pairing_heap.h

/*
 * vim: ts=4 sw=4 et tw=0 wm=0
 *
 * libvpsc - A solver for the problem of Variable Placement with 
 *           Separation Constraints.
 *
 * Copyright (C) 2005  Mark Allen Weiss
 * Copyright (C) 2005-2008  Monash University
 *
 * ----------------------------------------------------------------------------
 * 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!
 * ----------------------------------------------------------------------------
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 * See the file LICENSE.LGPL distributed with the library.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *
 * Author(s):  Mark Allen Weiss
 *             Tim Dwyer
*/

#ifndef VPSC_PAIRING_HEAP_H
#define VPSC_PAIRING_HEAP_H

#include <cstdlib>
#include <fstream>
#include <vector>
#include <list>

#include "libvpsc/assertions.h"

class Underflow { };

// Pairing heap class
//
// CONSTRUCTION: with no parameters
//
// ******************PUBLIC OPERATIONS*********************
// PairNode & insert( x ) --> Insert x
// deleteMin( minItem )   --> Remove (and optionally return) smallest item
// T findMin( )  --> Return smallest item
// bool isEmpty( )        --> Return true if empty; else false
// void makeEmpty( )      --> Remove all items
// void decreaseKey( PairNode p, newVal )
//                        --> Decrease value in node p
// ******************ERRORS********************************
// Throws Underflow as warranted


template <class T>
struct PairNode
{
        T   element;
        PairNode    *leftChild;
        PairNode    *nextSibling;
        PairNode    *prev;

        PairNode( const T & theElement ) :
                element( theElement ),
                leftChild(nullptr), nextSibling(nullptr), prev(nullptr)
        { }
};

template <class T, class TCompare>
class PairingHeap;

template <class T,class TCompare>
std::ostream& operator <<(std::ostream &os, const PairingHeap<T,TCompare> &b);

template <class T, class TCompare = std::less<T> >
class PairingHeap
{
#ifndef SWIG
        friend std::ostream& operator<< <T,TCompare> (std::ostream &os, const PairingHeap<T,TCompare> &b);
#endif
public:
        PairingHeap() : root(nullptr), counter(0), siblingsTreeArray(5) { }
        PairingHeap(const PairingHeap & rhs) { 
                // uses operator= to make deep copy
                *this = rhs; 
        }
        ~PairingHeap() { makeEmpty(); }
        const PairingHeap & operator=( const PairingHeap & rhs );
        bool isEmpty() const { return root == nullptr; }
        unsigned size() const { return counter; }
        PairNode<T> *insert( const T & x );
        const T & findMin( ) const;
        void deleteMin( );
        const T extractMin( ) {
                T v = findMin();
                deleteMin();
                return v;
        }
        void makeEmpty() {
                reclaimMemory(root);
                root = nullptr;
                counter = 0;
        }
        void decreaseKey( PairNode<T> *p, const T & newVal );
        void merge( PairingHeap<T,TCompare> *rhs );
protected:
        // Destructively gets the root for merging into another heap.
        PairNode<T> * removeRootForMerge(unsigned& size) {
                PairNode<T> *r=root;
                root=nullptr;
                size=counter;
                counter=0;
                return r;
        }
        TCompare lessThan;
private:
        PairNode<T> *root;
        unsigned counter;

    // Used by PairingHeap::combineSiblings().  We keep this as member 
    // variable to save some vector resize operations during subsequent uses.
        std::vector<PairNode<T> *> siblingsTreeArray;

        void reclaimMemory( PairNode<T> *t ) const;
        void compareAndLink( PairNode<T> * & first, PairNode<T> *second ) const;
        PairNode<T> * combineSiblings( PairNode<T> *firstSibling );
        PairNode<T> * clone( PairNode<T> * t ) const;
};


template <class T,class TCompare>
PairNode<T> *
PairingHeap<T,TCompare>::insert( const T & x )
{
        PairNode<T> *newNode = new PairNode<T>( x );

        if( root == nullptr )
                root = newNode;
        else
                compareAndLink( root, newNode );
        counter++;
        return newNode;
}

template <class T,class TCompare>
const T & PairingHeap<T,TCompare>::findMin( ) const
{
        if( isEmpty( ) )
                throw Underflow( );
        return root->element;
}
template <class T,class TCompare>
void PairingHeap<T,TCompare>::deleteMin( )
{
    if( isEmpty( ) )
        throw Underflow( );

    PairNode<T> *oldRoot = root;

    if( root->leftChild == nullptr )
        root = nullptr;
    else
        root = combineSiblings( root->leftChild );
    COLA_ASSERT(counter);
    counter--;
    delete oldRoot;
}

template <class T,class TCompare>
const PairingHeap<T,TCompare> &
PairingHeap<T,TCompare>::operator=( const PairingHeap<T,TCompare> & rhs )
{
        if( this != &rhs )
        {
                makeEmpty( );
                root = clone( rhs.root );
                counter = rhs.size();
        }

        return *this;
}

template <class T,class TCompare>
void PairingHeap<T,TCompare>::reclaimMemory( PairNode<T> * t ) const
{
        if( t != nullptr )
        {
                reclaimMemory( t->leftChild );
                reclaimMemory( t->nextSibling );
                delete t;
        }
}

template <class T,class TCompare>
void PairingHeap<T,TCompare>::decreaseKey( PairNode<T> *p,
                                  const T & newVal )
{
        COLA_ASSERT(!lessThan(p->element,newVal)); // newVal cannot be bigger
        p->element = newVal;
        if( p != root )
        {
                if( p->nextSibling != nullptr )
                        p->nextSibling->prev = p->prev;
                if( p->prev->leftChild == p )
                        p->prev->leftChild = p->nextSibling;
                else
                        p->prev->nextSibling = p->nextSibling;

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

template <class T,class TCompare>
void PairingHeap<T,TCompare>::merge( PairingHeap<T,TCompare> *rhs )
{       
        unsigned rhsSize;
        PairNode<T> *broot=rhs->removeRootForMerge(rhsSize);
        if (root == nullptr) {
                root = broot; 
        } else {
                compareAndLink(root, broot);
        }
        counter+=rhsSize;
}

template <class T,class TCompare>
void PairingHeap<T,TCompare>::
compareAndLink( PairNode<T> * & first,
                PairNode<T> *second ) const
{
        if( second == nullptr )
                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 != nullptr )
                        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 != nullptr )
                        first->nextSibling->prev = first;
                second->nextSibling = first->leftChild;
                if( second->nextSibling != nullptr )
                        second->nextSibling->prev = second;
                first->leftChild = second;
        }
}

template <class T,class TCompare>
PairNode<T> *
PairingHeap<T,TCompare>::combineSiblings( PairNode<T> *firstSibling )
{
        if( firstSibling->nextSibling == nullptr )
                return firstSibling;

        // Store the subtrees in an array
        int numSiblings = 0;
        for( ; firstSibling != nullptr; numSiblings++ )
        {
                if( numSiblings == (int)siblingsTreeArray.size( ) )
                        siblingsTreeArray.resize( numSiblings * 2 );
                siblingsTreeArray[ numSiblings ] = firstSibling;
                firstSibling->prev->nextSibling = nullptr;  // break links
                firstSibling = firstSibling->nextSibling;
        }
        if( numSiblings == (int)siblingsTreeArray.size( ) )
                siblingsTreeArray.resize( numSiblings + 1 );
        siblingsTreeArray[ numSiblings ] = nullptr;

        // Combine subtrees two at a time, going left to right
        int i = 0;
        for( ; i + 1 < numSiblings; i += 2 )
                compareAndLink( siblingsTreeArray[ i ], siblingsTreeArray[ 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( siblingsTreeArray[ j ], siblingsTreeArray[ 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( siblingsTreeArray[ j - 2 ], siblingsTreeArray[ j ] );
        return siblingsTreeArray[ 0 ];
}

template <class T,class TCompare>
PairNode<T> *
PairingHeap<T,TCompare>::clone( PairNode<T> * t ) const
{
        if( t == nullptr ) 
                return nullptr;
        else
        {
                PairNode<T> *p = new PairNode<T>( t->element );
                if( ( p->leftChild = clone( t->leftChild ) ) != nullptr )
                        p->leftChild->prev = p;
                if( ( p->nextSibling = clone( t->nextSibling ) ) != nullptr )
                        p->nextSibling->prev = p;
                return p;
        }
}

template <class T,class TCompare>
std::ostream& operator <<(std::ostream &os, const PairingHeap<T,TCompare> &b)
{
        os<<"Heap:";
        if (b.root != nullptr) {
                PairNode<T> *r = b.root;
                std::list<PairNode<T>*> q;
                q.push_back(r);
                while (!q.empty()) {
                        r = q.front();
                        q.pop_front();
                        if (r->leftChild != nullptr) {
                                os << *r->element << ">";
                                PairNode<T> *c = r->leftChild;
                                while (c != nullptr) {
                                        q.push_back(c);
                                        os << "," << *c->element;
                                        c = c->nextSibling;
                                }
                                os << "|";
                        }
                }
        }
        return os;
}

#endif /* VPSC_PAIRING_HEAP_H */