图方法：二分无向图的联通子图查找

         连通域查找使用并行方法，需要对图片接触行列进行标签合并，连通域标签合并过程可以形式化为一个二分图。

         二分图又称作二部图，是图论中的一种特殊模型。 设G=(V,E)是一个无向图，如果顶点V可分割为两个互不相交的子集(A,B)，并且图中的每条边（i，j）所关联的两个顶点i和j分别属于这两个不同的顶点集(i in A,j in B)，则称图G为一个二分图。

        寻找二分图的连通子图，用于解决传导等价类问题。

       

                                      图1  中有两个连通子图

C++代码：

//输入为二部图的边集合，无重复int findEqualSetBinGraph(std::hash_multimap<int,int>  &equelHashL,std::hash_multimap<int,int>  &equelHashR,std::vector<int>  &vetexL,std::vector<int>  &vetexR,std::vector< std::pair<std::vector<int>,std::vector<int> > >  &equelSet,bool bStack ){//使用堆栈，删除遍历过的边if ( equelHashL.size() >0 ){std::stack<std::pair< int, int > > edgeEs;//使用边堆栈std::stack< int >  pSL,pSR;//左边堆栈std::vector< int >  pVL,pVR;//左右等价集合for ( int i=0; i< vetexL.size();++i){//从左侧开始//遍历过的顶点边的个数为0pVL.resize(0);pVR.resize(0);int VL = vetexL[i];pSL.push(vetexL[i]);pVL.push_back(VL);while ( !pSL.empty() ){VL = pSL.top();auto ptr =equelHashR.find(VL);int C = equelHashR.count(VL);if ( C> 0){auto ptr1 =equelHashR.lower_bound(VL);auto ptr2 =equelHashR.upper_bound(VL);for (int i=0;i<C;++i){pSR.push(ptr1->second);pVR.push_back(ptr1->second);++ptr1;}pSL.pop();//去除掉相连的边equelHashR.erase( VL );//遍历对方的边while ( !pSR.empty() ){int VR = pSR.top();auto ptr =equelHashL.find(VR);int C = equelHashL.count(VR);if ( C > 1 ){auto ptr1 =equelHashL.lower_bound(VR);auto ptr2 =equelHashL.upper_bound(VR);for (int i=0;i<C;++i)//绕过第一个，必须要顺序排列才能使用{if ( ptr1->second != VL ){pSL.push(ptr1->second);pVL.push_back( ptr1->second );//删除右边元素auto ptrR =equelHashR.lower_bound( ptr1->second );for ( int i =0; i< equelHashR.count( ptr1->second ); ++i ){if ( ptrR->second == VR){equelHashR.erase(ptrR);break;}else{++ptrR;}}}++ptr1;}pSR.pop();equelHashL.erase( VR );}else{//删除右边元素int VR = pSR.top();auto ptrR = equelHashL.lower_bound( VR );for ( int i =0; i< equelHashL.count( VR ); ++i ){if ( ptrR->second == VL){equelHashL.erase(ptrR);break;}else{++ptrR;}}pSR.pop();}}} else{pSL.pop();}}if ( pVL.size()>0 && pVR.size()>0 ){equelSet.push_back( std::make_pair( pVL,pVR ) );}}}return 1;}//输入为二部图的边集合，有重复int findEqualSetBinGraph(std::vector< std::pair<int,int>  >  &edgeSet,std::vector< std::pair<std::vector<int>,std::vector<int> > > &equelSet,bool bStack ){//4.2筛选集合//划分等价类//使用查找划分等价类std::vector< std::pair<int,int> > equelLabelL,equelLabelR,equelLabelMin,equelLabelMinMirro;equelLabelL.reserve(edgeSet.size() );//等价集合std::vector< std::pair<std::vector<int>,std::vector<int> > > equelSetL,equelSetR;//,equelSet,;std::map<int,int>  equelMapL,equelMapR;//使用多值哈希//设置重复集合//用于最后合并连通域std::hash_multimap<int,int>  equelHashL,equelHashR;std::vector<int>  vetexL,vetexR;//顶点集合if ( edgeSet.size()>0 ){std::qsort(&edgeSet[0],edgeSet.size(),sizeof(edgeSet[0]) ,cvWish::Operater::cmpPairIntFirst);//使用基数排序//一次合并完成{int idxS =0;int idxE =0;int vL;vL = edgeSet[0].first;for ( idxE ; idxE< edgeSet.size();  ++idxE ){if ( idxE == 0 ){continue;}if ( vL == edgeSet[idxE].first ){}else{vL = edgeSet[idxE].first;std::qsort(&edgeSet[idxS],idxE-idxS,sizeof(edgeSet[0]) ,cvWish::Operater::cmpPairIntSecond );idxS = idxE;}}std::qsort(&edgeSet[idxS],idxE-idxS,sizeof(edgeSet[0]) ,cvWish::Operater::cmpPairIntSecond );}equelLabelMin.reserve( edgeSet.size() );//equelLabelMin.reserve( equelLabelR.size() );{int vL,vR;vL = edgeSet.begin()->first;vR = edgeSet.begin()->second;equelLabelMin.push_back( std::make_pair(vL,vR) );for ( auto ptr = edgeSet.begin(); ptr!= edgeSet.end();  ++ptr){if (ptr == edgeSet.begin()){//跳过第一个continue;}if ( vL == ptr->first && vR == ptr->second){}else{vL = ptr->first;vR = ptr->second;equelLabelMin.push_back(  std::make_pair(vL,vR) );}//vL = ptr->first;//vR = ptr->second;}}for ( auto ptr = equelLabelMin.begin(); ptr!= equelLabelMin.end();  ++ptr){equelHashR.insert( *ptr );equelLabelMinMirro.push_back( std::make_pair( ptr->second,ptr->first ) );}std::qsort(&equelLabelMinMirro[0],equelLabelMinMirro.size(),sizeof(equelLabelMinMirro[0]) ,cvWish::Operater::cmpPairIntFirst );{int idxS =0;int idxE =0;int vL   = equelLabelMinMirro[0].first;for ( idxE ; idxE< equelLabelMinMirro.size();  ++idxE ){if ( idxE == 0 ){continue;}if ( vL == equelLabelMinMirro[idxE].first ){}else{vL = equelLabelMinMirro[idxE].first;std::qsort(&equelLabelMinMirro[idxS],idxE-idxS,sizeof(equelLabelMinMirro[0]) ,cvWish::Operater::cmpPairIntSecond );idxS = idxE;}}std::qsort(&equelLabelMinMirro[idxS],idxE-idxS,sizeof(equelLabelMinMirro[0]) ,cvWish::Operater::cmpPairIntSecond );}for ( auto ptr = equelLabelMinMirro.begin(); ptr!= equelLabelMinMirro.end();  ++ptr){equelHashL.insert(*ptr );//多值hash和多值map都不能剔除重复条目，不应该啊！}bool bStack = true;//4.3 找出顶点集合//暂时不需要，根据所有的边找出顶点vetexL.reserve(equelLabelMin.size());{int vL,vR;vL = equelLabelMin.begin()->first;vetexL.push_back(vL);for (auto ptr = equelLabelMin.begin(); ptr!= equelLabelMin.end();++ptr){if (ptr == equelLabelMin.begin()){//跳过第一个continue;}if ( vL == ptr->first ){}else{vL = ptr->first;vetexL.push_back(vL);}}}vetexR.reserve( equelLabelMinMirro.size() );{int vL,vR;vR = equelLabelMinMirro.begin()->first;vetexR.push_back(vR);for (auto ptr = equelLabelMinMirro.begin(); ptr!= equelLabelMinMirro.end();++ptr){if ( ptr == equelLabelMinMirro.begin()){//跳过第一个continue;}if ( vR == ptr->first ){}else{vR = ptr->first;vetexR.push_back(vR);}}}}//使用堆栈法寻找连通子图//边集合： equelLabelMin,equelLabelMinMirros，但使用equelHashL equelHashR 顶点集合： vetexL,vetexRfindEqualSetBinGraph(equelHashL,equelHashR,vetexL,vetexR,equelSet,bStack );return 1;}