点双联通分量 – OceanEye's Blog

Date Time

17/05/27 21:13

Author

点双联通分量乱搞
一遍DFS可以处理出一个点周围的连通分量 [tarjan]
还可以处理出他们的和
尝试用树形DP的思想来思考的话会很简单
但是~~玩点歌姬~~细节打错于是调了很久quq
代码

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cmath>
#define ll long long
#define INF 1000000000
#define p(x) ('0'<=x&&x<='9')
#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}

using namespace std;

#define N 100010

struct node
{
	int fa,dfn,mn,siz;
	bool vis;
}pool[N];
#define FA pool[x].fa
#define DFN pool[x].dfn
#define MN pool[x].mn
#define SIZ pool[x].siz
#define VIS pool[x].vis

struct Tedge
{
	int from,to;
	bool use;
	Tedge(int _=0,int __=0) { from=_; to=__; use=0; }
}edge[1000010];
int TOP;
#define E edge[i]
#define TO E.to
#define FROM E.from
#define USE E.use

int e_tot,NXT[1000010],fst[N];

void add_e(const int &a,const int &b)
{
	edge[e_tot]=Tedge(a,b); NXT[e_tot]=fst[a]; fst[a]=e_tot++;
	edge[e_tot]=Tedge(b,a); NXT[e_tot]=fst[b]; fst[b]=e_tot++;
}

void cp(int &x,int y) { x>y?x=y:x=x; }

ll ans[N];
int cd,n,m;
void tarjan(int x)
{
	DFN=MN=++cd; VIS=true;
	SIZ++;
	int pcnt=0;
	for(int i=fst[x];~i;i=NXT[i])
	{
		if(USE||TO==FA) continue;
		USE=true; i^=1; USE=true; i^=1;
		if(!pool[TO].vis)
		{
			pool[TO].fa=x;
			tarjan(TO);
			cp(MN,pool[TO].mn);
			if(pool[TO].mn>=DFN)
			{
				ans[x]+=(ll)pcnt*pool[TO].siz;
				pcnt+=pool[TO].siz;
			}
			SIZ+=pool[TO].siz;
		}
		else cp(MN,pool[TO].dfn);
	}
	ans[x]+=(ll)(n-pcnt-1)*pcnt;
}

int main()
{
	freopen("BZOJ1123.in","r",stdin);
	int __,_;
	memset(fst,-1,sizeof(fst));
	read(n); read(m);
	while(m--)
	{
		read(_); read(__);
		add_e(_,__);
	}
	tarjan(1);
	for(int i=1;i<=n;i++) printf("%lld\n",(ans[i]+(n-1))*2);
	return 0;
}

100

#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

#include <cmath>

#define ll long long

#define INF 1000000000

#define p(x) ('0'<=x&&x<='9')

#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

using namespace std;

#define N 100010

struct node

{

int fa,dfn,mn,siz;

bool vis;

}pool[N];

#define FA pool[x].fa

#define DFN pool[x].dfn

#define MN pool[x].mn

#define SIZ pool[x].siz

#define VIS pool[x].vis

struct Tedge

{

int from,to;

bool use;

Tedge(int _=0,int __=0) { from=_; to=__; use=0; }

}edge[1000010];

int TOP;

#define E edge[i]

#define TO E.to

#define FROM E.from

#define USE E.use

int e_tot,NXT[1000010],fst[N];

void add_e(const int &a,const int &b)

{

edge[e_tot]=Tedge(a,b); NXT[e_tot]=fst[a]; fst[a]=e_tot++;

edge[e_tot]=Tedge(b,a); NXT[e_tot]=fst[b]; fst[b]=e_tot++;

}

void cp(int &x,int y) { x>y?x=y:x=x; }

ll ans[N];

int cd,n,m;

void tarjan(int x)

{

DFN=MN=++cd; VIS=true;

SIZ++;

int pcnt=0;

for(int i=fst[x];~i;i=NXT[i])

{

if(USE||TO==FA) continue;

USE=true; i^=1; USE=true; i^=1;

if(!pool[TO].vis)

{

pool[TO].fa=x;

tarjan(TO);

cp(MN,pool[TO].mn);

if(pool[TO].mn>=DFN)

{

ans[x]+=(ll)pcnt*pool[TO].siz;

pcnt+=pool[TO].siz;

}

SIZ+=pool[TO].siz;

}

else cp(MN,pool[TO].dfn);

}

ans[x]+=(ll)(n-pcnt-1)*pcnt;

}

int main()

{

freopen("BZOJ1123.in","r",stdin);

int __,_;

memset(fst,-1,sizeof(fst));

read(n); read(m);

while(m--)

{

read(_); read(__);

add_e(_,__);

}

tarjan(1);

for(int i=1;i<=n;i++) printf("%lld\n",(ans[i]+(n-1))*2);

return 0;

}

Date Time

17/05/26 14:55

Author

OceanEye

XDDD YY了半天的点双联通忽略了最初点双的性质—-割点可能属于多个块

点双学习Link 1 2 3

~~代码施工中~~

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector>
#include <cstdlib>
#define ll long long
#define p(x) ('0'<=x&&x<='9')
#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}

using namespace std;
#define SIZ 1010
#define N 1000
struct node
{
	int fa,dfn,mn,childcnt;
	bool iscut;
	vector <int> belong;
	void init()
	{
		belong.clear();
		fa=dfn=mn=childcnt=iscut=0;
	}
}pool[SIZ];
#define FA pool[x].fa
#define MN pool[x].mn
#define DFN pool[x].dfn
#define CNT pool[x].childcnt
#define ISCUT pool[x].iscut
struct Tedge
{
	int from,to;
	bool use;
	Tedge(int _=0,int __=0,bool ___=false) { from=_; to=__; use=false; }
	bool operator != (const Tedge &x) { return (from!=x.from||to!=x.to); }
} edge[N<<1],STA[N];
int TOP;
#define E edge[i]
#define TO E.to
int e_tot,fst[SIZ],cur[SIZ],NXT[N<<1];
void add_e(int a,int b)
{
	edge[e_tot]=Tedge(a,b,false); NXT[e_tot]=fst[a]; fst[a]=e_tot++;
	edge[e_tot]=Tedge(b,a,false); NXT[e_tot]=fst[b]; fst[b]=e_tot++;
}
vector <int> BCC[SIZ];
int siz[SIZ],cnt[SIZ],tot;
int sta[SIZ],top;
bool use[SIZ];
unsigned ll ans1,ans2;

//
void init(int n)
{
	memset(fst,-1,sizeof(fst));
	memset(siz,0,sizeof(siz)); memset(cnt,0,sizeof(cnt));
	e_tot=0; tot=0; ans1=0; ans2=1;
	for(int i=1;i<=N;i++) BCC[i].clear();
	int _,__;
	For(i,1,n)
	{
		read(_); read(__); use[_]|=1; use[__]|=1;
		add_e(_,__);
	}
}

void cp(int &x,int y) { x>y?x=y:x=x; }
int cd;
void tarjan(int x)
{
	use[x]=false; DFN=MN=++cd;
	for(int i=fst[x];~i;i=NXT[i])
	{
		if(TO==FA) continue;
		if(edge[i].use) continue;
		STA[++TOP]=E;
		E.use=true; i^=1; E.use=true; i^=1;
		if(!use[TO]) cp(MN,pool[TO].dfn);
		else
		{
			CNT++;
			pool[TO].fa=x;
			tarjan(TO);
			MN=min(MN,pool[TO].mn);
			if(pool[TO].mn>=DFN)
			{
				Tedge cur;
				tot++;
				ISCUT=true;
				do
				{
					cur=STA[TOP--];
					if(pool[cur.from].belong.size()==0||pool[cur.from].belong.back()!=tot)
					{
						pool[cur.from].belong.push_back(tot);
						BCC[tot].push_back(cur.from);
					}
					if(pool[cur.to].belong.size()==0||pool[cur.to].belong.back()!=tot)
					{
						pool[cur.to].belong.push_back(tot);
						BCC[tot].push_back(cur.to);
					}
				}
				while(cur!=E);
			}
		}
	}
	if(CNT<2&&!FA) ISCUT=false;
}

int time;

void Main(int _)
{
	time++;
	init(_);
	For(i,1,1000) cur[i]=fst[i],pool[i].init();
	For(i,1,1000) if(use[i]) tarjan(i);
	For(i,1,1000)
	{
		if(!pool[i].dfn) continue;
		if(!pool[i].iscut)
		{
			siz[pool[i].belong[0]]++;
			continue;
		}
		for(int j=0;j<pool[i].belong.size();j++) cnt[pool[i].belong[j]]++,siz[pool[i].belong[j]]++;
	}
	For(i,1,tot) if(cnt[i]==1)
	{ ans1++; ans2*=(unsigned ll)(siz[i]==1?1:(siz[i]-1)); }
	else if(cnt[i]==0)
	{ ans1+=min(siz[i],2); ans2*=(unsigned ll)siz[i]*(siz[i]-1)/2; }
	printf("Case %d: %llu %llu\n",time,ans1,ans2);
}

int main()
{
	freopen("BZOJ2730.in","r",stdin);
	memset(cur,-1,sizeof(cur));
	int T; read(T);
	for(;T;read(T)) Main(T);
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstring>

#include <vector>

#include <cstdlib>

#define ll long long

#define p(x) ('0'<=x&&x<='9')

#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

using namespace std;

#define SIZ 1010

#define N 1000

struct node

{

int fa,dfn,mn,childcnt;

bool iscut;

vector <int> belong;

void init()

{

belong.clear();

fa=dfn=mn=childcnt=iscut=0;

}

}pool[SIZ];

#define FA pool[x].fa

#define MN pool[x].mn

#define DFN pool[x].dfn

#define CNT pool[x].childcnt

#define ISCUT pool[x].iscut

struct Tedge

{

int from,to;

bool use;

Tedge(int _=0,int __=0,bool ___=false) { from=_; to=__; use=false; }

bool operator != (const Tedge &x) { return (from!=x.from||to!=x.to); }

} edge[N<<1],STA[N];

int TOP;

#define E edge[i]

#define TO E.to

int e_tot,fst[SIZ],cur[SIZ],NXT[N<<1];

void add_e(int a,int b)

{

edge[e_tot]=Tedge(a,b,false); NXT[e_tot]=fst[a]; fst[a]=e_tot++;

edge[e_tot]=Tedge(b,a,false); NXT[e_tot]=fst[b]; fst[b]=e_tot++;

}

vector <int> BCC[SIZ];

int siz[SIZ],cnt[SIZ],tot;

int sta[SIZ],top;

bool use[SIZ];

unsigned ll ans1,ans2;

void init(int n)

{

memset(fst,-1,sizeof(fst));

memset(siz,0,sizeof(siz)); memset(cnt,0,sizeof(cnt));

e_tot=0; tot=0; ans1=0; ans2=1;

for(int i=1;i<=N;i++) BCC[i].clear();

int _,__;

For(i,1,n)

{

read(_); read(__); use[_]|=1; use[__]|=1;

add_e(_,__);

}

void cp(int &x,int y) { x>y?x=y:x=x; }

int cd;

void tarjan(int x)

{

use[x]=false; DFN=MN=++cd;

for(int i=fst[x];~i;i=NXT[i])

{

if(TO==FA) continue;

if(edge[i].use) continue;

STA[++TOP]=E;

E.use=true; i^=1; E.use=true; i^=1;

if(!use[TO]) cp(MN,pool[TO].dfn);

else

{

CNT++;

pool[TO].fa=x;

tarjan(TO);

MN=min(MN,pool[TO].mn);

if(pool[TO].mn>=DFN)

{

Tedge cur;

tot++;

ISCUT=true;

{

cur=STA[TOP--];

if(pool[cur.from].belong.size()==0||pool[cur.from].belong.back()!=tot)

{

pool[cur.from].belong.push_back(tot);

BCC[tot].push_back(cur.from);

}

if(pool[cur.to].belong.size()==0||pool[cur.to].belong.back()!=tot)

{

pool[cur.to].belong.push_back(tot);

BCC[tot].push_back(cur.to);

}

while(cur!=E);

}

if(CNT<2&&!FA) ISCUT=false;

}

int time;

void Main(int _)

{

time++;

init(_);

For(i,1,1000) cur[i]=fst[i],pool[i].init();

For(i,1,1000) if(use[i]) tarjan(i);

For(i,1,1000)

{

if(!pool[i].dfn) continue;

if(!pool[i].iscut)

{

siz[pool[i].belong[0]]++;

continue;

}

for(int j=0;j<pool[i].belong.size();j++) cnt[pool[i].belong[j]]++,siz[pool[i].belong[j]]++;

}

For(i,1,tot) if(cnt[i]==1)

{ ans1++; ans2*=(unsigned ll)(siz[i]==1?1:(siz[i]-1)); }

else if(cnt[i]==0)

{ ans1+=min(siz[i],2); ans2*=(unsigned ll)siz[i]*(siz[i]-1)/2; }

printf("Case %d: %llu %llu\n",time,ans1,ans2);

}

int main()

{

freopen("BZOJ2730.in","r",stdin);

memset(cur,-1,sizeof(cur));

int T; read(T);

for(;T;read(T)) Main(T);

return 0;

}

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很多人即使只见过一面，已经算见过了最后一面。

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