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Binomial Queue
#ifndef BINOMIAL_QUEUE_H
#define BINOMIAL_QUEUE_H
#include <iostream>
#include <vector>
#include "dsexceptions.h"
using namespace std;
template <typename Comparable>
class BinomialQueue
{
public:
BinomialQueue( ) : theTrees( DEFAULT_TREES )
{
for( auto & root : theTrees )
root = nullptr;
currentSize = 0;
}
BinomialQueue( const Comparable & item ) : theTrees( 1 ), currentSize{ 1 }
{ theTrees[ 0 ] = new BinomialNode{ item, nullptr, nullptr }; }
BinomialQueue( const BinomialQueue & rhs )
: theTrees( rhs.theTrees.size( ) ),currentSize{ rhs.currentSize }
{
for( int i = 0; i < rhs.theTrees.size( ); ++i )
theTrees[ i ] = clone( rhs.theTrees[ i ] );
}
BinomialQueue( BinomialQueue && rhs )
: theTrees{ std::move( rhs.theTrees ) }, currentSize{ rhs.currentSize } { }
~BinomialQueue( )
{ makeEmpty( ); }
BinomialQueue & operator=( const BinomialQueue & rhs )
{
BinomialQueue copy = rhs;
std::swap( *this, copy );
return *this;
}
BinomialQueue & operator=( BinomialQueue && rhs )
{
std::swap( currentSize, rhs.currentSize );
std::swap( theTrees, rhs.theTrees );
return *this;
}
bool isEmpty( ) const
{ return currentSize == 0; }
const Comparable & findMin( ) const
{
if( isEmpty( ) )
throw UnderflowException{ };
return theTrees[ findMinIndex( ) ]->element;
}
void insert( const Comparable & x )
{ BinomialQueue oneItem{ x }; merge( oneItem ); }
void insert( Comparable && x )
{ BinomialQueue oneItem{ std::move( x ) }; merge( oneItem ); }
void deleteMin( )
{
Comparable x;
deleteMin( x );
}
void deleteMin( Comparable & minItem )
{
if( isEmpty( ) )
throw UnderflowException{ };
int minIndex = findMinIndex( );
minItem = theTrees[ minIndex ]->element;
BinomialNode *oldRoot = theTrees[ minIndex ];
BinomialNode *deletedTree = oldRoot->leftChild;
delete oldRoot;
// Construct H''
BinomialQueue deletedQueue;
deletedQueue.theTrees.resize( minIndex );
deletedQueue.currentSize = ( 1 << minIndex ) - 1;
for( int j = minIndex - 1; j >= 0; --j )
{
deletedQueue.theTrees[ j ] = deletedTree;
deletedTree = deletedTree->nextSibling;
deletedQueue.theTrees[ j ]->nextSibling = nullptr;
}
// Construct H'
theTrees[ minIndex ] = nullptr;
currentSize -= deletedQueue.currentSize + 1;
merge( deletedQueue );
}
void makeEmpty( )
{
currentSize = 0;
for( auto & root : theTrees )
makeEmpty( root );
}
void merge( BinomialQueue & rhs )
{
if( this == &rhs ) // Avoid aliasing problems
return;
currentSize += rhs.currentSize;
if( currentSize > capacity( ) )
{
int oldNumTrees = theTrees.size( );
int newNumTrees = max( theTrees.size( ), rhs.theTrees.size( ) ) + 1;
theTrees.resize( newNumTrees );
for( int i = oldNumTrees; i < newNumTrees; ++i )
theTrees[ i ] = nullptr;
}
BinomialNode *carry = nullptr;
for( int i = 0, j = 1; j <= currentSize; ++i, j *= 2 )
{
BinomialNode *t1 = theTrees[ i ];
BinomialNode *t2 = i < rhs.theTrees.size( ) ? rhs.theTrees[ i ] : nullptr;
int whichCase = t1 == nullptr ? 0 : 1;
whichCase += t2 == nullptr ? 0 : 2;
whichCase += carry == nullptr ? 0 : 4;
switch( whichCase )
{
case 0: /* No trees */
case 1: /* Only this */
break;
case 2: /* Only rhs */
theTrees[ i ] = t2;
rhs.theTrees[ i ] = nullptr;
break;
case 4: /* Only carry */
theTrees[ i ] = carry;
carry = nullptr;
break;
case 3: /* this and rhs */
carry = combineTrees( t1, t2 );
theTrees[ i ] = rhs.theTrees[ i ] = nullptr;
break;
case 5: /* this and carry */
carry = combineTrees( t1, carry );
theTrees[ i ] = nullptr;
break;
case 6: /* rhs and carry */
carry = combineTrees( t2, carry );
rhs.theTrees[ i ] = nullptr;
break;
case 7: /* All three */
theTrees[ i ] = carry;
carry = combineTrees( t1, t2 );
rhs.theTrees[ i ] = nullptr;
break;
}
}
for( auto & root : rhs.theTrees )
root = nullptr;
rhs.currentSize = 0;
}
private:
struct BinomialNode
{
Comparable element;
BinomialNode *leftChild;
BinomialNode *nextSibling;
BinomialNode( const Comparable & e, BinomialNode *lt, BinomialNode *rt )
: element{ e }, leftChild{ lt }, nextSibling{ rt } { }
BinomialNode( Comparable && e, BinomialNode *lt, BinomialNode *rt )
: element{ std::move( e ) }, leftChild{ lt }, nextSibling{ rt } { }
};
const static int DEFAULT_TREES = 1;
vector<BinomialNode *> theTrees; // An array of tree roots
int currentSize; // Number of items in the priority queue
int findMinIndex( ) const
{
int i;
int minIndex;
for( i = 0; theTrees[ i ] == nullptr; ++i )
;
for( minIndex = i; i < theTrees.size( ); ++i )
if( theTrees[ i ] != nullptr &&
theTrees[ i ]->element < theTrees[ minIndex ]->element )
minIndex = i;
return minIndex;
}
int capacity( ) const
{ return ( 1 << theTrees.size( ) ) - 1; }
BinomialNode * combineTrees( BinomialNode *t1, BinomialNode *t2 )
{
if( t2->element < t1->element )
return combineTrees( t2, t1 );
t2->nextSibling = t1->leftChild;
t1->leftChild = t2;
return t1;
}
void makeEmpty( BinomialNode * & t )
{
if( t != nullptr )
{
makeEmpty( t->leftChild );
makeEmpty( t->nextSibling );
delete t;
t = nullptr;
}
}
BinomialNode * clone( BinomialNode * t ) const
{
if( t == nullptr )
return nullptr;
else
return new BinomialNode{ t->element, clone( t->leftChild ), clone( t->nextSibling ) };
}
};
#endif
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