quickSort.h

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/*
MIT License
 
Copyright (c) 2021 Brian T. Park
 
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
 
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
 
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
 
#ifndef ACE_SORTING_QUICK_SORT_H
#define ACE_SORTING_QUICK_SORT_H
 
#include "swap.h"
 
#if ! defined(ACE_SORTING_DIRECT_QUICK_SORT)
 
  #define ACE_SORTING_DIRECT_QUICK_SORT 1
#endif
 
namespace ace_sorting {
 
#if ACE_SORTING_DIRECT_QUICK_SORT
template <typename T>
void quickSortMiddle(T data[], uint16_t n) {
  if (n <= 1) return;
 
  T pivot = data[n / 2];
  T* left = data;
  T* right = data + n - 1;
 
  while (left <= right) {
    if (*left < pivot) {
      left++;
    } else if (pivot < *right) {
      right--;
    } else {
      swap(*left, *right);
      left++;
      right--;
    }
  }
 
  quickSortMiddle(data, right - data + 1);
  quickSortMiddle(left, data + n - left);
}
#else
template <typename T>
void quickSortMiddle(T data[], uint16_t n) {
  // This lambda expression does not perform any captures, so the compiler ought
  // to be able to optimize and inline the less-than expression. However, the
  // optimization does not seem to work, probably because of the recursive call
  // into itself. So we set ACE_SORTING_DIRECT_QUICK_SORT=1 to use the direct
  // inlined version.
  auto&& lessThan = [](const T& a, const T& b) -> bool { return a < b; };
  quickSortMiddle(data, n, lessThan);
}
#endif
 
template <typename T, typename F>
void quickSortMiddle(T data[], uint16_t n, F&& lessThan) {
  if (n <= 1) return;
 
  T pivot = data[n / 2];
  T* left = data;
  T* right = data + n - 1;
 
  while (left <= right) {
    if (lessThan(*left, pivot)) {
      left++;
    } else if (lessThan(pivot, *right)) {
      right--;
    } else {
      swap(*left, *right);
      left++;
      right--;
    }
  }
 
  quickSortMiddle(data, right - data + 1, lessThan);
  quickSortMiddle(left, data + n - left, lessThan);
}
 
//-----------------------------------------------------------------------------
 
#if ACE_SORTING_DIRECT_QUICK_SORT
template <typename T>
void quickSortMedian(T data[], uint16_t n) {
  if (n <= 1) return;
 
  // Select the median of data[low], data[mid], and data[high] as the estimate
  // of the ideal pivot. Don't swap (low, mid) or (mid, high) (compare that
  // quickSortMedianSwapped()) to save flash memory. They will get swapped in
  // the partitioning while-loop below.
  uint16_t mid = n / 2;
  T pivot = data[mid];
  if (data[n - 1] < data[0]) {
    swap(data[0], data[n - 1]);
  }
  if (pivot < data[0]) {
    pivot = data[0];
  } else if (data[n - 1] < pivot) {
    pivot = data[n - 1];
  }
 
  T* left = data;
  T* right = data + n - 1;
 
  while (left <= right) {
    if (*left < pivot) {
      left++;
    } else if (pivot < *right) {
      right--;
    } else {
      swap(*left, *right);
      left++;
      right--;
    }
  }
 
  quickSortMedian(data, right - data + 1);
  quickSortMedian(left, data + n - left);
}
#else
template <typename T>
void quickSortMedian(T data[], uint16_t n) {
  // This lambda expression does not perform any captures, so the compiler will
  // optimize and inline the less-than expression.
  auto&& lessThan = [](const T& a, const T& b) -> bool { return a < b; };
  quickSortMedian(data, n, lessThan);
}
#endif
 
template <typename T, typename F>
void quickSortMedian(T data[], uint16_t n, F&& lessThan) {
  if (n <= 1) return;
 
  // Select the median of data[low], data[mid], and data[high] as the estimate
  // of the ideal pivot. Don't swap (low, mid) or (mid, high) (compare that
  // quickSortMedianSwapped()) to save flash memory. They will get swapped in
  // the partitioning while-loop below.
  uint16_t mid = n / 2;
  T pivot = data[mid];
  if (lessThan(data[n - 1], data[0])) {
    swap(data[0], data[n - 1]);
  }
  if (lessThan(pivot, data[0])) {
    pivot = data[0];
  } else if (lessThan(data[n - 1], pivot)) {
    pivot = data[n - 1];
  }
 
  T* left = data;
  T* right = data + n - 1;
 
  while (left <= right) {
    if (lessThan(*left, pivot)) {
      left++;
    } else if (lessThan(pivot, *right)) {
      right--;
    } else {
      swap(*left, *right);
      left++;
      right--;
    }
  }
 
  quickSortMedian(data, right - data + 1, lessThan);
  quickSortMedian(left, data + n - left, lessThan);
}
 
//-----------------------------------------------------------------------------
 
#if ACE_SORTING_DIRECT_QUICK_SORT
template <typename T>
void quickSortMedianSwapped(T data[], uint16_t n) {
  if (n <= 1) return;
 
  // Select the median of data[low], data[mid], and data[high] as the estimate
  // of the ideal pivot. In the process, the (low, mid, high) become sorted.
  uint16_t mid = n / 2;
  T pivot = data[mid];
  if (data[n - 1] < data[0]) {
    swap(data[0], data[n - 1]);
  }
  if (pivot < data[0]) {
    swap(data[0], data[mid]);
  } else if (data[n - 1] < pivot) {
    swap(data[mid], data[n - 1]);
  }
  pivot = data[mid];
 
  // We can skip the low and high because they are already sorted.
  T* left = data + 1;
  T* right = data + n - 2;
 
  while (left <= right) {
    if (*left < pivot) {
      left++;
    } else if (pivot < *right) {
      right--;
    } else {
      swap(*left, *right);
      left++;
      right--;
    }
  }
 
  quickSortMedianSwapped(data, right - data + 1);
  quickSortMedianSwapped(left, data + n - left);
}
#else
template <typename T>
void quickSortMedianSwapped(T data[], uint16_t n) {
  // This lambda expression does not perform any captures, so the compiler will
  // optimize and inline the less-than expression.
  auto&& lessThan = [](const T& a, const T& b) -> bool { return a < b; };
  quickSortMedianSwapped(data, n, lessThan);
}
#endif
 
template <typename T, typename F>
void quickSortMedianSwapped(T data[], uint16_t n, F&& lessThan) {
  if (n <= 1) return;
 
  // Select the median of data[low], data[mid], and data[high] as the estimate
  // of the ideal pivot. In the process, the (low, mid, high) become sorted.
  uint16_t mid = n / 2;
  T pivot = data[mid];
  if (lessThan(data[n - 1], data[0])) {
    swap(data[0], data[n - 1]);
  }
  if (lessThan(pivot, data[0])) {
    swap(data[0], data[mid]);
  } else if (lessThan(data[n - 1], pivot)) {
    swap(data[mid], data[n - 1]);
  }
  pivot = data[mid];
 
  // We can skip the low and high because they are already sorted.
  T* left = data + 1;
  T* right = data + n - 2;
 
  while (left <= right) {
    if (lessThan(*left, pivot)) {
      left++;
    } else if (lessThan(pivot, *right)) {
      right--;
    } else {
      swap(*left, *right);
      left++;
      right--;
    }
  }
 
  quickSortMedianSwapped(data, right - data + 1, lessThan);
  quickSortMedianSwapped(left, data + n - left, lessThan);
}
 
}
 
#endif