//Runs with ./get4eComponentsLinear <input_graph> <output_4components>
#include <stdio.h>
#include <stdlib.h>
#include <chrono>
void get_adj(int,int,int*,int**,int**);
void read_graph(char*,int*,int**,int**);
void DFS(int,int*,int*,int**,int**,int**);
void get_low(int,int*,int*,int*,int*,int*,int**);
void get_l_and_bcount(int,int*,int*,int*,int*,int*,int**,int**);
void get_lowChildren(int,int*,int*,int*,int*,int**,int**);
void get_M(int,int*,int*,int*,int*,int*,int*,int**,int**);
int get_4e_components_linear(int,int*,int*,int**);
int get_4e_components_connected_linear(int,int*,int*,int**);
int get_4e_components_2econnected_linear(int,int*,int*,int**);
int get_4e_components_3econnected_linear(int,int*,int*,int**,int*,int**);
int get_3cuts_contr(int,int*,int*,int**);
int get_3cuts_2tree(int,int*,int*,int**);
void get_l1l2_and_bcount(int,int*,int*,int*,int*,int*,int**,int**,int**);
void get_lowM(int,int*,int*,int*,int*,int*,int*,int*,int*,int*,int**,int**);
void sortAdjInc(int,int*,int*,int*);
void get_allM(int,int*,int*,int*,int*,int*,int*,int*,int**,int**,int**);
void get_2low(int,int*,int*,int*,int*,int*,int**,int**,int**,int**);
using namespace std::chrono;
int numberOfComponents=0;
int numberOf2eComponents=0;
int numberOf3eComponents=0;
int numberOf4eComponents=0;
int numberOf1Cuts=0;
int numberOf2Cuts=0;
int numberOf3Cuts=0;
double timeForComponents=0;
double timeFor2eComponents=0;
double timeFor3eComponents=0;
double timeFor4eComponents=0;
int main(int n_args, char** args)
{
int n; int* adj; int* firstOut;
read_graph(args[1],&n,&adj,&firstOut);
int* C;
high_resolution_clock::time_point t1 = high_resolution_clock::now();
int k=get_4e_components_linear(n,adj,firstOut,&C);
high_resolution_clock::time_point t2 = high_resolution_clock::now();
FILE* fp = fopen(args[2],"w");
fprintf(fp,"%d\n",n);
for(int i=0;i<n;i++){fprintf(fp,"%d\n",C[i]);}
duration<double> time_span = duration_cast<duration<double>>(t2 - t1);
fprintf(fp,"%f\n",time_span.count());
fprintf(fp,"%f\n",timeFor4eComponents);
fclose(fp);
free(adj); free(firstOut); free(C);
printf("number of components: %d\n",numberOfComponents);
printf("time to compute components: %f\n\n",timeForComponents);
printf("number of 1-cuts: %d\n",numberOf1Cuts);
printf("number of 2e-components: %d\n",numberOf2eComponents);
printf("time to compute 2e-components: %f\n\n",timeFor2eComponents);
printf("number of 2-cuts: %d\n",numberOf2Cuts);
printf("number of 3e-components: %d\n",numberOf3eComponents);
printf("time to compute 3e-components: %f\n\n",timeFor3eComponents);
printf("number of 3-cuts: %d\n",numberOf3Cuts);
printf("number of 4e-components: %d\n",numberOf4eComponents);
printf("time to compute 4e-components: %f\n\n",timeFor4eComponents);
printf("total time: %f\n",time_span.count());
return 0;
}
int get_4e_components_linear(int n, int* adj, int* firstOut, int** C)
{
high_resolution_clock::time_point t1;
high_resolution_clock::time_point t2;
duration<double> time_span;
double temp_time=0;
t1 = high_resolution_clock::now();
(*C) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*C)[i]=-1;}
int* Q = (int*)malloc(sizeof(int)*n);
int* edges = (int*)malloc(sizeof(int)*firstOut[n]);
char* found = (char*)malloc(sizeof(char)*n);
int* map = (int*)malloc(sizeof(int)*n);
int* imap = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){found[i]=0;}
int k=0;
for(int r=0;r<n;r++)
{
if(found[r]){continue;}
int Nr=0;
int first=0; int last=0;
Q[last++]=r; found[r]=1; map[r]=Nr; imap[Nr++]=r;
while(first!=last)
{
int x=Q[first++];
for(int i=firstOut[x];i<firstOut[x+1];i++)
{
int y=adj[i];
if(!found[y])
{
Q[last++]=y; found[y]=1; map[y]=Nr; imap[Nr++]=y;
}
}
}
int nC = last;
if(nC>1)
{
high_resolution_clock::time_point temp_t1 = high_resolution_clock::now();
int edgeIndx=0;
for(int i=0;i<nC;i++)
{
int x=Q[i];
for(int j=firstOut[x];j<firstOut[x+1];j++)
{
int y=adj[j];
if(x<y){edges[2*edgeIndx]=map[x];edges[2*edgeIndx+1]=map[y];edgeIndx++;}
}
}
int* adjC; int* firstOutC;
get_adj(nC,edgeIndx,edges,&adjC,&firstOutC);
int* C2;
int k2 = get_4e_components_connected_linear(nC,adjC,firstOutC,&C2);
for(int i=0;i<nC;i++){(*C)[imap[i]]=C2[i]+k;}
k+=k2;
free(adjC); free(firstOutC); free(C2);
high_resolution_clock::time_point temp_t2 = high_resolution_clock::now();
duration<double> temp_time_span = duration_cast<duration<double>>(temp_t2 - temp_t1);
temp_time += temp_time_span.count();
}
else
{
(*C)[r]=k;
k++;
numberOf2eComponents++;
numberOf3eComponents++;
numberOf4eComponents++;
}
numberOfComponents++;
}
free(Q); free(edges); free(found);
free(map); free(imap);
t2 = high_resolution_clock::now();
time_span = duration_cast<duration<double>>(t2 - t1);
timeForComponents = time_span.count()-temp_time;
return k;
}
int get_4e_components_connected_linear(int n, int* adj, int* firstOut, int** C)
{
high_resolution_clock::time_point t1;
high_resolution_clock::time_point t2;
duration<double> time_span;
double temp_time=0;
t1 = high_resolution_clock::now();
(*C) = (int*)malloc(sizeof(int)*n);
int* dfs; int* idfs; int* p;
DFS(n,adj,firstOut,&dfs,&idfs,&p);
int* low;
get_low(n,adj,firstOut,dfs,idfs,p,&low);
int* Q = (int*)malloc(sizeof(int)*n);
int* map = (int*)malloc(sizeof(int)*n);
int* imap = (int*)malloc(sizeof(int)*n);
char* found = (char*)malloc(sizeof(char)*n);
int* edges = (int*)malloc(sizeof(int)*firstOut[n]);
for(int i=0;i<n;i++){found[i]=0;}
int k=0;
for(int v=1;v<n;v++){numberOf1Cuts+=low[v]==v;}
for(int r=0;r<n;r++)
{
if(found[r]){continue;}
int Nr=0;
int first=0; int last=0;
Q[last++]=r; found[r]=1; map[r]=Nr; imap[Nr++]=r;
while(first!=last)
{
int x=Q[first++];
for(int i=firstOut[x];i<firstOut[x+1];i++)
{
int y=adj[i];
if(found[y]){continue;}
if((x==p[y]&&low[y]==y)||(y==p[x]&&low[x]==x)){continue;}
Q[last++]=y; found[y]=1; map[y]=Nr; imap[Nr++]=y;
}
}
int nC = last;
if(nC>1)
{
high_resolution_clock::time_point temp_t1 = high_resolution_clock::now();
int edgeIndx=0;
for(int i=0;i<last;i++)
{
int x=Q[i];
for(int j=firstOut[x];j<firstOut[x+1];j++)
{
int y=adj[j];
if(y<x){continue;}
if((x==p[y]&&low[y]==y)||(y==p[x]&&low[x]==x)){continue;}
edges[2*edgeIndx]=map[x]; edges[2*edgeIndx+1]=map[y]; edgeIndx++;
}
}
int* adjC; int* firstOutC;
get_adj(nC,edgeIndx,edges,&adjC,&firstOutC);
int* C3;
int k3=get_4e_components_2econnected_linear(nC,adjC,firstOutC,&C3);
for(int i=0;i<nC;i++){(*C)[imap[i]]=C3[i]+k;}
k+=k3;
free(adjC); free(firstOutC); free(C3);
high_resolution_clock::time_point temp_t2 = high_resolution_clock::now();
duration<double> temp_time_span = duration_cast<duration<double>>(temp_t2 - temp_t1);
temp_time += temp_time_span.count();
}
else
{
(*C)[r]=k;
k++;
numberOf3eComponents++;
numberOf4eComponents++;
}
numberOf2eComponents++;
}
free(dfs); free(idfs); free(p); free(low);
free(Q); free(found); free(map); free(imap); free(edges);
t2 = high_resolution_clock::now();
time_span = duration_cast<duration<double>>(t2 - t1);
timeFor2eComponents += time_span.count()-temp_time;
return k;
}
int get_4e_components_2econnected_linear(int n, int* adj, int* firstOut, int** C3)
{
high_resolution_clock::time_point t1;
high_resolution_clock::time_point t2;
duration<double> time_span;
double temp_time=0;
t1 = high_resolution_clock::now();
int* dfs; int* idfs; int* p;
DFS(n,adj,firstOut,&dfs,&idfs,&p);
int* low;
get_low(n,adj,firstOut,dfs,idfs,p,&low);
int* l; int* bcount;
get_l_and_bcount(n,adj,firstOut,dfs,idfs,p,&l,&bcount);
int* low1C; int* low2C;
get_lowChildren(n,dfs,idfs,p,low,&low1C,&low2C);
int* M; int* nextM;
get_M(n,dfs,idfs,l,low,low1C,low2C,&M,&nextM);
int* prevM = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){prevM[i]=-1;}
for(int i=1;i<n;i++){if(nextM[i]!=-1){prevM[nextM[i]]=i;}}
int* vEdgeStack = (int*)malloc(sizeof(int)*4*n);
int* vEdgeFirst = (int*)malloc(sizeof(int)*n);
int* vEdgeNext = (int*)malloc(sizeof(int)*4*n);
int* firstVertex = (int*)malloc(sizeof(int)*4*n);
for(int i=0;i<n;i++){vEdgeFirst[i]=-1;}
int SP=0;
char* isCutEdge = (char*)malloc(sizeof(char)*n);
char* isCutEdgeLow = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){isCutEdge[i]=0;isCutEdgeLow[i]=0;}
int* cutEdgeStack = (int*)malloc(sizeof(int)*4*n);
int* cutEdgeFirst = (int*)malloc(sizeof(int)*n);
int* cutEdgeNext = (int*)malloc(sizeof(int)*2*n);
for(int i=0;i<n;i++){cutEdgeFirst[i]=-1;}
int cutEdgeSP=0;
int* cutEdgeCount = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){cutEdgeCount[i]=0;}
for(int m=1;m<n;m++)
{
if(M[m]!=m){continue;}
int u=m;
while(u!=-1)
{
int z=nextM[u];
if(z!=-1 && bcount[z]==bcount[u])
{
int last;
while(z!=-1 && bcount[z]==bcount[u]){last=z; z=nextM[z];}
if(bcount[u]==1)
{
isCutEdgeLow[m]=1;
if(u!=m)
{
vEdgeNext[SP]=vEdgeFirst[u]; vEdgeFirst[u]=SP; vEdgeStack[SP]=m; firstVertex[SP++]=u;
vEdgeNext[SP]=vEdgeFirst[m]; vEdgeFirst[m]=SP; vEdgeStack[SP]=u; firstVertex[SP++]=u;
}
if(p[last]!=low[m])
{
vEdgeNext[SP]=vEdgeFirst[p[last]]; vEdgeFirst[p[last]]=SP; vEdgeStack[SP]=low[m]; firstVertex[SP++]=u;
vEdgeNext[SP]=vEdgeFirst[low[m]]; vEdgeFirst[low[m]]=SP; vEdgeStack[SP]=p[last]; firstVertex[SP++]=u;
}
cutEdgeNext[cutEdgeSP]=cutEdgeFirst[u]; cutEdgeFirst[u]=cutEdgeSP;
cutEdgeStack[2*cutEdgeSP]=m; cutEdgeStack[2*cutEdgeSP+1]=low[m]; cutEdgeSP++;
cutEdgeCount[u]++;
}
else
{
vEdgeNext[SP]=vEdgeFirst[u]; vEdgeFirst[u]=SP; vEdgeStack[SP]=p[last]; firstVertex[SP++]=u;
vEdgeNext[SP]=vEdgeFirst[p[last]]; vEdgeFirst[p[last]]=SP; vEdgeStack[SP]=u; firstVertex[SP++]=u;
}
int v=u;
while(v!=nextM[last])
{
isCutEdge[v]=1;
if(v!=last&&p[v]!=nextM[v])
{
vEdgeNext[SP]=vEdgeFirst[p[v]]; vEdgeFirst[p[v]]=SP; vEdgeStack[SP]=nextM[v]; firstVertex[SP++]=u;
vEdgeNext[SP]=vEdgeFirst[nextM[v]]; vEdgeFirst[nextM[v]]=SP; vEdgeStack[SP]=p[v]; firstVertex[SP++]=u;
}
cutEdgeNext[cutEdgeSP]=cutEdgeFirst[u]; cutEdgeFirst[u]=cutEdgeSP;
cutEdgeStack[2*cutEdgeSP]=v; cutEdgeStack[2*cutEdgeSP+1]=p[v]; cutEdgeSP++;
cutEdgeCount[u]++;
v=nextM[v];
}
}
else if(bcount[u]==1)
{
isCutEdge[u]=1; isCutEdgeLow[m]=1;
if(u!=m)
{
vEdgeNext[SP]=vEdgeFirst[u]; vEdgeFirst[u]=SP; vEdgeStack[SP]=m; firstVertex[SP++]=u;
vEdgeNext[SP]=vEdgeFirst[m]; vEdgeFirst[m]=SP; vEdgeStack[SP]=u; firstVertex[SP++]=u;
}
if(p[u]!=low[m])
{
vEdgeNext[SP]=vEdgeFirst[p[u]]; vEdgeFirst[p[u]]=SP; vEdgeStack[SP]=low[m]; firstVertex[SP++]=u;
vEdgeNext[SP]=vEdgeFirst[low[m]]; vEdgeFirst[low[m]]=SP; vEdgeStack[SP]=p[u]; firstVertex[SP++]=u;
}
cutEdgeNext[cutEdgeSP]=cutEdgeFirst[u]; cutEdgeFirst[u]=cutEdgeSP;
cutEdgeStack[2*cutEdgeSP]=u; cutEdgeStack[2*cutEdgeSP+1]=p[u]; cutEdgeSP++;
cutEdgeNext[cutEdgeSP]=cutEdgeFirst[u]; cutEdgeFirst[u]=cutEdgeSP;
cutEdgeStack[2*cutEdgeSP]=m; cutEdgeStack[2*cutEdgeSP+1]=low[m]; cutEdgeSP++;
cutEdgeCount[u]=2;
}
u=z;
}
}
int* C = (int*)malloc(sizeof(int)*n);
int* Q = (int*)malloc(sizeof(int)*n);
int* map = (int*)malloc(sizeof(int)*n);
int* imapStack = (int*)malloc(sizeof(int)*n);
int* imapFirst = (int*)malloc(sizeof(int)*n);
int* imapNext = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){C[i]=-1;imapFirst[i]=-1;}
SP=0;
int k=0;
for(int r=0;r<n;r++)
{
if(C[r]!=-1){continue;}
int first=0; int last=0;
C[r]=k; Q[last++]=r;
int Nr=0;
map[r]=Nr++;
imapNext[SP]=imapFirst[k]; imapFirst[k]=SP; imapStack[SP++]=r;
while(first!=last)
{
int v=Q[first++];
for(int i=firstOut[v];i<firstOut[v+1];i++)
{
int u=adj[i];
if((u==p[v]&&isCutEdge[v])||(v==p[u]&&isCutEdge[u])){continue;}
if((M[u]==u&&v==low[u]&&isCutEdgeLow[u])||(M[v]==v&&u==low[v]&&isCutEdgeLow[v])){continue;}
if(C[u]==-1)
{
C[u]=k; Q[last++]=u; map[u]=Nr++;
imapNext[SP]=imapFirst[k]; imapFirst[k]=SP; imapStack[SP++]=u;
}
}
for(int i=vEdgeFirst[v];i!=-1;i=vEdgeNext[i])
{
int u=vEdgeStack[i];
if(C[u]==-1)
{
C[u]=k; Q[last++]=u; map[u]=Nr++;
imapNext[SP]=imapFirst[k]; imapFirst[k]=SP; imapStack[SP++]=u;
}
}
}
k++;
}
numberOf3eComponents+=k;
for(int v=1;v<n;v++){numberOf2Cuts+=bcount[v]==1;}
for(int x=1;x<n;x++)
{
if(M[x]!=x){continue;}
int u=x;
while(u!=-1)
{
int v=u;
int temp_num=1;
while(nextM[v]!=-1 && bcount[nextM[v]]==bcount[v])
{
temp_num++;
v=nextM[v];
}
numberOf2Cuts+=(temp_num*(temp_num-1))/2;
u=nextM[v];
}
}
t2 = high_resolution_clock::now();
time_span = duration_cast<duration<double>>(t2 - t1);
timeFor3eComponents += time_span.count();
t1 = high_resolution_clock::now();
int* nC = (int*)malloc(sizeof(int)*k);
int** adjC = (int**)malloc(sizeof(int*)*k);
int** firstOutC = (int**)malloc(sizeof(int*)*k);
int* edges = (int*)malloc(sizeof(int)*(firstOut[n]+n));
for(int c=0;c<k;c++)
{
nC[c]=0;
int eIndx=0;
for(int t=imapFirst[c];t!=-1;t=imapNext[t])
{
nC[c]++;
int x=imapStack[t];
for(int i=firstOut[x];i<firstOut[x+1];i++)
{
int y=adj[i];
if(dfs[x]<dfs[y]){continue;}
if((y==p[x]&&isCutEdge[x])||(x==M[x]&&y==low[x]&&isCutEdgeLow[x])){continue;}
edges[2*eIndx]=map[x]; edges[2*eIndx+1]=map[y]; eIndx++;
}
for(int i=vEdgeFirst[x];i!=-1;i=vEdgeNext[i])
{
int y=vEdgeStack[i];
if(y>x){continue;}
edges[2*eIndx]=map[x]; edges[2*eIndx+1]=map[y]; eIndx++;
}
}
if(nC[c]==1){continue;}
get_adj(nC[c],eIndx,edges,adjC+c,firstOutC+c);
}
int* nCcuts = (int*)malloc(sizeof(int)*k);
int** Ccuts = (int**)malloc(sizeof(int*)*k);
(*C3) = (int*)malloc(sizeof(int)*n);
int c_num=0;
for(int c=0;c<k;c++)
{
if(nC[c]>1)
{
int* C4;
int k4=get_4e_components_3econnected_linear(nC[c],adjC[c],firstOutC[c],&C4,nCcuts+c,Ccuts+c);
for(int t=imapFirst[c];t!=-1;t=imapNext[t])
{
int x=imapStack[t];
(*C3)[x]=C4[map[x]]+c_num;
}
c_num+=k4;
free(C4);
numberOf4eComponents+=k4;
}
else
{
int x=imapStack[imapFirst[c]];
(*C3)[x]=c_num;
c_num++;
numberOf4eComponents++;
}
}
t2 = high_resolution_clock::now();
time_span = duration_cast<duration<double>>(t2 - t1);
timeFor4eComponents += time_span.count();
/*get the number of 3-edge cuts*/
int* imap = (int*)malloc(sizeof(int)*n);
for(int c=0;c<k;c++)
{
if(nC[c]==1){continue;}
SP=1; int temp;
for(int i=imapFirst[c];i!=-1;i=imapNext[i])
{
imap[nC[c]-SP]=imapStack[i]; SP++;
}
for(int i=0;i<nCcuts[c];i++)
{
for(int t=0;t<6;t++){Ccuts[c][6*i+t]=imap[Ccuts[c][6*i+t]];}
}
}
int* cut3Stack_ = (int*)malloc(sizeof(int)*12*n);
int* cut3First_ = (int*)malloc(sizeof(int)*n);
int* cut3Next_ = (int*)malloc(sizeof(int)*12*n);
int* CIndx_ = (int*)malloc(sizeof(int)*12*n);
int* cutIndx_ = (int*)malloc(sizeof(int)*12*n);
int* edgeIndx_ = (int*)malloc(sizeof(int)*12*n);
for(int i=0;i<n;i++){cut3First_[i]=-1;}
SP=0;
for(int c=0;c<k;c++)
{
if(nC[c]==1){continue;}
for(int i=0;i<nCcuts[c];i++)
{
for(int t=0;t<3;t++)
{
int x=Ccuts[c][6*i+2*t]; int y=Ccuts[c][6*i+2*t+1];
cut3Next_[SP]=cut3First_[x]; cut3First_[x]=SP; cut3Stack_[SP]=y; CIndx_[SP]=c; cutIndx_[SP]=i; edgeIndx_[SP++]=t;
cut3Next_[SP]=cut3First_[y]; cut3First_[y]=SP; cut3Stack_[SP]=x; CIndx_[SP]=c; cutIndx_[SP]=i; edgeIndx_[SP++]=t;
}
}
}
int* cut3Stack = (int*)malloc(sizeof(int)*12*n);
int* cut3First = (int*)malloc(sizeof(int)*n);
int* cut3Next = (int*)malloc(sizeof(int)*12*n);
int* CIndx = (int*)malloc(sizeof(int)*12*n);
int* cutIndx = (int*)malloc(sizeof(int)*12*n);
int* edgeIndx = (int*)malloc(sizeof(int)*12*n);
for(int i=0;i<n;i++){cut3First[i]=-1;}
SP=0;
for(int x=0;x<n;x++)
{
for(int i=cut3First_[x];i!=-1;i=cut3Next_[i])
{
int y=cut3Stack_[i];
cut3Next[SP]=cut3First[y]; cut3First[y]=SP; cut3Stack[SP]=x;
CIndx[SP]=CIndx_[i]; cutIndx[SP]=cutIndx_[i]; edgeIndx[SP++]=edgeIndx_[i];
}
}
int* vEdgesStackS = (int*)malloc(sizeof(int)*4*n);
int* vEdgesFirstS = (int*)malloc(sizeof(int)*n);
int* vEdgesNextS = (int*)malloc(sizeof(int)*4*n);
int* firstVertexS = (int*)malloc(sizeof(int)*4*n);
for(int i=0;i<n;i++){vEdgesFirstS[i]=-1;}
SP=0;
for(int x=0;x<n;x++)
{
for(int i=vEdgeFirst[x];i!=-1;i=vEdgeNext[i])
{
int y=vEdgeStack[i];
vEdgesNextS[SP]=vEdgesFirstS[y]; vEdgesFirstS[y]=SP; vEdgesStackS[SP]=x; firstVertexS[SP++]=firstVertex[i];
}
}
int** corVertex = (int**)malloc(sizeof(int*)*k);
for(int c=0;c<k;c++){if(nC[c]!=1){corVertex[c]=(int*)malloc(sizeof(int)*nCcuts[c]*3);}}
for(int c=0;c<k;c++){if(nC[c]!=1){for(int i=0;i<3*nCcuts[c];i++){corVertex[c][i]=-1;}}}
for(int x=0;x<n;x++)
{
for(int i=cut3First[x];i!=-1;i=cut3Next[i])
{
int y=cut3Stack[i];
if(y<x){continue;}
int j=vEdgesFirstS[x];
while(j!=-1)
{
int z=vEdgesStackS[j];
if(z>y){j=vEdgesNextS[j]; vEdgesFirstS[x]=j; continue;}
if(z<y){break;}
int c=CIndx[i]; int t=cutIndx[i]; int e=edgeIndx[i];
corVertex[c][3*t+e]=firstVertexS[j];
vEdgesFirstS[x]=j;
int i1=cut3Next[i];
if(i1==-1){break;}
int y1=cut3Stack[i1];
if(y1!=y){break;}
if(cutIndx[i1]!=t){break;}
i=i1;
j=vEdgesNextS[j]; vEdgesFirstS[x]=j;
if(j==-1){break;}
z=vEdgesStackS[j];
if(z!=y){break;}
e=edgeIndx[i];
corVertex[c][3*t+e]=firstVertexS[j];
i1=cut3Next[i];
if(i1==-1){break;}
y1=cut3Stack[i1];
if(y1!=y){break;}
if(cutIndx[i1]!=t){break;}
i=i1;
j=vEdgesNextS[j]; vEdgesFirstS[x]=j;
if(j==-1){break;}
z=vEdgesStackS[j];
if(z!=y){break;}
e=edgeIndx[i];
corVertex[c][3*t+e]=firstVertexS[j];
break;
}
}
}
int n3Cuts=0;
for(int c=0;c<k;c++)
{
if(nC[c]==1){continue;}
for(int i=0;i<nCcuts[c];i++)
{
int num=1;
for(int t=0;t<3;t++)
{
if(corVertex[c][3*i+t]!=-1){num*=cutEdgeCount[corVertex[c][3*i+t]];}
}
n3Cuts+=num;
}
}
numberOf3Cuts+=n3Cuts;
/*end: get the number of 3-edge cuts*/
free(vEdgeStack); free(vEdgeFirst); free(vEdgeNext); free(firstVertex);
free(vEdgesStackS); free(vEdgesFirstS); free(vEdgesNextS); free(firstVertexS);
free(cutEdgeStack); free(cutEdgeFirst); free(cutEdgeNext); free(cutEdgeCount);
free(cut3Stack_); free(cut3First_); free(cut3Next_); free(CIndx_); free(cutIndx_); free(edgeIndx_);
free(cut3Stack); free(cut3First); free(cut3Next); free(CIndx); free(cutIndx); free(edgeIndx);
free(imap);
for(int i=0;i<k;i++){if(nC[i]>1){free(Ccuts[i]); free(corVertex[i]);}}
free(nCcuts); free(Ccuts); free(corVertex);
for(int i=0;i<k;i++){if(nC[i]>1){free(adjC[i]);free(firstOutC[i]);}}
free(adjC); free(firstOutC); free(edges); free(nC);
free(dfs); free(idfs); free(p); free(low);
free(l); free(bcount); free(low1C); free(low2C);
free(M); free(nextM); free(prevM);
free(isCutEdge); free(isCutEdgeLow);
free(C); free(Q); free(map); free(imapStack); free(imapFirst); free(imapNext);
return c_num;
}
int get_4e_components_3econnected_linear(int n, int* adj, int* firstOut, int** C, int* n3cuts, int** cuts3)
{
int* cuts;
int k = get_3cuts_contr(n,adj,firstOut,&cuts);
(*cuts3) = (int*)malloc(sizeof(int)*6*k);
*n3cuts=k; for(int i=0;i<6*k;i++){(*cuts3)[i]=cuts[i];}
int* dfs; int* idfs; int* p;
DFS(n,adj,firstOut,&dfs,&idfs,&p);
int* ND = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){ND[i]=1;}
for(int i=n-1;i>0;i--){int v=idfs[i];ND[p[v]]+=ND[v];}
char* type = (char*)malloc(sizeof(char)*k);
int* size = (int*)malloc(sizeof(int)*k);
for(int i=0;i<k;i++)
{
int temp;
if(dfs[cuts[6*i+0]]<dfs[cuts[6*i+1]]){temp=cuts[6*i+0];cuts[6*i+0]=cuts[6*i+1];cuts[6*i+1]=temp;}
if(dfs[cuts[6*i+2]]<dfs[cuts[6*i+3]]){temp=cuts[6*i+2];cuts[6*i+2]=cuts[6*i+3];cuts[6*i+3]=temp;}
if(dfs[cuts[6*i+4]]<dfs[cuts[6*i+5]]){temp=cuts[6*i+4];cuts[6*i+4]=cuts[6*i+5];cuts[6*i+5]=temp;}
for(int t=0;t<3;t++)
{
for(int s=t+1;s<3;s++)
{
if(dfs[cuts[6*i+2*t]]<dfs[cuts[6*i+2*s]])
{
temp=cuts[6*i+2*t]; cuts[6*i+2*t]=cuts[6*i+2*s]; cuts[6*i+2*s]=temp;
temp=cuts[6*i+2*t+1]; cuts[6*i+2*t+1]=cuts[6*i+2*s+1]; cuts[6*i+2*s+1]=temp;
}
}
}
}
for(int i=0;i<k;i++)
{
int x1=cuts[6*i+0]; int y1=cuts[6*i+1];
int x2=cuts[6*i+2]; int y2=cuts[6*i+3];
int x3=cuts[6*i+4]; int y3=cuts[6*i+5];
type[i]=0;
if(y1==p[x1]){type[i]++;}
if(y2==p[x2]){type[i]++;}
if(y3==p[x3]){type[i]++;}
if(type[i]==3)
{
if(x1==x2&&x1==x3){type[i]=0;}
else if(x1==x2){type[i]=1;x2=x3;cuts[6*i+2]=cuts[6*i+4];}
else if(x2==x3){type[i]=1;}
else{type[i]=2;}
}
else if(type[i]==2)
{
if(y1==p[x1]&&y2==p[x2])
{
if(x1==x2){type[i]=0;}
else{type[i]=1;}
}
else if(y2==p[x2]&&y3==p[x3])
{
if(x2==x3){type[i]=0;x1=x2;cuts[6*i]=cuts[6*i+2];}
else{type[i]=1;x1=x2;x2=x3;cuts[6*i]=cuts[6*i+2];cuts[6*i+2]=cuts[6*i+4];}
}
else if(y1==p[x1]&&y3==p[x3])
{
type[i]=1; x2=x3; cuts[6*i+2]=cuts[6*i+4];
}
}
else if(type[i]==1)
{
type[i]=0;
if(y2==p[x2]){x1=x2;cuts[6*i]=cuts[6*i+2];}
else if(y3==p[x3]){x1=x3;cuts[6*i]=cuts[6*i+4];}
}
if(type[i]==0){size[i]=ND[x1];}
else if(type[i]==1){size[i]=ND[x2]-ND[x1];}
else if(type[i]==2)
{
if(dfs[x2]<dfs[x1] && dfs[x1]<dfs[x2]+ND[x2])
{
size[i]=ND[x3]-ND[x2]+ND[x1];
}
else
{
size[i]=ND[x3]-ND[x2]-ND[x1];
}
}
}
int* sizeStack = (int*)malloc(sizeof(int)*k);
int* sizeFirst = (int*)malloc(sizeof(int)*n);
int* sizeNext = (int*)malloc(sizeof(int)*k);
for(int i=0;i<n;i++){sizeFirst[i]=-1;}
int SP=0;
for(int i=0;i<k;i++)
{
int s=size[i];
sizeNext[SP]=sizeFirst[s]; sizeFirst[s]=SP; sizeStack[SP++]=i;
}
int* cutStack = (int*)malloc(sizeof(int)*3*k);
int* cutFirst = (int*)malloc(sizeof(int)*n);
int* cutNext = (int*)malloc(sizeof(int)*3*k);
for(int i=0;i<n;i++){cutFirst[i]=-1;}
SP=0;
for(int s=0;s<n;s++)
{
for(int t=sizeFirst[s];t!=-1;t=sizeNext[t])
{
int i=sizeStack[t];
int u=-1; int v=-1; int w=-1;
u=cuts[6*i+0];
if(type[i]>0){v=cuts[6*i+2];}
if(type[i]>1){w=cuts[6*i+4];}
cutNext[SP]=cutFirst[u]; cutFirst[u]=SP; cutStack[SP++]=i;
if(v!=-1)
{
cutNext[SP]=cutFirst[v]; cutFirst[v]=SP; cutStack[SP++]=i;
}
if(w!=-1)
{
cutNext[SP]=cutFirst[w]; cutFirst[w]=SP; cutStack[SP++]=i;
}
}
}
int* Cstack = (int*)malloc(sizeof(int)*3*n);
int* cactusParent = (int*)malloc(sizeof(int)*3*n);
int* parentCut = (int*)malloc(sizeof(int)*3*n);
char* marked = (char*)malloc(sizeof(char)*k);
for(int i=0;i<k;i++){marked[i]=0;}
int* phi = (int*)malloc(sizeof(int)*k);
for(int i=0;i<k;i++){phi[i]=-1;}
int* cactusNode = (int*)malloc(sizeof(int)*n);
(*C) = (int*)malloc(sizeof(int)*n);
(*C)[0]=0; cactusNode[0]=0;
int n_comp=1; int Nr=1;
for(int i=1;i<n;i++)
{
int v=idfs[i];
int x=cactusNode[p[v]];
SP=0;
while(x!=0)
{
int c=parentCut[x];
char found=0;
if(type[c]==0&&v==cuts[6*c+0])
{
marked[c]=1; Cstack[SP++]=c; found=1;
}
else if(type[c]==1&&(v==cuts[6*c+0]||v==cuts[6*c+2]))
{
marked[c]=1; Cstack[SP++]=c; found=1;
}
else if(type[c]==2&&(v==cuts[6*c+0]||v==cuts[6*c+2]||v==cuts[6*c+4]))
{
marked[c]=1; Cstack[SP++]=c; found=1;
}
if(!found){break;}
x=cactusParent[x];
}
char new_comp=0;
for(int t=cutFirst[v];t!=-1;t=cutNext[t])
{
int c=cutStack[t];
if(marked[c]){continue;}
if(phi[c]==-1)
{
phi[c]=Nr; parentCut[Nr]=c; cactusParent[Nr++]=x; new_comp=1;
}
x=phi[c];
}
cactusNode[v]=x;
while(SP!=0){marked[Cstack[SP-1]]=0;SP--;}
if(new_comp){x=n_comp++;}
(*C)[v]=x;
}
free(sizeStack); free(sizeFirst); free(sizeNext);
free(cutStack); free(cutFirst); free(cutNext); free(Cstack);
free(cactusParent); free(parentCut); free(marked); free(phi); free(cactusNode);
free(dfs); free(idfs); free(p); free(ND);
free(type); free(size);
free(cuts);
return n_comp;
}
int get_3cuts_contr(int n, int* adj, int* firstOut, int** cuts)
{
(*cuts) = (int*)malloc(sizeof(int)*n*12);
int k=0; int k2;
int* cuts_2tree;
k2 = get_3cuts_2tree(n,adj,firstOut,&cuts_2tree);
for(int i=0;i<k2;i++)
{
for(int t=0;t<6;t++){(*cuts)[6*k+t]=cuts_2tree[6*i+t];}k++;
}
free(cuts_2tree);
int* dfs; int* idfs; int* p;
DFS(n,adj,firstOut,&dfs,&idfs,&p);
char* foundP = (char*)malloc(sizeof(char)*n);
char* foundC = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){foundP[i]=0;foundC[i]=0;}
int* C = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){C[i]=-1;}
int* Q = (int*)malloc(sizeof(int)*n);
int cIndx=0;
for(int r=0;r<n;r++)
{
if(C[r]!=-1){continue;}
int first=0; int last=0;
Q[last++]=r; C[r]=cIndx;
while(first!=last)
{
int v=Q[first++];
for(int i=firstOut[v];i<firstOut[v+1];i++)
{
int u=adj[i];
if(v==p[u]&&!foundC[u]){foundC[u]=1;continue;}
if(u==p[v]&&!foundP[v]){foundP[v]=1;continue;}
if(C[u]==-1)
{
Q[last++]=u; C[u]=cIndx;
}
}
}
cIndx++;
}
if(cIndx==1){free(dfs); free(idfs); free(p); free(foundP); free(C); free(Q); return k;}
int* stackT_ = (int*)malloc(sizeof(int)*2*n);
int* firstT_ = (int*)malloc(sizeof(int)*n);
int* nextT_ = (int*)malloc(sizeof(int)*2*n);
int* tree_edge_ = (int*)malloc(sizeof(int)*4*n);
int SP=0;
for(int i=0;i<n;i++){firstT_[i]=-1;}
for(int v=1;v<n;v++)
{
int u=p[v];
if(C[u]==C[v]){continue;}
nextT_[SP]=firstT_[C[u]];
firstT_[C[u]]=SP;
stackT_[SP]=C[v];
tree_edge_[2*SP]=u; tree_edge_[2*SP+1]=v; SP++;
nextT_[SP]=firstT_[C[v]];
firstT_[C[v]]=SP;
stackT_[SP]=C[u];
tree_edge_[2*SP]=u; tree_edge_[2*SP+1]=v; SP++;
}
int* stackT = (int*)malloc(sizeof(int)*2*n);
int* firstT = (int*)malloc(sizeof(int)*n);
int* nextT = (int*)malloc(sizeof(int)*2*n);
int* tree_edge = (int*)malloc(sizeof(int)*4*n);
SP=0;
for(int i=0;i<n;i++){firstT[i]=-1;}
for(int c=cIndx-1;c>=0;c--)
{
for(int s=firstT_[c];s!=-1;s=nextT_[s])
{
int d=stackT_[s];
nextT[SP]=firstT[d];
firstT[d]=SP;
stackT[SP]=c;
tree_edge[2*SP]=tree_edge_[2*s]; tree_edge[2*SP+1]=tree_edge_[2*s+1]; SP++;
}
}
int* adj_new = (int*)malloc(sizeof(int)*2*n);
int* firstOut_new = (int*)malloc(sizeof(int)*(cIndx+1));
for(int i=0;i<=cIndx;i++){firstOut_new[i]=0;}
for(int v=1;v<n;v++)
{
int u=p[v];
if(C[u]==C[v]){continue;}
firstOut_new[C[u]+1]++; firstOut_new[C[v]+1]++;
}
int* currentOut = (int*)malloc(sizeof(int)*(cIndx+1));
currentOut[0]=0;
for(int i=1;i<=cIndx;i++){firstOut_new[i]+=firstOut_new[i-1]; currentOut[i]=firstOut_new[i];}
for(int v=1;v<n;v++)
{
int u=p[v];
if(C[u]==C[v]){continue;}
adj_new[currentOut[C[v]]++]=C[u]; adj_new[currentOut[C[u]]++]=C[v];
}
int* cuts_new;
k2 = get_3cuts_contr(cIndx,adj_new,firstOut_new,&cuts_new);
int* stackC_ = (int*)malloc(sizeof(int)*cIndx*12);
int* firstC_ = (int*)malloc(sizeof(int)*cIndx);
int* nextC_ = (int*)malloc(sizeof(int)*cIndx*12);
for(int i=0;i<cIndx;i++){firstC_[i]=-1;}
int* cutIndx_ = (int*)malloc(sizeof(int)*cIndx*12);
SP=0;
for(int i=0;i<k2;i++)
{
for(int t=0;t<3;t++)
{
int x=cuts_new[6*i+2*t]; int y=cuts_new[6*i+2*t+1];
nextC_[SP]=firstC_[x];
firstC_[x]=SP;
stackC_[SP]=y;
cutIndx_[SP++]=i;
nextC_[SP]=firstC_[y];
firstC_[y]=SP;
stackC_[SP]=x;
cutIndx_[SP++]=i;
}
}
int* stackC = (int*)malloc(sizeof(int)*cIndx*12);
int* firstC = (int*)malloc(sizeof(int)*cIndx);
int* nextC = (int*)malloc(sizeof(int)*cIndx*12);
for(int i=0;i<cIndx;i++){firstC[i]=-1;}
int* cutIndx = (int*)malloc(sizeof(int)*cIndx*12);
SP=0;
for(int x=cIndx-1;x>=0;x--)
{
for(int indx=firstC_[x];indx!=-1;indx=nextC_[indx])
{
int y=stackC_[indx];
nextC[SP]=firstC[y];
firstC[y]=SP;
stackC[SP]=x;
cutIndx[SP++]=cutIndx_[indx];
}
}
int* currentEdge = (int*)malloc(sizeof(int)*k2);
for(int i=0;i<k2;i++){currentEdge[i]=0;}
for(int x=0;x<cIndx;x++)
{
for(int indx=firstC[x];indx!=-1;indx=nextC[indx])
{
int y=stackC[indx];
if(y<x){continue;}
int t=firstT[x];
while(stackT[t]!=y){t=nextT[t];}
firstT[x]=t;
if(nextT[t]!=-1 && stackT[nextT[t]]==y){firstT[x]=nextT[t];}
int cut_indx=cutIndx[indx];
(*cuts)[6*k+6*cut_indx+2*currentEdge[cut_indx]]=tree_edge[2*t];
(*cuts)[6*k+6*cut_indx+2*currentEdge[cut_indx]+1]=tree_edge[2*t+1];
currentEdge[cut_indx]++;
}
}
k+=k2;
free(dfs); free(idfs); free(p); free(foundP);
free(C); free(Q);
free(stackT_); free(firstT_); free(nextT_); free(tree_edge_);
free(stackT); free(firstT); free(nextT); free(tree_edge);
free(adj_new); free(firstOut_new); free(currentOut);
free(stackC_); free(firstC_); free(nextC_); free(cutIndx_);
free(stackC); free(firstC); free(nextC); free(cutIndx);
free(currentEdge);
free(cuts_new);
return k;
}
int get_3cuts_2tree(int n, int* adj, int* firstOut, int** cuts)
{
(*cuts) = (int*)malloc(sizeof(int)*n*12);
int* dfs; int* idfs; int* p;
DFS(n,adj,firstOut,&dfs,&idfs,&p);
int* low1; int* low1D; int* low2; int* low2D;
get_2low(n,adj,firstOut,dfs,idfs,p,&low1,&low1D,&low2,&low2D);
int* l1; int* l2; int* bcount;
get_l1l2_and_bcount(n,adj,firstOut,dfs,idfs,p,&l1,&l2,&bcount);
int* low1C; int* low2C;
get_lowChildren(n,dfs,idfs,p,low1,&low1C,&low2C);
int* M; int* nextM;
get_M(n,dfs,idfs,l1,low1,low1C,low2C,&M,&nextM);
int* Ml; int* Mlow1; int* Mlow2;
get_allM(n,dfs,idfs,l1,low1,M,low1C,low2C,&Ml,&Mlow1,&Mlow2);
int* ND = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){ND[i]=1;}
for(int i=n-1;i>0;i--){int v=idfs[i];ND[p[v]]+=ND[v];}
int* prevM = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){prevM[i]=-1;}
for(int i=0;i<n;i++){if(nextM[i]!=-1){prevM[nextM[i]]=i;}}
int* lowM; int* lowMD;
get_lowM(n,adj,firstOut,dfs,idfs,p,ND,low1C,M,prevM,&lowM,&lowMD);
int* low3C = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){low3C[i]=-1;}
for(int c=1;c<n;c++)
{
int v=p[c];
if(low1C[v]==c||low2C[v]==c){continue;}
if(low3C[v]==-1||dfs[low1[c]]<dfs[low1[low3C[v]]]){low3C[v]=c;}
}
int k=0;
int* currentVertex = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){currentVertex[i]=i;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
int m=Ml[v];
if(m==-1){continue;}
int u=currentVertex[m];
while(nextM[u]!=-1 && dfs[nextM[u]]>dfs[v]){u=nextM[u];}
currentVertex[m]=u;
if(bcount[v]==bcount[u]+1 && dfs[l2[M[v]]]>=dfs[v] && (low2C[M[v]]==-1 || dfs[low1[low2C[M[v]]]]>=dfs[v]))
{
(*cuts)[6*k+0]=u; (*cuts)[6*k+1]=p[u];
(*cuts)[6*k+2]=v; (*cuts)[6*k+3]=p[v];
(*cuts)[6*k+4]=M[v]; (*cuts)[6*k+5]=l1[M[v]];
k++;
}
}
for(int i=0;i<n;i++){currentVertex[i]=i;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
int m=Mlow1[v];
if(m==-1){continue;}
int u=currentVertex[m];
while(nextM[u]!=-1 && dfs[nextM[u]]>dfs[v]){u=nextM[u];}
currentVertex[m]=u;
if(bcount[v]==bcount[u]+1 && dfs[low2[Mlow2[v]]]>=dfs[v] && (low3C[M[v]]==-1 || dfs[low1[low3C[M[v]]]]>=dfs[v]))
{
(*cuts)[6*k+0]=u; (*cuts)[6*k+1]=p[u];
(*cuts)[6*k+2]=v; (*cuts)[6*k+3]=p[v];
(*cuts)[6*k+4]=Mlow2[v]; (*cuts)[6*k+5]=l1[Mlow2[v]];
k++;
}
}
for(int i=0;i<n;i++){currentVertex[i]=i;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
int m=Mlow2[v];
if(m==-1){continue;}
int u=currentVertex[m];
while(nextM[u]!=-1 && dfs[nextM[u]]>dfs[v]){u=nextM[u];}
currentVertex[m]=u;
if(bcount[v]==bcount[u]+1 && dfs[low2[Mlow1[v]]]>=dfs[v] && (low3C[M[v]]==-1 || dfs[low1[low3C[M[v]]]]>=dfs[v]))
{
(*cuts)[6*k+0]=u; (*cuts)[6*k+1]=p[u];
(*cuts)[6*k+2]=v; (*cuts)[6*k+3]=p[v];
(*cuts)[6*k+4]=Mlow1[v]; (*cuts)[6*k+5]=l1[Mlow1[v]];
k++;
}
}
for(int u=1;u<n;u++)
{
if(nextM[u]!=-1 && bcount[u]==bcount[nextM[u]]+1)
{
(*cuts)[6*k+0]=u; (*cuts)[6*k+1]=p[u];
(*cuts)[6*k+2]=nextM[u]; (*cuts)[6*k+3]=p[nextM[u]];
(*cuts)[6*k+4]=lowMD[u]; (*cuts)[6*k+5]=lowM[u];
k++;
}
}
for(int i=0;i<n;i++){currentVertex[i]=i;}
for(int i=n-1;i>0;i--)
{
int u=idfs[i];
int m=Ml[u];
if(m==-1 || Ml[u]==M[u]){continue;}
int v=currentVertex[m];
while(v!=-1 && dfs[v]>=dfs[u]){v=nextM[v];}
currentVertex[m]=v;
if(v!=-1 && bcount[u]==bcount[v]+1)
{
(*cuts)[6*k+0]=u; (*cuts)[6*k+1]=p[u];
(*cuts)[6*k+2]=v; (*cuts)[6*k+3]=p[v];
(*cuts)[6*k+4]=M[u]; (*cuts)[6*k+5]=l1[M[u]];
k++;
}
}
for(int i=0;i<n;i++){currentVertex[i]=i;}
for(int i=n-1;i>0;i--)
{
int u=idfs[i];
int m=Mlow1[u];
if(m==-1){continue;}
int v=currentVertex[m];
while(v!=-1 && dfs[v]>=dfs[u]){v=nextM[v];}
currentVertex[m]=v;
if(v!=-1 && bcount[u]==bcount[v]+1)
{
(*cuts)[6*k+0]=u; (*cuts)[6*k+1]=p[u];
(*cuts)[6*k+2]=v; (*cuts)[6*k+3]=p[v];
(*cuts)[6*k+4]=Mlow2[u]; (*cuts)[6*k+5]=l1[Mlow2[u]];
k++;
}
}
for(int v=1;v<n;v++)
{
if(bcount[v]==2)
{
(*cuts)[6*k+0]=v; (*cuts)[6*k+1]=p[v];
(*cuts)[6*k+2]=low1D[v]; (*cuts)[6*k+3]=low1[v];
(*cuts)[6*k+4]=low2D[v]; (*cuts)[6*k+5]=low2[v];
k++;
}
}
free(dfs); free(idfs); free(p); free(ND);
free(low1); free(low1D); free(low2); free(low2D); free(lowM); free(lowMD);
free(l1); free(l2); free(bcount);
free(low1C); free(low2C); free(low3C);
free(M); free(nextM); free(prevM);
free(Ml); free(Mlow1); free(Mlow2); free(currentVertex);
return k;
}
void get_allM(int n, int* dfs, int* idfs, int* l, int* low, int* M, int* low1C, int* low2C, int** Ml, int** Mlow1, int** Mlow2)
{
(*Ml) = (int*)malloc(sizeof(int)*n);
(*Mlow1) = (int*)malloc(sizeof(int)*n);
(*Mlow2) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++)
{
(*Ml)[i]=-1; (*Mlow1)[i]=-1; (*Mlow2)[i]=-1;
}
int* currentM = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){currentM[i]=i;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
int m=M[v];
if(dfs[l[m]]>=dfs[v]){continue;}
if(low1C[m]==-1 || dfs[low[low1C[m]]]>=dfs[v]){continue;}
if(low2C[m]!=-1 && dfs[low[low2C[m]]]<dfs[v])
{
(*Ml)[v]=m;
continue;
}
int tempM=low1C[m];
m=currentM[low1C[m]];
while(1)
{
if(dfs[l[m]]<dfs[v]){break;}
if(low2C[m]!=-1 && dfs[low[low2C[m]]]<dfs[v]){break;}
m=currentM[low1C[m]];
}
(*Ml)[v]=m;
currentM[tempM]=m;
}
for(int i=0;i<n;i++){currentM[i]=i;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
int m=M[v];
if(dfs[l[m]]<dfs[v]){continue;}
if(low1C[m]==-1 || dfs[low[low1C[m]]]>=dfs[v]){continue;}
int tempM=low1C[m];
m=currentM[low1C[m]];
while(1)
{
if(dfs[l[m]]<dfs[v]){break;}
if(low2C[m]!=-1 && dfs[low[low2C[m]]]<dfs[v]){break;}
m=currentM[low1C[m]];
}
(*Mlow1)[v]=m;
currentM[tempM]=m;
}
for(int i=0;i<n;i++){currentM[i]=i;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
int m=M[v];
if(dfs[l[m]]<dfs[v]){continue;}
if(low2C[m]==-1 || dfs[low[low2C[m]]]>=dfs[v]){continue;}
int tempM=low2C[m];
m=currentM[low2C[m]];
while(1)
{
if(dfs[l[m]]<dfs[v]){break;}
if(low2C[m]!=-1 && dfs[low[low2C[m]]]<dfs[v]){break;}
m=currentM[low1C[m]];
}
(*Mlow2)[v]=m;
currentM[tempM]=m;
}
free(currentM);
}
void get_M(int n, int* dfs, int* idfs, int* l, int* low, int* low1C, int* low2C, int** M, int** nextM)
{
(*M) = (int*)malloc(sizeof(int)*n);
(*nextM) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*M)[i]=-1; (*nextM)[i]=-1;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
int c=v; int m=v;
while(1)
{
if(dfs[l[m]]<i){(*M)[v]=m;break;}
if(low2C[m]!=-1 && dfs[low[low2C[m]]]<i){(*M)[v]=m;break;}
c=low1C[m]; m=(*M)[c];
}
if(c!=v)
{
(*nextM)[c]=v;
}
}
}
void get_lowChildren(int n, int* dfs, int* idfs, int* p, int* low, int** low1C, int** low2C)
{
(*low1C) = (int*)malloc(sizeof(int)*n);
(*low2C) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*low1C)[i]=-1; (*low2C)[i]=-1;}
for(int i=1;i<n;i++)
{
int x=idfs[i];
int y=p[x];
if((*low1C)[y]==-1){(*low1C)[y]=x;}
else if(dfs[low[x]]<dfs[low[(*low1C)[y]]]){(*low1C)[y]=x;}
}
for(int i=1;i<n;i++)
{
int x=idfs[i];
int y=p[x];
if(x!=(*low1C)[y])
{
if((*low2C)[y]==-1){(*low2C)[y]=x;}
else if(dfs[low[x]]<dfs[low[(*low2C)[y]]]){(*low2C)[y]=x;}
}
}
}
void get_lowM(int n, int* adj, int* firstOut, int* dfs, int* idfs, int* p, int* ND, int* low1C, int* M, int* prevM, int** lowM, int** lowMD)
{
sortAdjInc(n,adj,firstOut,idfs);
(*lowMD) = (int*)malloc(sizeof(int)*n);
(*lowM) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*lowMD)[i]=-1; (*lowM)[i]=-1;}
int* currentOut = (int*)malloc(sizeof(int)*n);
char* foundC = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){foundC[i]=0;}
for(int i=0;i<n;i++){currentOut[i]=firstOut[i];}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
if(prevM[v]==-1){continue;}
int u=prevM[v];
int y=v;
while((*lowM)[u]==-1)
{
while(currentOut[y]!=firstOut[y+1])
{
int x=adj[currentOut[y]];
if(dfs[x]<dfs[y]){currentOut[y]++;continue;}
if(y==p[x]&&foundC[x]==0){foundC[x]=1;currentOut[y]++;continue;}
if(dfs[x]<dfs[M[u]]){currentOut[y]++;continue;}
if(dfs[x]<dfs[M[u]]+ND[M[u]])
{
(*lowMD)[u]=x; (*lowM)[u]=y;
}
break;
}
if((*lowM)[u]==-1)
{
if(prevM[low1C[y]]==-1){y=low1C[y];}
else{y=(*lowM)[prevM[low1C[y]]];}
}
}
}
free(currentOut); free(foundC);
}
void get_l1l2_and_bcount(int n, int* adj, int* firstOut, int* dfs, int* idfs, int* p, int** l1, int** l2, int** bcount)
{
(*l1) = (int*)malloc(sizeof(int)*n);
(*l2) = (int*)malloc(sizeof(int)*n);
(*bcount) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*l1)[i]=i; (*l2)[i]=i; (*bcount)[i]=0;}
char* found_p = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){found_p[i]=0;}
char* found_c = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){found_c[i]=0;}
for(int i=n-1;i>0;i--)
{
int x=idfs[i];
for(int t=firstOut[x];t<firstOut[x+1];t++)
{
int y=adj[t];
if(dfs[y]<dfs[x])
{
if(y==p[x]&&!found_p[x])
{
found_p[x]=1;
}
else
{
if(dfs[y]<=dfs[(*l1)[x]]){(*l2)[x]=(*l1)[x]; (*l1)[x]=y;}
else if(dfs[y]<dfs[(*l2)[x]]){(*l2)[x]=y;}
(*bcount)[x]++; (*bcount)[y]--;
}
}
else if(x==p[y]&&!found_c[y])
{
(*bcount)[x]+=(*bcount)[y];
found_c[y]=1;
}
}
}
free(found_p); free(found_c);
}
void sortAdjInc(int n, int* adj, int* firstOut, int* idfs)
{
int* adj_copy = (int*)malloc(sizeof(int)*firstOut[n]);
int* currentOut = (int*)malloc(sizeof(int)*(n+1));
for(int i=0;i<firstOut[n];i++){adj_copy[i]=adj[i];}
for(int i=0;i<=n;i++){currentOut[i]=firstOut[i];}
for(int i=0;i<n;i++)
{
int x=idfs[i];
for(int t=firstOut[x];t<firstOut[x+1];t++)
{
int y=adj_copy[t];
adj[currentOut[y]++]=x;
}
}
free(adj_copy); free(currentOut);
}
void DFS(int n, int* adj, int* firstOut, int** dfs, int** idfs, int** p)
{
*dfs = (int*)malloc(sizeof(int)*n);
*idfs = (int*)malloc(sizeof(int)*n);
*p = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*dfs)[i]=-1; (*p)[i]=-1;}
int* temp_vertex = (int*)malloc(sizeof(int)*n);
int* temp_out = (int*)malloc(sizeof(int)*n);
int nr=0;
(*dfs)[0]=nr; (*idfs)[nr++]=0;
temp_vertex[0]=0; temp_out[0]=firstOut[0];
int SP=0;
while(SP!=-1)
{
int v=temp_vertex[SP];
char descend=0;
for(int i=temp_out[SP];i<firstOut[v+1];i++)
{
int u=adj[i];
if((*dfs)[u]==-1)
{
(*dfs)[u]=nr; (*idfs)[nr++]=u; (*p)[u]=v;
temp_vertex[SP+1]=u; temp_out[SP+1]=firstOut[u]; temp_out[SP]=i+1;
descend=1; break;
}
}
if(descend){SP++;continue;}
SP--;
}
free(temp_vertex); free(temp_out);
}
void get_l_and_bcount(int n, int* adj, int* firstOut, int* dfs, int* idfs, int* p, int** l, int** bcount)
{
(*l) = (int*)malloc(sizeof(int)*n);
(*bcount) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*l)[i]=i; (*bcount)[i]=0;}
char* found_p = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){found_p[i]=0;}
char* found_c = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){found_c[i]=0;}
for(int i=n-1;i>0;i--)
{
int x=idfs[i];
for(int t=firstOut[x];t<firstOut[x+1];t++)
{
int y=adj[t];
if(dfs[y]<dfs[x])
{
if(y==p[x]&&!found_p[x])
{
found_p[x]=1;
}
else
{
if(dfs[y]<dfs[(*l)[x]]){(*l)[x]=y;}
(*bcount)[x]++; (*bcount)[y]--;
}
}
else if(x==p[y]&&!found_c[y])
{
(*bcount)[x]+=(*bcount)[y];
found_c[y]=1;
}
}
}
free(found_p); free(found_c);
}
void get_2low(int n, int* adj, int* firstOut, int* dfs, int* idfs, int* p, int** low1, int** low1D, int** low2, int** low2D)
{
(*low1) = (int*)malloc(sizeof(int)*n);
(*low1D) = (int*)malloc(sizeof(int)*n);
(*low2) = (int*)malloc(sizeof(int)*n);
(*low2D) = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*low1)[i]=i; (*low2)[i]=i;}
char* foundP = (char*)malloc(sizeof(char)*n);
char* foundC = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){foundP[i]=0;foundC[i]=0;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
for(int j=firstOut[v];j<firstOut[v+1];j++)
{
int u=adj[j];
if(u==p[v]&&!foundP[v]){foundP[v]=1;continue;}
if(dfs[u]<dfs[v])
{
if(dfs[u]<=dfs[(*low1)[v]])
{
(*low2)[v]=(*low1)[v]; (*low2D)[v]=(*low1D)[v];
(*low1)[v]=u; (*low1D)[v]=v;
}
else if(dfs[u]<dfs[(*low2)[v]])
{
(*low2)[v]=u; (*low2D)[v]=v;
}
}
else if(v==p[u]&&!foundC[u])
{
if(dfs[(*low2)[u]]<=dfs[(*low1)[v]])
{
(*low1)[v]=(*low1)[u]; (*low1D)[v]=(*low1D)[u];
(*low2)[v]=(*low2)[u]; (*low2D)[v]=(*low2D)[u];
}
else if(dfs[(*low1)[u]]<=dfs[(*low1)[v]])
{
if(dfs[(*low1)[v]]<dfs[(*low2)[v]])
{
(*low2)[v]=(*low1)[v]; (*low2D)[v]=(*low1D)[v];
}
else if(dfs[(*low2)[u]]<dfs[(*low2)[v]])
{
(*low2)[v]=(*low2)[u]; (*low2D)[u]=(*low2D)[u];
}
(*low1)[v]=(*low1)[u]; (*low1D)[v]=(*low1D)[u];
}
else if(dfs[(*low1)[u]]<dfs[(*low2)[v]])
{
(*low2)[v]=(*low1)[u]; (*low2D)[v]=(*low1D)[u];
}
foundC[u]=1;
}
}
}
free(foundP); free(foundC);
}
void get_low(int n, int* adj, int* firstOut, int* dfs, int* idfs, int* p, int** low)
{
*low = (int*)malloc(sizeof(int)*n);
for(int i=0;i<n;i++){(*low)[i]=i;}
char* found_p = (char*)malloc(sizeof(char)*n);
for(int i=0;i<n;i++){found_p[i]=0;}
for(int i=n-1;i>0;i--)
{
int v=idfs[i];
for(int t=firstOut[v];t<firstOut[v+1];t++)
{
int u=adj[t];
if(dfs[u]<dfs[v])
{
if(u==p[v] && !found_p[v])
{
found_p[v]=1;
}
else
{
if(dfs[u]<dfs[(*low)[v]]){(*low)[v]=u;}
}
}
else if(v==p[u])
{
if(dfs[(*low)[u]]<dfs[(*low)[v]]){(*low)[v]=(*low)[u];}
}
}
}
free(found_p);
}
void get_adj(int n, int m, int* edges, int** adj, int** firstOut)
{
*adj = (int*)malloc(sizeof(int)*2*m);
*firstOut = (int*)malloc(sizeof(int)*(n+1));
for(int i=0;i<=n;i++){(*firstOut)[i]=0;}
for(int i=0;i<m;i++){(*firstOut)[edges[2*i]+1]++; (*firstOut)[edges[2*i+1]+1]++;}
for(int i=1;i<=n;i++){(*firstOut)[i]+=(*firstOut)[i-1];}
int* nextOut = (int*)malloc(sizeof(int)*(n+1));
for(int i=0;i<=n;i++){nextOut[i]=(*firstOut)[i];}
for(int i=0;i<m;i++)
{
int x=edges[2*i]; int y=edges[2*i+1];
(*adj)[nextOut[x]++]=y; (*adj)[nextOut[y]++]=x;
}
free(nextOut);
}
void read_graph(char* filename, int* n, int** adj, int** firstOut)
{
int m;
FILE* fp = fopen(filename,"r");
fscanf(fp,"%d %d",n,&m);
int* edges = (int*)malloc(sizeof(int)*2*m);
for(int i=0;i<m;i++){fscanf(fp,"%d %d",edges+2*i,edges+2*i+1);}
fclose(fp);
get_adj(*n,m,edges,adj,firstOut);
free(edges);
}