190908 CSP-S 2019 模拟

A

ddDP
ddSTD
$f_{i,j,k}$表示长度为 $j$ 的序列放了 $k$ 种长度不超过 $k$ 的连续颜色段
然后我开的long long而不是long double成功败北
告辞
代码：

#include
#define ri register int
#define fi first
#define se second
using namespace std;
const int rlen=1<<18|1;
char buf[rlen],*ib=buf,*ob=buf;
#define gc() (((ib==ob)&&(ob=(ib=buf)+fread(buf,1,rlen,stdin)),ib==ob)?-1:*ib++)
typedef pair<int,int> pii;
inline int read(){
	int ans=0;
	char ch=gc();
	while(!isdigit(ch))ch=gc();
	while(isdigit(ch))ans=((ans<<2)+ans<<1)+(ch^48),ch=gc();
	return ans;
}
const int N=255;
int n,m;
long double f[N][N][N];
inline void init(int lm=250){
	memset(f,0,sizeof(f));
	for(ri len=1;len<=lm;++len){
		f[len][0][0]=1;
		for(ri i=1;i<=lm;++i){
			for(ri j=1;j<=i;++j){
				f[len][i][j]=f[len][i-1][j]+f[len][i-1][j-1];
				(i-len-1>=0)&&(f[len][i][j]-=f[len][i-len-1][j-1]);
			}
		}		
	}
}
inline long double calc(int len){
	long double A=0,B=0,C=n,D=1;
	for(ri i=1;i<=m;++i){
		A+=C*f[len][m][i];
		B+=C*D;
		C/=i+1,C*=n-i;
		D/=i,D*=m-i;
	}
	return A/B;
}
int main(){
	#ifdef ldxcaicai
	freopen("lx.in","r",stdin);
	#endif
	init();
	for(ri tt=read();tt;--tt){
		m=read(),n=read();
		long double ans=0,cur,lst=0;
		for(ri i=1;i<=m;++i,lst=cur)ans+=i*((cur=calc(i))-lst);
		printf("%.10lf\n",(double)ans);
	}
	return 0;
}

B

考虑对每条狗搞一个很妙的构造：

然后这样你每用一个人匹配掉一个点剩下的匹配数都是对的，就成了一般图最大匹配，带花树即可。
代码：

#include
#define ri register int
#define pb push_back
using namespace std;
const int N=805,M=1e6+5,Lim=800;
int n,m;
const int rlen=1<<18|1;
inline char gc(){
	static char buf[rlen],*ib,*ob;
	(ib==ob)&&(ob=(ib=buf)+fread(buf,1,rlen,stdin));
	return ib==ob?-1:*ib++;
}
inline int read(){
	int ans=0;
	char ch=gc();
	while(!isdigit(ch))ch=gc();
	while(isdigit(ch))ans=((ans<<2)+ans<<1)+(ch^48),ch=gc();
	return ans;
}
namespace Blossom{
	int q[N],hd,tl,len,tot=0,tim,vs[N],tg[N],mch[N],ft[N],pre[N];
	vector<int>e[N];
	inline void clear(){
		for(ri i=1;i<=tot;++i)e[i].clear(),mch[i]=0;
		tot=0;
	}
	inline void add(int u,int v){e[u].pb(v),e[v].pb(u),tot=max(tot,u),tot=max(tot,v);}
	inline int find(int x){return x^ft[x]?ft[x]=find(ft[x]):x;}
	inline int lca(int x,int y){
		++tim;
		while(1){
			if(x){
				if(vs[x=find(x)]==tim)return x;
				vs[x]=tim,x=pre[mch[x]];
			}
			swap(x,y);
		}
	}
	inline void shrink(int x,int y,int t){
		while(find(x)^t){
			pre[x]=y,y=mch[x];
			if(tg[y]==2)tg[q[++len,tl=tl==tot?1:tl+1]=y]=1;
			if(find(x)==x)ft[x]=t;
			if(find(y)==y)ft[y]=t;
			x=pre[y];
		}
	}
	inline bool bfs(int x){
		tim=0;
		for(ri i=1;i<=tot;++i)tg[i]=q[i]=vs[i]=pre[i]=0,ft[i]=i;
		tg[q[hd=tl=len=1]=x]=1;
		while(len){
			int x=q[hd];
			--len,hd=hd==tot?1:hd+1;
			for(ri t,i=0,v;i<e[x].size();++i){
				if(find(x)==find(v=e[x][i])||tg[v]==2)continue;
				if(!tg[v]){
					pre[v]=x,tg[v]=2;
					if(!mch[v]){
						for(ri a=v,b,nxt;a;a=nxt){
							b=pre[a];
							nxt=mch[b];
							mch[a]=b,mch[b]=a;
						}
						return 1;
					}
					tg[(++len,q[tl=tl==tot?1:tl+1]=mch[v])]=1;
				}
				else t=lca(x,v),shrink(x,v,t),shrink(v,x,t);
			}
		}
		return 0;
	}
	inline int solve(){
		int res=0;
		for(ri i=1;i<=tot;++i)if(!mch[i]&&bfs(i))++res;
		return res-n;
	}
}
inline int idx(int a,int b){return n+(a-1)*7+b+1;}
int main(){
	#ifdef ldxcaicai
	freopen("lx.in","r",stdin);
	#endif
	for(ri tt=read();tt;--tt){
		n=read(),m=read();
		Blossom::clear();
		for(ri i=1;i<=m;++i){
			for(ri j=0;j<5;++j){
				Blossom::add(idx(i,j),idx(i,(j+1)%5));
				Blossom::add(idx(i,j),idx(i,5));
				Blossom::add(idx(i,j),idx(i,6));
			}
		}
		for(ri i=1;i<=n;++i){
			for(ri ttt=read(),vl;ttt;--ttt){
				vl=read();
				for(ri j=0;j<5;++j)Blossom::add(idx(vl,j),i);
			}
		}
		cout<<Blossom::solve()<<'\n';
	}
	return 0;
}

C

ddDFS序维护fib数
ddSTD居然写两个log
注：我代码里的HLD是拿来求lca的（捂脸
代码：

#include
#define ri register int
#define fi first
#define se second
#define pb push_back
using namespace std;
const int rlen=1<<18|1;
char buf[rlen],*ib=buf,*ob=buf;
#define gc() (((ib==ob)&&(ob=(ib=buf)+fread(buf,1,rlen,stdin)),ib==ob)?-1:*ib++)
typedef pair<int,int> pii;
inline int read(){
	int ans=0;
	char ch=gc();
	while(!isdigit(ch))ch=gc();
	while(isdigit(ch))ans=((ans<<2)+ans<<1)+(ch^48),ch=gc();
	return ans;
}
typedef long long ll;
inline ll readl(){
	ll ans=0;
	char ch=gc();
	while(!isdigit(ch))ch=gc();
	while(isdigit(ch))ans=((ans<<2)+ans<<1)+(ch^48),ch=gc();
	return ans;
}
inline char gcr(){
	char ch=gc();
	while(!isalpha(ch))ch=gc();
	return ch;
}
const int mod=1e9+7;
inline int add(int a,int b){return (a+=b)<mod?a:a-mod;}
inline int dec(int a,int b){return (a-=b)<0?a+mod:a;}
inline int mul(int a,int b){return (ll)a*b%mod;}
inline void Add(int&a,int b){(a+=b)<mod?a:(a-=mod);}
inline void Dec(int&a,int b){(a-=b)<0?(a+=mod):a;}
inline void Mul(int&a,int b){a=(ll)a*b%mod;}
inline int ksm(int a,int p){int ret=1;for(;p;p>>=1,Mul(a,a))if(p&1)Mul(ret,a);return ret;}
struct F{
	int a,b;
	F(int a=0,int b=0):a(a),b(b){}
	inline F conj()const{return F(a,mod-b);}
	friend inline F operator+(F a,F b){return F(add(a.a,b.a),add(a.b,b.b));}
	friend inline F operator-(F a,F b){return F(dec(a.a,b.a),dec(a.b,b.b));}
	friend inline F operator*(F a,F b){return F(add(mul(a.a,b.a),mul(5,mul(a.b,b.b))),add(mul(a.a,b.b),mul(a.b,b.a)));}
	friend inline F operator*(F a,int b){return F(mul(a.a,b),mul(a.b,b));}
	friend inline void operator+=(F&a,F b){a=a+b;}
	friend inline void operator-=(F&a,F b){a=a-b;}
	friend inline void operator*=(F&a,F b){a=a*b;}
	friend inline void operator*=(F&a,int b){a=a*b;}
	friend inline F operator^(F a,ll p){F ret=F(1,0);for(;p;p>>=1,a*=a)if(p&1)ret*=a;return ret;}
}t1,t2,t3;
const int N=1e5+5;
int n,m;
int fa[N],hson[N],dep[N],top[N],in[N],out[N],siz[N],tot=0;
vector<int>e[N];
void dfs1(int p){
	siz[p]=1;
	for(ri i=0,v;i<e[p].size();++i){
		fa[v=e[p][i]]=p,dep[v]=dep[p]+1,dfs1(v),siz[p]+=siz[v];
		if(siz[v]>siz[hson[p]])hson[p]=v;
	}
}
void dfs2(int p,int tp){
	top[p]=tp;
	in[p]=++tot;
	if(!hson[p]){out[p]=tot;return;}
	dfs2(hson[p],tp);
	for(ri i=0,v;i<e[p].size();++i)if((v=e[p][i])^hson[p])dfs2(v,v);
	out[p]=tot;
}
inline int lca(int x,int y){
	while(top[x]^top[y]){
		if(dep[top[x]]<dep[top[y]])swap(x,y);
		x=fa[top[x]];
	}
	return dep[x]<dep[y]?x:y;
}
struct BIT{
	#define lowbit(x) ((x)&(-(x)))
	F bit[N];
	inline void update(int p,F v){for(;p<=n;p+=lowbit(p))bit[p]+=v;}
	inline F query(int p){F ret;for(;p;p^=lowbit(p))ret+=bit[p];return ret;}
}T1,T2;
int main(){
	int iv2=mod+1>>1;
	t1=F(iv2,iv2);
	t2=F(mod-iv2,iv2);
	t3=F(mod-iv2,mod-iv2);
	n=read(),m=read();
	for(ri i=2;i<=n;++i)e[read()].pb(i);
	dfs1(1),dfs2(1,1);
	ll k;
	F vl,tp;
	for(ri x,y,t;m;--m){
		char ch=gcr();
		if(ch=='U'){
			x=read(),k=readl();
			vl=t1^k;
			tp=t2^dep[x];
			T1.update(in[x],vl*t3);
			T1.update(out[x]+1,vl*t3*(mod-1));
			T2.update(in[x],(vl*t3*tp)*(mod-1));
			T2.update(out[x]+1,vl*t3*tp);
		}
		else{
			x=read(),y=read(),t=lca(x,y);
			tp=T1.query(in[x])+T1.query(in[y])-T1.query(in[t])-T1.query(in[fa[t]]);
			tp+=T2.query(in[x])*(t1^(dep[x]+1))+T2.query(in[y])*(t1^(dep[y]+1))-T2.query(in[t])*(t1^(dep[t]+1))-T2.query(in[fa[t]])*(t1^(dep[fa[t]]+1));
			cout<<mul(tp.b,2)<<'\n';
		}
	}
	return 0;
}