数据结构-二叉堆

实现：

#ifndef BINARY_HEAP_H
#define BINARY_HEAP_H

#include "dsexceptions.h"
#include <vector>
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 <typename Comparable>
class BinaryHeap
{
  public:
    explicit BinaryHeap( int capacity = 100 )
      : array( capacity + 1 ), currentSize( 0 )
    {
    }

    explicit BinaryHeap( const vector<Comparable> & 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;
        for( ; hole > 1 && x < array[ hole / 2 ]; hole /= 2 )
            array[ hole ] = array[ hole / 2 ];
        array[ hole ] = x;
    }

    /**
     * Remove the minimum item.
     * Throws UnderflowException if empty.
     */
    void deleteMin( )
    {
        if( isEmpty( ) )
            throw UnderflowException( );

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

    void makeEmpty( )
      { currentSize = 0; }

  private:
    int                currentSize;  // Number of elements in heap
    vector<Comparable> 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 = 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 ] = array[ child ];
            else
                break;
        }
        array[ hole ] = tmp;
    }
};

#endif

测试：

#include <iostream>
#include "BinaryHeap.h"
using namespace std;

    // Test program
int main( )
{
    int numItems = 99999;
    BinaryHeap<int> h;
    int i = 37;
    int x;

    cout << "Begin test... " << endl;

    for( i = 37; i != 0; i = ( i + 37 ) % numItems )
        h.insert( i );
    for( i = 1; i < numItems; i++ )
    {
        h.deleteMin( x );
        if( x != i )
            cout << "Oops! " << i << endl;
    }
    for( i = 37; i != 0; i = ( i + 37 ) % numItems )
        h.insert( i );
    h.insert( 0 );

    cout << "End test... no other output is good" << endl;
    return 0;
}