問題描述：
在計算機科學中，并查集是一種樹型的數據結構，其保持著用于處理一些不相交集合（Disjoint Sets）的合并及查詢問題。有一個聯合-查找算法（union-find algorithm）定義了兩個操作用于此數據結構：
Find：確定元素屬于哪一個子集。它可以被用來確定兩個元素是否屬于同一子集；
Union：將兩個子集合并成同一個集合；
實現并查集的關鍵是實現union-find algorithm, 本文根據常用的四種算法，實現了這個類，具體算法實現請參看維基百科；
制造測試數據集，測試幾種方法之間性能的指標；
程序代碼：
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[cpp]?view plaincopy
#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?? };?? ?? ? ? ? ?? ?? #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();?? ????}?? ?? ????? ? ? ?? ????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;?? ????????}?? ????}?? ?? ?? ????? ? ? ?? ????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
下面圖片是幾種方法運行時間之比較，最直白方法的時間到現在還沒輸出，所以就沒有顯示：
總結
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