ListMergeSort.h

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*/
 
#ifndef LIST_MERGE_SORT_H
#define LIST_MERGE_SORT_H
 
/** \file
 * DoubleLinkedList-based Merge Sort
 */
 
#ifndef DOUBLE_LINKED_LIST_H
#include "DoubleLinkedList.h"
#endif // DOUBLE_LINKED_LIST_H
 
namespace Experiment {
  
  /** Do-nothing Metric-collector for major actions done by ListMergeSort.
   *
   * This serves as a placeholder should you wish to perform metrics on a sort.
   *
   * \tparam type of data being sorted
   */
  template<class T>
    class NoSortMetrics {
  public:
    /** a and b are compared */
    void compare(const T& a, const T&b) { }
 
    /** Two items were swapped */
    void swap() { }
 
    /** The sort completed */
    void done() { }
 
    /** Metrics should be reset due to starting a new sort */
    void reset() { }
  };
  
  /** Merge Sort algorithm using lists to hold the data.
   *
   * The real advantage of this class is that sort() taking a DoubleLinkedList
   * will sort without copying the values in the List -- the list will be
   * disassembled and reassembled in the correct order.
   *
   * \tparam T the data type being sorted
   * \tparam Lessor to compare items
   * \tparam Metrics to collect metrics on the sort -- \see NoSortMetrics as an example
   */
  template<class T, class Iterator = T*, class Lessor = std::less<T>, class Metrics = NoSortMetrics<T> >
    class ListMergeSort {
  public:
  /** Convenience typedef of the type of data in the list */
  typedef T value_type;
 
  /** Convenience typedef of the type of list used in this sort */
  typedef DoubleLinkedList<T> DataList;
 
  /** Convenience typedef of the iterator of DataList */
  typedef typename DataList::iterator DataIter;
  
  private:
  /** Convenience typedef of the type of a list of DataList used in this sort */  
  typedef DoubleLinkedList<DataList> ListList;
 
  /** Convenience typedef of the iterator of ListList */
  typedef typename ListList::iterator ListIter;
  
  public:
  
  /** Sort from begin to end by copying.
   *
   * First, this copies all values to temporary storage.  Then it stores.
   * Finally, it copies the results back.
   *
   * This avoids copying values at each stage of the sort as an array-based
   * merge sort would; however, it still copies the values twice.
   *
   * \param begin first value to sort
   * \param end the position after the last value to sort
   */ 
  void sort(const Iterator begin, const Iterator end) {
    if(end == begin) {
      return;
    }
    
    // Load initial list
    ListList listA;
    for(Iterator iter = begin; iter != end; ++iter) {
      listA.push_back(DataList());
      ListIter added = listA.end() - 1;
      added->push_back(*iter);
    }
    
    // Create second ListList, location flag, and merge
    ListList listB;
    bool dataInListA = true;
    DataList& sorted = mergeSort(listA, listB, dataInListA);
    // NOTE: listA, listB and dataInListA must stay in scope with sorted
    
    // Overwrite original list
    {
      Iterator originalIter = begin;
      DataIter sortedIter = sorted.begin();
      for( ; originalIter != end && sorted.end() != sortedIter; ++originalIter, ++sortedIter) {
    *originalIter = *sortedIter; 
      }
 
      // We should do something to ensure we ddidn't lose values...
    }
    metrics.done();
  }
 
  /** Sort the values in data in constant memory by removing the disassembling
   * data, sorting the values and reassembling it.
   */
  void sort(DataList& data) {
    if(data.isEmpty() || data.end() == data.begin() + 1) {
      return;
    }
    
    // Remove from argument
    ListList listA;
    for(Iterator iter = data.begin(); data.end() != data.begin(); iter = data.begin()) {
      listA.push_back(DataList());
      ListIter added = listA.end() - 1;
      DataIter dest = added->end();
      moveBefore(iter, dest);
    }
 
    // Create second ListList, location flag, and merge
    ListList listB;
    bool dataInListA = true;
    DataList& sorted = mergeSort(listA, listB, dataInListA);
    // NOTE: listA, listB and dataInListA must stay in scope with sorted
 
    // Populate argument
    moveAll(sorted, data);
  }
 
  private:
 
  /** merge listA and listB such that which list data is in at the start and
   * end is determined by dataInListA.
   *
   * listA and listB each contain DataLists.
   *
   * At the start of each round of merging, the one used for input has N > 1 
   * DataLists with the first N-1 of length M and the last of length <M. 
   * Merging will move the data back and for between each of listA
   * and listB.  After each pass of merging, the one merged into will have N/2
   * (rounded up) DataLists.
   * 
   * Upon completion, the list with data will have one DataList -- the results.
   *
   * \param listA to be used in merge sorting and, if dataInListA contains the data to be merged
   * \param listB to be used in merge sorting and, if dataInListB contains the data to be merged
   *
   * \return convenience reference to the final DataList which is the only
   * element contained in (dataIsInListA ? listA or listB).
   *
   * \note The return value is \code *(dataInListA ? listA : listB).begin(); \endcode
   * This means that all three arguments must remain in scope for the return value to
   * remain valid.
   */
  DataList& mergeSort(ListList& listA, ListList& listB, bool& dataInListA) {
    metrics.reset();
    while(true) {
      ListList& input = dataInListA ? listA : listB;
      ListList& output = dataInListA ? listB : listA;
       
      if(input.end() == input.begin() + 1) {
    break;
      }
       
      dataInListA = ! dataInListA;
      mergeLists(input, output);
    }
     
    return *(dataInListA ? listA : listB).begin();
  }
 
  /** Perform one iteration of merging of sequential pairs of lists in input
   * to ouput.
   *
   * Each pair of lists in input is merged to a single list in output.  If 
   * input has an odd number of lists, the last list is moved in without
   * any merge necessary.
   *
   * \param input List of sequential pairs of sorted DataList to merge together
   * \param output the list to write the output DataLists to.
   */
  void mergeLists(ListList& input, ListList& output) {
    output.clear();
    // Pass across input list
    ListIter listIter = input.begin();
    while(input.end() != listIter) {
      // Create new DataList for merge(DataList, DataList) -> DataList
      output.push_back(DataList());
      ListIter current = output.end() - 1;
     
      // Grab next one or two (if available) from input
      ListIter first = listIter;
      ++listIter;
     
      ListIter second = listIter;
      ++listIter;
     
      // Merge the one and possible second list together
      if(input.end() == second) {
    // No second list, copy first as new entry in output
    moveAll(*first, *current);
      } else {
    // Two lists, just merge them
    mergeTwo(*first, *second, *current);
      }
    }
  }
 
  /** Merge two sorted DataList elements, first and second, into out
   *
   * \param first DataList to merge with second into out
   * \param second DataList to merge with first into out
   * \param out DataList containing the merge sort of first and second
   */
  void mergeTwo(DataList& first, DataList& second, DataList& out) {
    // Merge first and second into new entry in output
    DataIter dest = out.end();
    while(!first.isEmpty() && !second.isEmpty()) {
      DataIter firstIter = first.begin();
      DataIter secondIter = second.begin();
      metrics.compare(*firstIter, *secondIter);
      if(lessor(*firstIter, *secondIter)) {
    metrics.swap();
    moveBefore(firstIter, dest);
      } else {
    moveBefore(secondIter, dest);
      }
    }
 
    // When first or second is empty, we 'merge' by moving the remaining values
    // of the other to the end of out.
    moveAll(first, out);
    moveAll(second, out);
  }
 
  /** Move all values from from to the end of to
   *
   * \param from to move all values, if any, to the end of to
   * \param to to move all values, if any, from from to the end of
   */
  void moveAll(DataList& from, DataList& to) {
    while(!from.isEmpty()) {
      DataIter iter = from.begin();
      DataIter dest = to.end();
      moveBefore(iter, dest);
    }
  }
 
  private:
  /** Comparator to decide if one value is less than another */
  Lessor lessor;
 
  public:
  /** Collection of metrics for the caller to inspect details of the sort */
  Metrics metrics;
  };
 
} // namespace Experiment
 
#endif // LIST_MERGE_SORT_H