/**
 * \brief Pairing heap datastructure implementation
 *
 * Based on example code in "Data structures and Algorithm Analysis in C++"
 * by Mark Allen Weiss, used and released under the LGPL by permission
 * of the author.
 *
 * No promises about correctness.  Use at your own risk!
 *
 * Authors:
 *   Mark Allen Weiss
 *   Tim Dwyer <tgdwyer@gmail.com>
 *
 * Copyright (C) 2005 Authors
 *
 * Released under GNU LGPL.  Read the file 'COPYING' for more information.
 */

#include <vector>
#include <list>
#include "dsexceptions.h"
#include "PairingHeap.h"

#ifndef PAIRING_HEAP_CPP
#define PAIRING_HEAP_CPP
using namespace std;

/**
* Construct the pairing heap.
*/
template <class T>
PairingHeap<T>::PairingHeap( bool (*lessThan)(T const &lhs, T const &rhs) ) {
  root = NULL;
  counter=0;
  this->lessThan=lessThan;
}


/**
* Copy constructor
*/
template <class T>
PairingHeap<T>::PairingHeap( const PairingHeap<T> & rhs ) {
  root = NULL;
  counter=rhs->size();
  *this = rhs;
}

/**
* Destroy the leftist heap.
*/
template <class T>
PairingHeap<T>::~PairingHeap( ) {
  makeEmpty( );
}

/**
* Insert item x into the priority queue, maintaining heap order.
* Return a pointer to the node containing the new item.
*/
template <class T>
PairNode<T> *
PairingHeap<T>::insert( const T & x ) {
  PairNode<T> *newNode = new PairNode<T>( x );

  if( root == NULL )
    root = newNode;
  else
    compareAndLink( root, newNode );

  counter++;
  return newNode;
}
template <class T>
int PairingHeap<T>::size() {
  return counter;
}
/**
* Find the smallest item in the priority queue.
* Return the smallest item, or throw Underflow if empty.
*/
template <class T>
const T & PairingHeap<T>::findMin( ) const {
  if( isEmpty( ) )
    throw Underflow( );

  return root->element;
}
/**
 * Remove the smallest item from the priority queue.
 * Throws Underflow if empty.
 */
template <class T>
void PairingHeap<T>::deleteMin( ) {
  if( isEmpty( ) )
    throw Underflow( );

  PairNode<T> *oldRoot = root;

  if( root->leftChild == NULL )
    root = NULL;
  else
    root = combineSiblings( root->leftChild );

  counter--;
  delete oldRoot;
}

/**
* Test if the priority queue is logically empty.
* Returns true if empty, false otherwise.
*/
template <class T>
bool PairingHeap<T>::isEmpty( ) const {
  return root == NULL;
}

/**
* Test if the priority queue is logically full.
* Returns false in this implementation.
*/
template <class T>
bool PairingHeap<T>::isFull( ) const {
  return false;
}

/**
* Make the priority queue logically empty.
*/
template <class T>
void PairingHeap<T>::makeEmpty( ) {
  reclaimMemory( root );
  root = NULL;
}

/**
* Deep copy.
*/
template <class T>
const PairingHeap<T> &
PairingHeap<T>::operator=( const PairingHeap<T> & rhs ) {
  if( this != &rhs ) {
    makeEmpty( );
    root = clone( rhs.root );
  }

  return *this;
}

/**
* Internal method to make the tree empty.
* WARNING: This is prone to running out of stack space.
*/
template <class T>
void PairingHeap<T>::reclaimMemory( PairNode<T> * t ) const {
  if( t != NULL ) {
    reclaimMemory( t->leftChild );
    reclaimMemory( t->nextSibling );
    delete t;
  }
}

/**
* Change the value of the item stored in the pairing heap.
* Does nothing if newVal is larger than currently stored value.
* p points to a node returned by insert.
* newVal is the new value, which must be smaller
*    than the currently stored value.
*/
template <class T>
void PairingHeap<T>::decreaseKey( PairNode<T> *p,
                                  const T & newVal ) {
  if( lessThan(p->element,newVal) )
    return;    // newVal cannot be bigger

  p->element = newVal;

  if( p != root ) {
    if( p->nextSibling != NULL )
      p->nextSibling->prev = p->prev;

    if( p->prev->leftChild == p )
      p->prev->leftChild = p->nextSibling;
    else
      p->prev->nextSibling = p->nextSibling;

    p->nextSibling = NULL;
    compareAndLink( root, p );
  }
}

/**
* Internal method that is the basic operation to maintain order.
* Links first and second together to satisfy heap order.
* first is root of tree 1, which may not be NULL.
*    first->nextSibling MUST be NULL on entry.
* second is root of tree 2, which may be NULL.
* first becomes the result of the tree merge.
*/
template <class T>
void PairingHeap<T>::
compareAndLink( PairNode<T> * & first,
                PairNode<T> *second ) const {
  if( second == NULL )
    return;

  if( lessThan(second->element,first->element) ) {
    // Attach first as leftmost child of second
    second->prev = first->prev;
    first->prev = second;
    first->nextSibling = second->leftChild;

    if( first->nextSibling != NULL )
      first->nextSibling->prev = first;

    second->leftChild = first;
    first = second;
  }
  else {
    // Attach second as leftmost child of first
    second->prev = first;
    first->nextSibling = second->nextSibling;

    if( first->nextSibling != NULL )
      first->nextSibling->prev = first;

    second->nextSibling = first->leftChild;

    if( second->nextSibling != NULL )
      second->nextSibling->prev = second;

    first->leftChild = second;
  }
}

/**
* Internal method that implements two-pass merging.
* firstSibling the root of the conglomerate;
*     assumed not NULL.
*/
template <class T>
PairNode<T> *
PairingHeap<T>::combineSiblings( PairNode<T> *firstSibling ) const {
  if( firstSibling->nextSibling == NULL )
    return firstSibling;

  // Allocate the array
  static vector<PairNode<T> *> treeArray( 5 );

  // Store the subtrees in an array
  int numSiblings = 0;

  for( ; firstSibling != NULL; numSiblings++ ) {
    if( numSiblings == (int)treeArray.size( ) )
      treeArray.resize( numSiblings * 2 );

    treeArray[ numSiblings ] = firstSibling;
    firstSibling->prev->nextSibling = NULL;  // break links
    firstSibling = firstSibling->nextSibling;
  }

  if( numSiblings == (int)treeArray.size( ) )
    treeArray.resize( numSiblings + 1 );

  treeArray[ numSiblings ] = NULL;

  // Combine subtrees two at a time, going left to right
  int i = 0;

  for( ; i + 1 < numSiblings; i += 2 )
    compareAndLink( treeArray[ i ], treeArray[ i + 1 ] );

  int j = i - 2;

  // j has the result of last compareAndLink.
  // If an odd number of trees, get the last one.
  if( j == numSiblings - 3 )
    compareAndLink( treeArray[ j ], treeArray[ j + 2 ] );

  // Now go right to left, merging last tree with
  // next to last. The result becomes the new last.
  for( ; j >= 2; j -= 2 )
    compareAndLink( treeArray[ j - 2 ], treeArray[ j ] );

  return treeArray[ 0 ];
}

/**
* Internal method to clone subtree.
* WARNING: This is prone to running out of stack space.
*/
template <class T>
PairNode<T> *
PairingHeap<T>::clone( PairNode<T> * t ) const {
  if( t == NULL )
    return NULL;
  else {
    PairNode<T> *p = new PairNode<T>( t->element );

    if( ( p->leftChild = clone( t->leftChild ) ) != NULL )
      p->leftChild->prev = p;

    if( ( p->nextSibling = clone( t->nextSibling ) ) != NULL )
      p->nextSibling->prev = p;

    return p;
  }
}
template <class T>
ostream& operator <<(ostream &os, const PairingHeap<T> &b) {
  os<<"Heap:";

  if (b.root != NULL) {
    PairNode<T> *r = b.root;
    list<PairNode<T>*> q;
    q.push_back(r);

    while (!q.empty()) {
      r = q.front();
      q.pop_front();

      if (r->leftChild != NULL) {
        os << *r->element << ">";
        PairNode<T> *c = r->leftChild;

        while (c != NULL) {
          q.push_back(c);
          os << "," << *c->element;
          c = c->nextSibling;
        }

        os << "|";
      }
    }
  }

  return os;
}
#endif