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Write valid C++ code to modify the class BinaryHeap listed below to support the

ID: 3819750 • Letter: W

Question

Write valid C++ code to modify the class BinaryHeap listed below to support the following operations:

(a) decreaseKey(p, d) - Lowers the value of the item at position p by a positive amount d.

(b) increaseKey(p, d) - Increases the value of the item at position p by a positive amount d.

(c) remove(p) - Removes the node at position p.

Also write code to test your routines above. Thank you!

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#ifndef BINARY_HEAP_H
#define BINARY_HEAP_H

#include "dsexceptions.h"
#include
using namespace std;

// BinaryHeap class
//
// CONSTRUCTION: with an optional capacity (that defaults to 100)
//
// ******************PUBLIC OPERATIONS*********************
// void insert( x )       --> Insert x
// deleteMin( minItem )   --> Remove (and optionally return) smallest item
// Comparable findMin( ) --> Return smallest item
// bool isEmpty( )        --> Return true if empty; else false
// void makeEmpty( )      --> Remove all items
// ******************ERRORS********************************
// Throws UnderflowException as warranted

template
class BinaryHeap
{
public:
    explicit BinaryHeap( int capacity = 100 )
      : array( capacity + 1 ), currentSize{ 0 }
    {
    }

    explicit BinaryHeap( const vector & items )
      : array( items.size( ) + 10 ), currentSize{ items.size( ) }
    {
        for( int i = 0; i < items.size( ); ++i )
            array[ i + 1 ] = items[ i ];
        buildHeap( );
    }

    bool isEmpty( ) const
      { return currentSize == 0; }

    /**
     * Find the smallest item in the priority queue.
     * Return the smallest item, or throw Underflow if empty.
     */
    const Comparable & findMin( ) const
    {
        if( isEmpty( ) )
            throw UnderflowException{ };
        return array[ 1 ];
    }
  
    /**
     * Insert item x, allowing duplicates.
     */
    void insert( const Comparable & x )
    {
        if( currentSize == array.size( ) - 1 )
            array.resize( array.size( ) * 2 );

            // Percolate up
        int hole = ++currentSize;
        Comparable copy = x;
      
        array[ 0 ] = std::move( copy );
        for( ; x < array[ hole / 2 ]; hole /= 2 )
            array[ hole ] = std::move( array[ hole / 2 ] );
        array[ hole ] = std::move( array[ 0 ] );
    }
  

    /**
     * Insert item x, allowing duplicates.
     */
    void insert( Comparable && x )
    {
        if( currentSize == array.size( ) - 1 )
            array.resize( array.size( ) * 2 );

            // Percolate up
        int hole = ++currentSize;
        for( ; hole > 1 && x < array[ hole / 2 ]; hole /= 2 )
            array[ hole ] = std::move( array[ hole / 2 ] );
        array[ hole ] = std::move( x );
    }
  
    /**
     * Remove the minimum item.
     * Throws UnderflowException if empty.
     */
    void deleteMin( )
    {
        if( isEmpty( ) )
            throw UnderflowException{ };

        array[ 1 ] = std::move( array[ currentSize-- ] );
        percolateDown( 1 );
    }

    /**
     * Remove the minimum item and place it in minItem.
     * Throws Underflow if empty.
     */
    void deleteMin( Comparable & minItem )
    {
        if( isEmpty( ) )
            throw UnderflowException{ };

        minItem = std::move( array[ 1 ] );
        array[ 1 ] = std::move( array[ currentSize-- ] );
        percolateDown( 1 );
    }

    void makeEmpty( )
      { currentSize = 0; }

private:
    int                currentSize; // Number of elements in heap
    vector array;        // The heap array

    /**
     * Establish heap order property from an arbitrary
     * arrangement of items. Runs in linear time.
     */
    void buildHeap( )
    {
        for( int i = currentSize / 2; i > 0; --i )
            percolateDown( i );
    }

    /**
     * Internal method to percolate down in the heap.
     * hole is the index at which the percolate begins.
     */
    void percolateDown( int hole )
    {
        int child;
        Comparable tmp = std::move( array[ hole ] );

        for( ; hole * 2 <= currentSize; hole = child )
        {
            child = hole * 2;
            if( child != currentSize && array[ child + 1 ] < array[ child ] )
                ++child;
            if( array[ child ] < tmp )
                array[ hole ] = std::move( array[ child ] );
            else
                break;
        }
        array[ hole ] = std::move( tmp );
    }
};

#endif

Explanation / Answer

#ifndef BINARY_HEAP_H
#define BINARY_HEAP_H

#include "dsexceptions.h"
#include
using namespace std;

// BinaryHeap class
//
// CONSTRUCTION: with an optional capacity (that defaults to 100)
//
// ******************PUBLIC OPERATIONS*********************
// void insert( x )       --> Insert x
// deleteMin( minItem )   --> Remove (and optionally return) smallest item
// Comparable findMin( ) --> Return smallest item
// bool isEmpty( )        --> Return true if empty; else false
// void makeEmpty( )      --> Remove all items
// ******************ERRORS********************************
// Throws UnderflowException as warranted

template
class BinaryHeap
{
public:
    explicit BinaryHeap( int capacity = 100 )
      : array( capacity + 1 ), currentSize{ 0 }
    {
    }

    explicit BinaryHeap( const vector & items )
      : array( items.size( ) + 10 ), currentSize{ items.size( ) }
    {
        for( int i = 0; i < items.size( ); ++i )
            array[ i + 1 ] = items[ i ];
        buildHeap( );
    }

    bool isEmpty( ) const
      { return currentSize == 0; }

    /**
     * Find the smallest item in the priority queue.
     * Return the smallest item, or throw Underflow if empty.
     */
    const Comparable & findMin( ) const
    {
        if( isEmpty( ) )
            throw UnderflowException{ };
        return array[ 1 ];
    }
  
    /**
     * Insert item x, allowing duplicates.
     */
    void insert( const Comparable & x )
    {
        if( currentSize == array.size( ) - 1 )
            array.resize( array.size( ) * 2 );

            // Percolate up
        int hole = ++currentSize;
        Comparable copy = x;
      
        array[ 0 ] = std::move( copy );
        for( ; x < array[ hole / 2 ]; hole /= 2 )
            array[ hole ] = std::move( array[ hole / 2 ] );
        array[ hole ] = std::move( array[ 0 ] );
    }
  

    /**
     * Insert item x, allowing duplicates.
     */
    void insert( Comparable && x )
    {
        if( currentSize == array.size( ) - 1 )
            array.resize( array.size( ) * 2 );

            // Percolate up
        int hole = ++currentSize;
        for( ; hole > 1 && x < array[ hole / 2 ]; hole /= 2 )
            array[ hole ] = std::move( array[ hole / 2 ] );
        array[ hole ] = std::move( x );
    }
  
    /**
     * Remove the minimum item.
     * Throws UnderflowException if empty.
     */
    void deleteMin( )
    {
        if( isEmpty( ) )
            throw UnderflowException{ };

        array[ 1 ] = std::move( array[ currentSize-- ] );
        percolateDown( 1 );
    }

    /**
     * Remove the minimum item and place it in minItem.
     * Throws Underflow if empty.
     */
    void deleteMin( Comparable & minItem )
    {
        if( isEmpty( ) )
            throw UnderflowException{ };

        minItem = std::move( array[ 1 ] );
        array[ 1 ] = std::move( array[ currentSize-- ] );
        percolateDown( 1 );
    }

    void makeEmpty( )
      { currentSize = 0; }

private:
    int                currentSize; // Number of elements in heap
    vector array;        // The heap array

    /**
     * Establish heap order property from an arbitrary
     * arrangement of items. Runs in linear time.
     */
    void buildHeap( )
    {
        for( int i = currentSize / 2; i > 0; --i )
            percolateDown( i );
    }

    /**
     * Internal method to percolate down in the heap.
     * hole is the index at which the percolate begins.
     */
    void percolateDown( int hole )
    {
        int child;
        Comparable tmp = std::move( array[ hole ] );

        for( ; hole * 2 <= currentSize; hole = child )
        {
            child = hole * 2;
            if( child != currentSize && array[ child + 1 ] < array[ child ] )
                ++child;
            if( array[ child ] < tmp )
                array[ hole ] = std::move( array[ child ] );
            else
                break;
        }
        array[ hole ] = std::move( tmp );
    }
};

#endif