问题描述：

在计算机科学中，并查集是一种树型的数据结构，其保持着用于处理一些不相交集合（Disjoint Sets）的合并及查询问题。有一个联合-查找算法（union-find algorithm）定义了两个操作用于此数据结构：

Find：确定元素属于哪一个子集。它可以被用来确定两个元素是否属于同一子集；

Union：将两个子集合并成同一个集合；

实现并查集的关键是实现union-find algorithm, 本文根据常用的四种算法，实现了这个类，具体算法实现请参看*；

制造测试数据集，测试几种方法之间性能的指标；

程序代码：

#ifndef _DISJOINT_SET_H_
#define _DISJOINT_SET_H_

#include <stdlib.h>
#include <stdio.h>
#include <assert.h>
#include <time.h>
#include <math.h>

#include "windows.h"


enum DISJOINTWAY
{
	COMMON_WAY,
	COMPREE_WAY,
	WEIGHT_WAY,
	WEIGHT_COMPRESS_WAY
};

/*
* encapsulate the class of disjoint set 
*
*/

#define MAXDISJOINTSET 0xffffff
class DisjointSet
{
public:
	DisjointSet( int maxSize = MAXDISJOINTSET ):m_item(0), m_size(maxSize)
	{
		m_item = new int[maxSize];
		for( int i = 0; i < m_size; i++ )
		{
			m_item[i] = i;
		}

		m_path = new int[maxSize];
		memset( m_path, 1, sizeof(int)*maxSize );
	}

	~DisjointSet()
	{
		Clear();
	}

	/*
	* find interface 
	*
	*/
	int Find( DISJOINTWAY way, int input )
	{
		assert( input <  m_size );
		switch( way )
		{
		case COMMON_WAY:
			return ImplFindFirst( input );
		case COMPREE_WAY:
			return ImplFindSecond( input );
		case WEIGHT_WAY:
			return ImplFindWeight( input );
		case WEIGHT_COMPRESS_WAY:
			return ImplFindWeightCompree( input );
		default:
			return -1;
		}
	}


	/*
	* make union
	*
	*/
	void Union( DISJOINTWAY way, int first, int second )
	{
		assert( first < m_size && second < m_size );
		switch( way )
		{
		case COMMON_WAY:
			ImplUnionFirst( first, second );
			break;
		case COMPREE_WAY:
			ImplUnionSecond( first, second );
			break;
		case WEIGHT_WAY:
			ImplUnionWeighted( first, second );
			break;
		case WEIGHT_COMPRESS_WAY:
			ImplUnionCompree( first, second );
			break;
		default:
			break;
		}
		
	}

	/*
	*
	*
	*/
	void Clear()
	{
		delete [] m_item;
		m_item = 0;

		delete [] m_path;
		m_path = 0;

		m_size = 0;
	}

protected:

	int ImplFindFirst( int input )
	{
		assert( input < m_size  );
		return m_item[input];
	}

	int ImplFindSecond( int input )
	{
		int i = input;
		for( ; i != m_item[i]; i = m_item[i] );

		return i;
	}

	int ImplFindWeight( int input )
	{
		int i = input;
		for( ; i != m_item[i]; i = m_item[i] );
		
		return i;

	}

	int ImplFindWeightCompree( int input )
	{
		int i = input;
		for( ; i != m_item[i]; i = m_item[i] )
			m_item[i] = m_item[m_item[i]];

		return i;
	}	

	/*
	*
	*
	*/
	void ImplUnionFirst( int first, int second )
	{
		int x = m_item[first];
		int y = m_item[second];

		if( x != y )
		{
			m_item[first] = y;
		}

		for( int i = 0; i < m_size; i++ )
		{
			if( x == m_item[i] )
				m_item[i] = y;
		}
	}

	/*
	*
	*
	*/
	void ImplUnionSecond( int& first, int& second )
	{
		if( first != second )
		{
			m_item[first] = second;
		}
	}

	/*
	*
	*
	*/
	void ImplUnionWeighted( int first, int second )
	{
		if( first != second )
		{
			if( m_path[first] < m_path[second] )
			{
				m_item[first] = second;
				m_path[second] += m_path[first];
			}
			else
			{
				m_item[second] = first;
				m_path[first] += m_path[second];
			}
		}
	}

	/*
	*
	*
	*/
	void ImplUnionCompree( int first, int second )
	{
		if( first != second )
		{
			if( m_path[first] < m_path[second] )
			{
				m_item[first] = second;
				m_path[second] += m_path[first];
			}
			else
			{
				m_item[second] = first;
				m_path[first] += m_path[second];
			}
		}


	}

protected:

	int*   m_item;
	int    m_size;

	int*   m_path;

};

void TestDisjointSetSimple()
{
	DisjointSet djoint;
	int i = djoint.Find( COMMON_WAY, 1 );
	int j = djoint.Find( COMMON_WAY, 3 );
	if( i != j )
		djoint.Union( COMMON_WAY, 1, 3 );

	i = djoint.Find( COMMON_WAY, 2 );
	j = djoint.Find( COMMON_WAY, 5 );
	if( i != j )
		djoint.Union( COMMON_WAY, i, j );

	i = djoint.Find( COMMON_WAY, 2 );
	j = djoint.Find( COMMON_WAY, 6 );
	if( i != j )
		djoint.Union( COMMON_WAY, i, j );

	i = djoint.Find( COMMON_WAY, 6 );
	j = djoint.Find( COMMON_WAY, 7 );
	if( i != j )
		djoint.Union( COMMON_WAY, i, j );

	assert( djoint.Find( COMMON_WAY, 2 ) == djoint.Find( COMMON_WAY, 7 ) );

	i = djoint.Find( COMMON_WAY, 1 );
	j = djoint.Find( COMMON_WAY, 7 );
	if( i != j )
		djoint.Union( COMMON_WAY, i, j );

	assert( djoint.Find( COMMON_WAY, 3 ) == djoint.Find( COMMON_WAY, 7 ) );
}

void TestDisjointSetComplex( DISJOINTWAY way, const char* str )
{
	
    unsigned long start = GetTickCount();
	DisjointSet djoint;

	const int len = 1000000;
	const int base = 60000;
	int halfLen = len / 2;
	srand( time(NULL) );
	for( int i = 0; i < len; i++ )
	{
		int first = rand() % base;
		int second = rand() % base;
		if( i > halfLen )
		{
			first += base;
			second += base;
		}


		if( first != second )
		{
			first = djoint.Find( way, first );
			second = djoint.Find( way, second );
			if( first != second )
				djoint.Union( way, first, second );


			assert( djoint.Find( way, first ) == djoint.Find( way, second )  );
		}
	}

	unsigned long interval = GetTickCount() - start;
	printf(" %s way consume time is %d \n", str, interval );

}

void TestSuiteDisjointSet()
{
	TestDisjointSetSimple();

	const char* str[] = {"common", "compress", "weight", "weight compress"};
	for( int i = WEIGHT_COMPRESS_WAY; i >= 0; i--)
	{
		TestDisjointSetComplex((DISJOINTWAY)i, str[i] );
	}

}




#endif 

compile and run in visual studio 2005

下面图片是几种方法运行时间之比较，最直白方法的时间到现在还没输出，所以就没有显示：

并查集类的c++封装，比较union_find algorithm四种实现方法之间的性能差别,布布扣,bubuko.com

并查集类的c++封装，比较union_find algorithm四种实现方法之间的性能差别