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/*
* Copyright (c) 2023, the SerenityOS developers.
*
* SPDX-License-Identifier: BSD-2-Clause
*/
#pragma once
#include <AK/Math.h>
#include <AK/Random.h>
#include <AK/StdLibExtras.h>
namespace AK {
static constexpr int MEDIAN_OF_MEDIAN_CUTOFF = 4500;
// FIXME: Stole and adapted these two functions from `Userland/Demos/Tubes/Tubes.cpp` we really need something like this in `AK/Random.h`
static inline double random_double()
{
return get_random<u32>() / static_cast<double>(NumericLimits<u32>::max());
}
static inline size_t random_int(size_t min, size_t max)
{
return min + round_to<size_t>(random_double() * (max - min));
}
// Implementations of common pivot functions
namespace PivotFunctions {
// Just use the first element of the range as the pivot
// Mainly used to debug the quick select algorithm
// Good with random data since it has nearly no overhead
// Attention: Turns the algorithm quadratic if used with already (partially) sorted data
template<typename Collection, typename LessThan>
size_t first_element([[maybe_unused]] Collection& collection, size_t left, [[maybe_unused]] size_t right, [[maybe_unused]] LessThan less_than)
{
return left;
}
// Just use the middle element of the range as the pivot
// This is what is used in AK::single_pivot_quick_sort in quicksort.h
// Works fairly well with random Data
// Works incredibly well with sorted data since the pivot is always a perfect split
template<typename Collection, typename LessThan>
size_t middle_element([[maybe_unused]] Collection& collection, size_t left, size_t right, [[maybe_unused]] LessThan less_than)
{
return (left + right) / 2;
}
// Pick a random Pivot
// This is the "Traditional" implementation of both quicksort and quick select
// Performs fairly well both with random and sorted data
template<typename Collection, typename LessThan>
size_t random_element([[maybe_unused]] Collection& collection, size_t left, size_t right, [[maybe_unused]] LessThan less_than)
{
return random_int(left, right);
}
// Implementation detail of median_of_medians
// Whilst this looks quadratic in runtime, it always gets called with 5 or fewer elements so can be considered constant runtime
template<typename Collection, typename LessThan>
size_t partition5(Collection& collection, size_t left, size_t right, LessThan less_than)
{
VERIFY((right - left) <= 5);
for (size_t i = left + 1; i <= right; i++) {
for (size_t j = i; j > left && less_than(collection.at(j), collection.at(j - 1)); j--) {
swap(collection.at(j), collection.at(j - 1));
}
}
return (left + right) / 2;
}
// https://en.wikipedia.org/wiki/Median_of_medians
// Use the median of medians algorithm to pick a really good pivot
// This makes quick select run in linear time but comes with a lot of overhead that only pays off with very large inputs
template<typename Collection, typename LessThan>
size_t median_of_medians(Collection& collection, size_t left, size_t right, LessThan less_than)
{
if ((right - left) < 5)
return partition5(collection, left, right, less_than);
for (size_t i = left; i <= right; i += 5) {
size_t sub_right = i + 4;
if (sub_right > right)
sub_right = right;
size_t median5 = partition5(collection, i, sub_right, less_than);
swap(collection.at(median5), collection.at(left + (i - left) / 5));
}
size_t mid = (right - left) / 10 + left + 1;
// We're using mutual recursion here, using quickselect_inplace to find the pivot for quickselect_inplace.
// Whilst this achieves True linear Runtime, it is a lot of overhead, so use only this variant with very large inputs
return quickselect_inplace(
collection, left, left + ((right - left) / 5), mid, [](auto collection, size_t left, size_t right, auto less_than) { return AK::PivotFunctions::median_of_medians(collection, left, right, less_than); }, less_than);
}
}
// This is the Lomuto Partition scheme which is simpler but less efficient than Hoare's partitioning scheme that is traditionally used with quicksort
// https://en.wikipedia.org/wiki/Quicksort#Lomuto_partition_scheme
template<typename Collection, typename PivotFn, typename LessThan>
static size_t partition(Collection& collection, size_t left, size_t right, PivotFn pivot_fn, LessThan less_than)
{
auto pivot_index = pivot_fn(collection, left, right, less_than);
auto pivot_value = collection.at(pivot_index);
swap(collection.at(pivot_index), collection.at(right));
auto store_index = left;
for (size_t i = left; i < right; i++) {
if (less_than(collection.at(i), pivot_value)) {
swap(collection.at(store_index), collection.at(i));
store_index++;
}
}
swap(collection.at(right), collection.at(store_index));
return store_index;
}
template<typename Collection, typename PivotFn, typename LessThan>
size_t quickselect_inplace(Collection& collection, size_t left, size_t right, size_t k, PivotFn pivot_fn, LessThan less_than)
{
// Bail if left is somehow bigger than right and return default constructed result
// FIXME: This can also occur when the collection is empty maybe propagate this error somehow?
// returning 0 would be a really bad thing since this returns and index and that might lead to memory errors
// returning in ErrorOr<size_t> here might be a good option but this is a very specific error that in nearly all circumstances should be considered a bug on the callers site
VERIFY(left <= right);
// If there's only one element, return that element
if (left == right)
return left;
auto pivot_index = partition(collection, left, right, pivot_fn, less_than);
// we found the thing we were searching for
if (k == pivot_index)
return k;
// Recurse on the left side
if (k < pivot_index)
return quickselect_inplace(collection, left, pivot_index - 1, k, pivot_fn, less_than);
// recurse on the right side
return quickselect_inplace(collection, pivot_index + 1, right, k, pivot_fn, less_than);
}
//
template<typename Collection, typename PivotFn, typename LessThan>
size_t quickselect_inplace(Collection& collection, size_t k, PivotFn pivot_fn, LessThan less_than)
{
return quickselect_inplace(collection, 0, collection.size() - 1, k, pivot_fn, less_than);
}
template<typename Collection, typename PivotFn>
size_t quickselect_inplace(Collection& collection, size_t k, PivotFn pivot_fn)
{
return quickselect_inplace(collection, 0, collection.size() - 1, k, pivot_fn, [](auto& a, auto& b) { return a < b; });
}
// All of these quick select implementation versions return the `index` of the resulting element, after the algorithm has run, not the element itself!
// As Part of the Algorithm, they all modify the collection in place, partially sorting it in the process.
template<typename Collection>
size_t quickselect_inplace(Collection& collection, size_t k)
{
if (collection.size() >= MEDIAN_OF_MEDIAN_CUTOFF)
return quickselect_inplace(
collection, 0, collection.size() - 1, k, [](auto collection, size_t left, size_t right, auto less_than) { return PivotFunctions::median_of_medians(collection, left, right, less_than); }, [](auto& a, auto& b) { return a < b; });
else
return quickselect_inplace(
collection, 0, collection.size() - 1, k, [](auto collection, size_t left, size_t right, auto less_than) { return PivotFunctions::random_element(collection, left, right, less_than); }, [](auto& a, auto& b) { return a < b; });
}
}
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