数据结构-左式堆

复杂度：

实现：

#ifndef LEFTIST_HEAP_H
#define LEFTIST_HEAP_H

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

// Leftist heap class
//
// CONSTRUCTION: with no parameters
//
// ******************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
// void merge( rhs )      --> Absorb rhs into this heap
// ******************ERRORS********************************
// Throws UnderflowException as warranted

template <typename Comparable>
class LeftistHeap
{
  public:
    LeftistHeap( ) : root{ nullptr }
      { }
    LeftistHeap( const LeftistHeap & rhs ) : root{ nullptr }
      { root = clone( rhs.root ); }
    
    LeftistHeap( LeftistHeap && rhs ) : root{ rhs.root }
    {
        rhs.root = nullptr;
    }
    
    ~LeftistHeap( )
      { makeEmpty( ); }
    
    
    /**
     * Deep copy.
     */
    LeftistHeap & operator=( const LeftistHeap & rhs )
    {
        LeftistHeap copy = rhs;
        std::swap( *this, copy );
        return *this;
    }
        
    /**
     * Move.
     */
    LeftistHeap & operator=( LeftistHeap && rhs )
    {
        std::swap( root, rhs.root );
        
        return *this;
    }
    
    /**
     * Returns true if empty, false otherwise.
     */
    bool isEmpty( ) const
      { return root == nullptr; }
    
    /**
     * 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 root->element;
    }

    /**
     * Inserts x; duplicates allowed.
     */
    void insert( const Comparable & x )
      { root = merge( new LeftistNode{ x }, root ); }

    /**
     * Inserts x; duplicates allowed.
     */
    void insert( Comparable && x )
      { root = merge( new LeftistNode{ std::move( x ) }, root ); }

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

        LeftistNode *oldRoot = root;
        root = merge( root->left, root->right );
        delete oldRoot;
    }

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

    /**
     * Make the priority queue logically empty.
     */
    void makeEmpty( )
    {
        reclaimMemory( root );
        root = nullptr;
    }

    /**
     * Merge rhs into the priority queue.
     * rhs becomes empty. rhs must be different from this.
     */
    void merge( LeftistHeap & rhs )
    {
        if( this == &rhs )    // Avoid aliasing problems
            return;

        root = merge( root, rhs.root );
        rhs.root = nullptr;
    }


  private:
    struct LeftistNode
    {
        Comparable   element;
        LeftistNode *left;
        LeftistNode *right;
        int          npl;

        LeftistNode( const Comparable & e, LeftistNode *lt = nullptr,
                        LeftistNode *rt = nullptr, int np = 0 )
          : element{ e }, left{ lt }, right{ rt }, npl{ np } { }
        
        LeftistNode( Comparable && e, LeftistNode *lt = nullptr,
                        LeftistNode *rt = nullptr, int np = 0 )
          : element{ std::move( e ) }, left{ lt }, right{ rt }, npl{ np } { }
    };

    LeftistNode *root;

    /**
     * Internal method to merge two roots.
     * Deals with deviant cases and calls recursive merge1.
     */
    LeftistNode * merge( LeftistNode *h1, LeftistNode *h2 )
    {
        if( h1 == nullptr )
            return h2;
        if( h2 == nullptr )
            return h1;
        if( h1->element < h2->element )
            return merge1( h1, h2 );
        else
            return merge1( h2, h1 );
    }

    /**
     * Internal method to merge two roots.
     * Assumes trees are not empty, and h1's root contains smallest item.
     */
    LeftistNode * merge1( LeftistNode *h1, LeftistNode *h2 )
    {
        if( h1->left == nullptr )   // Single node
            h1->left = h2;       // Other fields in h1 already accurate
        else
        {
            h1->right = merge( h1->right, h2 );
            if( h1->left->npl < h1->right->npl )
                swapChildren( h1 );
            h1->npl = h1->right->npl + 1;
        }
        return h1;
    }

    /**
     * Swaps t's two children.
     */
    void swapChildren( LeftistNode *t )
    {
        LeftistNode *tmp = t->left;
        t->left = t->right;
        t->right = tmp;
    }

    /**
     * Internal method to make the tree empty.
     * WARNING: This is prone to running out of stack space;
     *          exercises suggest a solution.
     */
    void reclaimMemory( LeftistNode *t )
    {
        if( t != nullptr )
        {
            reclaimMemory( t->left );
            reclaimMemory( t->right );
            delete t;
        }
    }
    
    /**
     * Internal method to clone subtree.
     * WARNING: This is prone to running out of stack space.
     *          exercises suggest a solution.
     */
    LeftistNode * clone( LeftistNode *t ) const
    {
        if( t == nullptr )
            return nullptr;
        else
            return new LeftistNode{ t->element, clone( t->left ), clone( t->right ), t->npl };
    }
};

#endif

应用：

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

int main( )
{
    int numItems = 10000;
    LeftistHeap<int> h;
    LeftistHeap<int> h1;
    LeftistHeap<int> h2;
    int i = 37;

    cout << "Begin test..." << endl;
    for( i = 37; i != 0; i = ( i + 37 ) % numItems )
        if( i % 2 == 0 )
            h1.insert( i );
        else
            h.insert( i );
    h.merge( h1 );
    h2 = h;

    for( i = 1; i < numItems; ++i )
    {
        int x;
        h2.deleteMin( x );
        if( x != i )
            cout << "Oops! " << i << endl;
    }

    if( !h1.isEmpty( ) )
        cout << "Oops! h1 should have been empty!" << endl;

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

    return 0;
}