[CERC2015]Juice Junctions(边双连通+字符串hash)

做法

考虑边数限制的特殊条件，显然答案仅有\(\{0,1,2,3\}\)

• 0：不联通

• 1：连通

• 2：边双连通

• 3：任意删掉一条边都为边双连通

考虑每次删边后记录各点的边双染色情况来特判\(3\)：是否所有情况都相同

Code

#include<bits/stdc++.h>
typedef int LL;
typedef long long ll;
const LL maxn=1e6+9,inf=0x3f3f3f3f;
const ll base_1=233,base_2=2333,mod1=99991,mod2=99989;
inline LL Read(){
    LL x(0),f(1); char c=getchar();
    while(c<'0' || c>'9'){
        if(c=='-') f=-1; c=getchar();
    }
    while(c>='0' && c<='9'){
        x=(x<<3)+(x<<1)+c-'0'; c=getchar();
    }return x*f;
}
struct node{
	LL to,nxt;
}dis[maxn];
LL n,m,top,num,nod,tim,ban,ans;
LL head[maxn],col[maxn],sta[maxn],dfn[maxn],low[maxn],f[maxn],hash_1[maxn],hash_2[maxn];
ll hash1[maxn],hash2[maxn];
inline void Add(LL u,LL v){
	dis[++num]=(node){v,head[u]}; head[u]=num;
}
void Tarjan(LL u,LL fa){
	dfn[u]=low[u]=++tim; sta[++top]=u;
	for(LL i=head[u];i;i=dis[i].nxt){
		LL v(dis[i].to);
		if(v==fa || i==ban || i==ban-1) continue;
		if(!dfn[v]){
			Tarjan(v,u); low[u]=std::min(low[u],low[v]);
		}else low[u]=std::min(low[u],dfn[v]);
	}
	if(low[u]==dfn[u]){
		LL now; ++nod;
		do{
			now=sta[top--]; col[now]=nod;
		}while(now!=u);
	}
}
LL Find(LL x){
	return f[x]==x?x:f[x]=Find(f[x]);
}
inline void Union(LL u,LL v){
	f[Find(u)]=Find(v);
}
int main(){
	n=Read(); m=Read();
	for(LL i=1;i<=n;++i) f[i]=i;
	for(LL i=1;i<=m;++i){
		LL u(Read()),v(Read());
		Add(u,v); Add(v,u);
		Union(u,v);
	}
	for(LL i=1;i<=n;++i)
	    if(!dfn[i])
	        Tarjan(i,0);
	for(LL i=1;i<=n;++i)
	    for(LL j=i+1;j<=n;++j)
	        ans+=(Find(i)==Find(j)) + (col[i]==col[j]);
	for(ban=2;ban<=(m<<1);ban+=2){
		memset(dfn,0,4*(n+1)); nod=top=tim=0;
		for(LL i=1;i<=n;++i)
		    if(!dfn[i])
		        Tarjan(i,0);
		for(LL i=1;i<=n;++i){
		    hash_1[i]=(hash_1[i]*base_1%mod1+col[i])%mod1;
		    hash_2[i]=(hash_2[i]*base_2%mod1+col[i])%mod2;
		}
	}
	for(LL i=1;i<=n;++i)
	    for(LL j=i+1;j<=n;++j)
	        ans+=(hash_1[i]==hash_1[j] && hash_2[i]==hash_2[j]);
	printf("%d\n",ans);
	return 0;
}