort. Quickselect allows to find the kth
smallest element in a unordered list with an average time complexity of
O(N) (worst case: O(N^2)).

* add quicksort benchmark

Create a top-level benchmarks folder. Add the benchmark implementation
for the quicksort algorithm.

Benchmarks can then be run in the same way as unit tests from the
root folder with:

	c3c compile-benchmarks benchmarks/stdlib/sort
This commit is contained in:
konimarti
2024-12-03 19:27:26 +01:00
committed by GitHub
parent 7381734913
commit 5463c398cb
3 changed files with 216 additions and 32 deletions
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116
lib/std/sort/quicksort.c3
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@@ -13,6 +13,21 @@ macro quicksort(list, cmp = EMPTY_MACRO_SLOT, context = EMPTY_MACRO_SLOT) @built
qs::qsort(<$typeof(list), $typeof(cmp), $typeof(context)>)(list, 0, (isz)len - 1, cmp, context);
}
<*
Select the (k+1)th smallest element in an unordered list using Hoare's
selection algorithm (Quickselect). k should be between 0 and len-1. The data
list will be partially sorted.
@require @is_sortable(list) "The list must be indexable and support .len or .len()"
@require @is_valid_cmp_fn(cmp, list, context) "expected a comparison function which compares values"
@require @is_valid_context(cmp, context) "Expected a valid context"
*>
macro quickselect(list, isz k, cmp = EMPTY_MACRO_SLOT, context = EMPTY_MACRO_SLOT) @builtin
{
usz len = sort::@len_from_list(list);
return qs::qselect(<$typeof(list), $typeof(cmp), $typeof(context)>)(list, 0, (isz)len - 1, k, cmp, context);
}
module std::sort::qs(<Type, CmpFn, Context>);
def ElementType = $typeof(Type{}[0]);
@@ -29,10 +44,6 @@ def Stack = StackElementItem[64] @private;
fn void qsort(Type list, isz low, isz high, CmpFn cmp, Context context)
{
var $has_cmp = @is_valid_macro_slot(cmp);
var $has_context = @is_valid_macro_slot(context);
var $cmp_by_value = $has_cmp &&& $assignable(list[0], $typefrom(CmpFn.paramsof[0].type));
if (low >= 0 && high >= 0 && low < high)
{
Stack stack;
@@ -48,34 +59,7 @@ fn void qsort(Type list, isz low, isz high, CmpFn cmp, Context context)
if (l < h)
{
ElementType pivot = list[l];
while (l < h)
{
$switch
$case $cmp_by_value && $has_context:
while (cmp(list[h], pivot, context) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(list[l], pivot, context) <= 0 && l < h) l++;
$case $cmp_by_value:
while (cmp(list[h], pivot) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(list[l], pivot) <= 0 && l < h) l++;
$case $has_cmp && $has_context:
while (cmp(&list[h], &pivot, context) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(&list[l], &pivot, context) <= 0 && l < h) l++;
$case $has_cmp:
while (cmp(&list[h], &pivot) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(&list[l], &pivot) <= 0 && l < h) l++;
$default:
while (greater_eq(list[h], pivot) && l < h) h--;
if (l < h) list[l++] = list[h];
while (less_eq(list[l], pivot) && l < h) l++;
$endswitch
if (l < h) list[h--] = list[l];
}
list[l] = pivot;
l = @partition(list, l, h, cmp, context);
stack[i + 1].low = l + 1;
stack[i + 1].high = stack[i].high;
stack[i++].high = l;
@@ -91,3 +75,71 @@ fn void qsort(Type list, isz low, isz high, CmpFn cmp, Context context)
}
}
}
<*
@require low <= k "kth smalles element is smaller than lower bounds"
@require k <= high "kth smalles element is larger than upper bounds"
*>
fn ElementType! qselect(Type list, isz low, isz high, isz k, CmpFn cmp, Context context)
{
if (low >= 0 && high >= 0 && low < high)
{
isz l = low;
isz h = high;
isz pivot;
usz max_retries = 64;
while (l <= h && max_retries--)
{
pivot = @partition(list, l, h, cmp, context);
if (k == pivot) return list[k];
if (k < pivot)
{
h = pivot - 1;
}
else
{
l = pivot + 1;
}
}
}
return SearchResult.MISSING?;
}
macro @partition(Type list, isz l, isz h, CmpFn cmp, Context context)
{
var $has_cmp = @is_valid_macro_slot(cmp);
var $has_context = @is_valid_macro_slot(context);
var $cmp_by_value = $has_cmp &&& $assignable(list[0], $typefrom(CmpFn.paramsof[0].type));
ElementType pivot = list[l];
while (l < h)
{
$switch
$case $cmp_by_value && $has_context:
while (cmp(list[h], pivot, context) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(list[l], pivot, context) <= 0 && l < h) l++;
$case $cmp_by_value:
while (cmp(list[h], pivot) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(list[l], pivot) <= 0 && l < h) l++;
$case $has_cmp && $has_context:
while (cmp(&list[h], &pivot, context) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(&list[l], &pivot, context) <= 0 && l < h) l++;
$case $has_cmp:
while (cmp(&list[h], &pivot) >= 0 && l < h) h--;
if (l < h) list[l++] = list[h];
while (cmp(&list[l], &pivot) <= 0 && l < h) l++;
$default:
while (greater_eq(list[h], pivot) && l < h) h--;
if (l < h) list[l++] = list[h];
while (less_eq(list[l], pivot) && l < h) l++;
$endswitch
if (l < h) list[h--] = list[l];
}
list[l] = pivot;
return l;
}