8.8 正睿暑期集训营 Day5

目录

• 2018.8.8 正睿暑期集训营 Day5
  • 总结
  • A 友谊巨轮(线段树 动态开点)
  • B 璀璨光滑
  • C 构解巨树
  • 考试代码
    • A
    • B
    • C

---

2018.8.8 正睿暑期集训营 Day5

时间：3.5h(实际)

期望得分：60+20+20

实际得分：20+20+20

比赛链接

这里也有一些

总结

线段树！！！

[Update]好了现在我已经见什么都想写线段树了。

A 友谊巨轮(线段树 动态开点)

题目链接

开n棵线段树，维护最大值及答案，动态开点就完了啊。。

//4810ms	71524kb
#include <cstdio>
#include <cctype>
#include <cstring>
#include <algorithm>
//#define gc() getchar()
#define MAXIN 300000
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
typedef long long LL;
const int N=1e5+5;

int n,K,m,root[N],Ans;
char IN[MAXIN],*SS=IN,*TT=IN;
struct Operation
{
	int a,b,c;
}opt[N];

struct Segment_Tree
{
	#define S N*50//每次最多4次Modify，但是有2次之前开过了，so N*17*2就够。
	#define ls son[x][0]
	#define rs son[x][1]
	#define lson ls,l,m
	#define rson rs,m+1,r
	int tot,son[S][2];
	struct Node
	{
		LL mxv; int tm,ans;
		bool operator <(const Node &x)const{
			return mxv==x.mxv?tm<x.tm:mxv<x.mxv;
		}
	}t[S];

	#define Update(x) t[x]=std::max(t[ls],t[rs])
	void Modify(int &x,int l,int r,int p,LL v,int tm)
	{
		if(!x) x=++tot, ls=rs=0, t[x]=(Node){0,0,0};//取max，tm也要清零啊
		if(l==r) {t[x].mxv+=v, t[x].tm=std::max(t[x].tm,tm), t[x].ans=p; return;}
		int m=l+r>>1;
		if(p<=m) Modify(lson,p,v,tm);
		else Modify(rson,p,v,tm);
		Update(x);
	}
}T;

inline int read()
{
	int now=0;register char c=gc();
	for(;!isdigit(c);c=gc());
	for(;isdigit(c);now=now*10+c-'0',c=gc());
	return now;
}
void Modify(int a,int b,int c,int tm)
{
	int bef=T.t[root[a]].ans;
	T.Modify(root[a],1,n,b,c,tm);
	int now=T.t[root[a]].ans;
	if(bef==now) return;
	if(bef)
		if(T.t[root[bef]].ans==a) ++Ans;
		else --Ans;
	if(now)
		if(T.t[root[now]].ans==a) --Ans;
		else ++Ans;
}

int main()
{
//	freopen("a.in","r",stdin);
//	freopen("my.out","w",stdout);

	T.t[0].tm=1000000;
	for(int Case=read(); Case--; )
	{
		memset(root,0,sizeof root);
		n=read(), K=read(), m=read(), T.tot=Ans=0;
		for(int i=1,a,b,c; i<=K; ++i)
		{
			opt[i]=(Operation){a=read(),b=read(),c=read()};
			Modify(a,b,c,i), Modify(b,a,c,i);
			if(i>m)
				Modify(opt[i-m].a,opt[i-m].b,-opt[i-m].c,i-m), Modify(opt[i-m].b,opt[i-m].a,-opt[i-m].c,i-m);
			printf("%d\n",Ans);
		}
	}
	return 0;
}

B 璀璨光滑

题目链接

C 构解巨树

题目链接

考试代码

A

//7.7K...(其实copy了两遍)
//暴力都可以O(n)得到答案，非得O(1)。。但是数组改map就可以60了啊
//巨难调。。
#include <map>
#include <queue>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <algorithm>
//#define gc() getchar()
#define MAXIN 300000
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
typedef long long LL;
const int N=1e5+5;

int n,K,m;
char IN[MAXIN],*SS=IN,*TT=IN;
struct Operation
{
	int a,b,c;
}opt[N];

inline int read()
{
	int now=0;register char c=gc();
	for(;!isdigit(c);c=gc());
	for(;isdigit(c);now=now*10+c-'0',c=gc());
	return now;
}
namespace Subtask1
{
	const int S=1005;
	int ship[S],tm[S][S];
	LL mx[S],val[S][S];
	bool alone[S];
//	struct Node
//	{
//		int mxv,tm,id;
//		bool operator <(const Node &x)const{
//			return mxv==x.mxv?tm<x.tm:mxv<x.mxv;
//		}
//	};
//	struct Heap
//	{
//		std::priority_queue<Node> q;
//		inline void Clear() {while(!q.empty()) q.pop();}
//	}hp[S];

	void Main()
	{
		memset(mx,0,sizeof mx);
		memset(tm,0,sizeof tm);
		memset(val,0,sizeof val);
//		memset(tag,0,sizeof tag);
		memset(ship,0,sizeof ship);
		memset(alone,0,sizeof alone);
//		for(int i=1; i<=n; ++i) hp[i].Clear();

		int ans=0; if(m>K) m=K;
		for(int i=1; i<=n; ++i) tm[i][0]=1000000;
		for(int i=1,a,b,c; i<=m; ++i)
		{
			a=read(), b=read(), c=read(), opt[i]=(Operation){a,b,c};
			tm[a][b]=tm[b][a]=i;

			if((val[a][b]+=c)>=mx[a] && ship[a]!=b)
			{
				if(ship[ship[a]]==a) ++ans, alone[ship[a]]=1;
				mx[a]=val[a][b], ship[a]=b;
			}
			if((val[b][a]+=c)>=mx[b] && ship[b]!=a)
			{
				if(ship[ship[b]]==b) ++ans, alone[ship[b]]=1;
				mx[b]=val[b][a], ship[b]=a;
			}
			if(!alone[a]&&ship[a]==b&&ship[b]!=a) ++ans, alone[a]=1;
			else if(alone[a]&&ship[ship[a]]==a) --ans, alone[a]=0;
			if(!alone[b]&&ship[b]==a&&ship[a]!=b) ++ans, alone[b]=1;
			else if(alone[b]&&ship[ship[b]]==b) --ans, alone[b]=0;
			printf("%d\n",ans);
		}
		for(int i=m+1,a,b,c; i<=K; ++i)
		{
			a=opt[i-m].a, b=opt[i-m].b, c=opt[i-m].c;
			val[a][b]-=c, val[b][a]-=c;
//			printf("Now:%d bef:%d a:%d b:%d\n",i,i-m,a,b);
			if(ship[a]==b)
			{
				int p=0;
				for(int j=1; j<=n; ++j) if(val[a][j]>val[a][p]||(val[a][j]==val[a][p]&&tm[a][j]>tm[a][p])) p=j;
//				printf("a: ship[%d]=%d p:%d\n",a,b,p);
				if(!p)
				{
					if(alone[a]) --ans, alone[a]=0;
					ship[a]=mx[a]=0;
				}
				else if(p!=b)
				{
					if(ship[b]==a) ++ans, alone[b]=1;
					ship[a]=p, mx[a]=val[a][p];
					if(ship[p]==a)
					{
						--ans, alone[p]=0;
						if(alone[a]) --ans, alone[a]=0;
					}
					else if(!alone[a]) ++ans, alone[a]=1;
				}
				else mx[a]-=c;
			}
//			printf("aa: %d\n",ans);
			if(ship[b]==a)
			{
				int p=0;
				for(int j=1; j<=n; ++j) if(val[b][j]>val[b][p]||(val[b][j]==val[b][p]&&tm[b][j]>tm[b][p])) p=j;
//				printf("b: ship[%d]=%d p:%d\n",b,a,p);
				if(!p)
				{
					if(alone[b]) --ans, alone[b]=0;
					ship[b]=mx[b]=0;
				}
				else if(p!=a)
				{
					if(ship[a]==b) ++ans, alone[a]=1;
					ship[b]=p, mx[b]=val[b][p];
					if(ship[p]==b)
					{
						--ans, alone[p]=0;
						if(alone[b]) --ans, alone[b]=0;
					}
					else if(!alone[b]) ++ans, alone[b]=1;
				}
				else mx[b]-=c;
			}
//			printf("bb: %d\n",ans);

			a=read(), b=read(), c=read(), opt[i]=(Operation){a,b,c};
			tm[a][b]=tm[b][a]=i;

			if((val[a][b]+=c)>=mx[a] && ship[a]!=b)
			{
				if(ship[ship[a]]==a) ++ans, alone[ship[a]]=1;
				mx[a]=val[a][b], ship[a]=b;
			}
			if((val[b][a]+=c)>=mx[b] && ship[b]!=a)
			{
				if(ship[ship[b]]==b) ++ans, alone[ship[b]]=1;
				mx[b]=val[b][a], ship[b]=a;
			}
			if(!alone[a]&&ship[a]==b&&ship[b]!=a) ++ans, alone[a]=1;
			else if(alone[a]&&ship[ship[a]]==a) --ans, alone[a]=0;
			if(!alone[b]&&ship[b]==a&&ship[a]!=b) ++ans, alone[b]=1;
			else if(alone[b]&&ship[ship[b]]==b) --ans, alone[b]=0;
			printf("%d\n",ans);
		}
	}
}
namespace Subtask2
{//m=k
	int ship[N];
	LL mx[N];
	bool alone[N];
	std::map<int,LL> val[N];

	void Main()
	{
		for(int i=1; i<=n; ++i) val[i].clear();
		memset(mx,0,sizeof mx);
		memset(ship,0,sizeof ship);
		memset(alone,0,sizeof alone);

		int ans=0;
		for(int i=1,a,b,c; i<=m; ++i)
		{
			a=read(), b=read(), c=read();
			if((val[a][b]+=c)>=mx[a] && ship[a]!=b)
			{
				if(ship[ship[a]]==a) ++ans, alone[ship[a]]=1;
				mx[a]=val[a][b], ship[a]=b;
			}
			if((val[b][a]+=c)>=mx[b] && ship[b]!=a)
			{
				if(ship[ship[b]]==b) ++ans, alone[ship[b]]=1;
				mx[b]=val[b][a], ship[b]=a;
			}
			if(!alone[a]&&ship[a]==b&&ship[b]!=a) ++ans, alone[a]=1;
			else if(alone[a]&&ship[ship[a]]==a) --ans, alone[a]=0;
			if(!alone[b]&&ship[b]==a&&ship[a]!=b) ++ans, alone[b]=1;
			else if(alone[b]&&ship[ship[b]]==b) --ans, alone[b]=0;
			printf("%d\n",ans);
		}
	}
}
namespace Subtask3
{
	int ship[N];
	LL mx[N];
	std::map<int,int> tm[N];
	std::map<int,LL> val[N];
	bool alone[N];

	void Main()
	{
		memset(mx,0,sizeof mx);
		memset(ship,0,sizeof ship);
		memset(alone,0,sizeof alone);
		for(int i=1; i<=n; ++i) tm[i].clear(), val[i].clear();

		int ans=0; if(m>K) m=K;
		for(int i=1; i<=n; ++i) tm[i][0]=1000000;
		for(int i=1,a,b,c; i<=m; ++i)
		{
			a=read(), b=read(), c=read(), opt[i]=(Operation){a,b,c};
			tm[a][b]=tm[b][a]=i;

			if((val[a][b]+=c)>=mx[a] && ship[a]!=b)
			{
				if(ship[ship[a]]==a) ++ans, alone[ship[a]]=1;
				mx[a]=val[a][b], ship[a]=b;
			}
			if((val[b][a]+=c)>=mx[b] && ship[b]!=a)
			{
				if(ship[ship[b]]==b) ++ans, alone[ship[b]]=1;
				mx[b]=val[b][a], ship[b]=a;
			}
			if(!alone[a]&&ship[a]==b&&ship[b]!=a) ++ans, alone[a]=1;
			else if(alone[a]&&ship[ship[a]]==a) --ans, alone[a]=0;
			if(!alone[b]&&ship[b]==a&&ship[a]!=b) ++ans, alone[b]=1;
			else if(alone[b]&&ship[ship[b]]==b) --ans, alone[b]=0;
			printf("%d\n",ans);
		}
		for(int i=m+1,a,b,c; i<=K; ++i)
		{
			a=opt[i-m].a, b=opt[i-m].b, c=opt[i-m].c;
			val[a][b]-=c, val[b][a]-=c;
			if(ship[a]==b)
			{
				int p=0;
				for(int j=1; j<=n; ++j) if(val[a][j]>val[a][p]||(val[a][j]==val[a][p]&&tm[a][j]>tm[a][p])) p=j;
				if(!p)
				{
					if(alone[a]) --ans, alone[a]=0;
					ship[a]=mx[a]=0;
				}
				else if(p!=b)
				{
					if(ship[b]==a) ++ans, alone[b]=1;
					ship[a]=p, mx[a]=val[a][p];
					if(ship[p]==a)
					{
						--ans, alone[p]=0;
						if(alone[a]) --ans, alone[a]=0;
					}
					else if(!alone[a]) ++ans, alone[a]=1;
				}
				else mx[a]-=c;
			}
			if(ship[b]==a)
			{
				int p=0;
				for(int j=1; j<=n; ++j) if(val[b][j]>val[b][p]||(val[b][j]==val[b][p]&&tm[b][j]>tm[b][p])) p=j;
				if(!p)
				{
					if(alone[b]) --ans, alone[b]=0;
					ship[b]=mx[b]=0;
				}
				else if(p!=a)
				{
					if(ship[a]==b) ++ans, alone[a]=1;
					ship[b]=p, mx[b]=val[b][p];
					if(ship[p]==b)
					{
						--ans, alone[p]=0;
						if(alone[b]) --ans, alone[b]=0;
					}
					else if(!alone[b]) ++ans, alone[b]=1;
				}
				else mx[b]-=c;
			}

			a=read(), b=read(), c=read(), opt[i]=(Operation){a,b,c};
			tm[a][b]=tm[b][a]=i;

			if((val[a][b]+=c)>=mx[a] && ship[a]!=b)
			{
				if(ship[ship[a]]==a) ++ans, alone[ship[a]]=1;
				mx[a]=val[a][b], ship[a]=b;
			}
			if((val[b][a]+=c)>=mx[b] && ship[b]!=a)
			{
				if(ship[ship[b]]==b) ++ans, alone[ship[b]]=1;
				mx[b]=val[b][a], ship[b]=a;
			}
			if(!alone[a]&&ship[a]==b&&ship[b]!=a) ++ans, alone[a]=1;
			else if(alone[a]&&ship[ship[a]]==a) --ans, alone[a]=0;
			if(!alone[b]&&ship[b]==a&&ship[a]!=b) ++ans, alone[b]=1;
			else if(alone[b]&&ship[ship[b]]==b) --ans, alone[b]=0;
			printf("%d\n",ans);
		}
	}
}

int main()
{
//	freopen("a2.in","r",stdin);
//	freopen("my.out","w",stdout);

	for(int Case=read(); Case--; )
	{
		n=read(), K=read(), m=read();
		if(m==K) {Subtask2::Main(); continue;}
		if(n<=1000) {Subtask1::Main(); continue;}
		Subtask3::Main();
//		for(int i=1; i<=K; ++i) opt[i]=(Operation){read(),read(),read()};

	}
	return 0;
}

B

#include <cstdio>
#include <cctype>
#include <cstring>
#include <algorithm>
//#define gc() getchar()
#define MAXIN 400000
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
#define mod (1000000007)
typedef long long LL;
const int N=5e5+5,M=4e5+5;

int n,m,lim,pw2[N],pw10[N],Enum,H[N],nxt[M],to[M],p[N];
bool vic,use[N];
char IN[MAXIN],*SS=IN,*TT=IN;

inline int read()
{
	int now=0;register char c=gc();
	for(;!isdigit(c);c=gc());
	for(;isdigit(c);now=now*10+c-'0',c=gc());
	return now;
}
inline void AddEdge(int u,int v)
{
	if(u<v) std::swap(u,v);
	to[++Enum]=v, nxt[Enum]=H[u], H[u]=Enum;//big->small
}
inline bool Check(int v1,int v2)
{
	for(int i=0,f=1; i<=n; ++i)
		if((v1>>i&1)^(v2>>i&1))
			if(f) f=0;
			else return 0;
	return 1;
}
inline bool OK(int x,int val)
{
	for(int i=H[x]; i; i=nxt[i])
		if(!Check(p[to[i]],val)) return 0;
	return 1;
}
void DFS(int now,LL ans)
{
	if(vic) return;
	if(now==lim) {vic=1, printf("%lld\n",ans%mod); return;}
	for(int x=0; x<lim; ++x)
		if(!use[x] && OK(now,x))
		{
			use[x]=1, p[now]=x;
			DFS(now+1,ans+1ll*x*pw10[now]%mod);
			if(vic) return;
			use[x]=0;
		}
}

int main()
{
//	freopen("b1.in","r",stdin);
//	freopen(".out","w",stdout);

	pw10[0]=1;
	for(int i=0; i<=18; ++i) pw2[i]=1<<i;
	for(int i=1; i<=pw2[12]/*pw2[18]*/; ++i) pw10[i]=1ll*pw10[i-1]*10%mod;
	for(int Case=read(); Case--; )
	{
		n=read(), m=read(), Enum=vic=0, lim=pw2[n];
		for(int i=1; i<=lim; ++i) H[i]=0;
		for(int i=1; i<=m; ++i) AddEdge(read()-1,read()-1);
		DFS(0,0);
		for(int i=0; i<lim; ++i) use[i]=0;
	}
	return 0;
}

C

#include <cstdio>
#include <cctype>
#include <assert.h>
#include <algorithm>
//#define gc() getchar()
#define MAXIN 400000
#define gc() (SS==TT&&(TT=(SS=IN)+fread(IN,1,MAXIN,stdin),SS==TT)?EOF:*SS++)
#define mod (1000000007)
typedef long long LL;
const int N=1e5+5,M=4e5+5;

int n,m,Enum,H[N],nxt[M],to[M],sz[N],sum[N],sz2[N],sum2[N],sz3[N],sum3[N];
LL Ans;
char IN[MAXIN],*SS=IN,*TT=IN;

inline int read()
{
	int now=0;register char c=gc();
	for(;!isdigit(c);c=gc());
	for(;isdigit(c);now=now*10+c-'0',c=gc());
	return now;
}
inline void AddEdge(int u,int v)
{
	to[++Enum]=v, nxt[Enum]=H[u], H[u]=Enum;
	to[++Enum]=u, nxt[Enum]=H[v], H[v]=Enum;
}
namespace Subtask1
{
	const int N=4e6+5,M=N<<1;
	int Enum,H[N],nxt[M],to[M],sz[N],sum[N];
	LL Ans;

	inline void AddEdge(int u,int v)
	{
//		printf("%d->%d\n",u,v);
		to[++Enum]=v, nxt[Enum]=H[u], H[u]=Enum;
		to[++Enum]=u, nxt[Enum]=H[v], H[v]=Enum;
	}
	void DFS(int x,int f)
	{
		sz[x]=1; LL tmp=0;
		for(int v,i=H[x]; i; i=nxt[i])
			if((v=to[i])!=f) DFS(v,x), sz[x]+=sz[v], tmp+=sum[v];
		sum[x]=(int)((tmp+sz[x])%mod);
		tmp=0;
		for(int v,i=H[x]; i; i=nxt[i])
			if((v=to[i])!=f) tmp+=1ll*(sz[x]-sz[v])*sum[v]%mod;
		Ans+=tmp%mod;
	}
	void Main()
	{
		for(int i=1; i<n; ++i)
			for(int u=read(),v=read(),j=0; j<m; ++j) AddEdge(j*n+u,j*n+v);
		for(int i=1,a,b; i<m; ++i) a=read()-1,b=read()-1,AddEdge(b*n+read(),a*n+read());//mmp忘了
		DFS(1,1);
		printf("%lld\n",Ans%mod);
	}
}
void DFS(int x,int f)
{
	sum[x]=0, sz[x]=1; LL tmp=0;
	for(int v,i=H[x]; i; i=nxt[i])
		if((v=to[i])!=f) DFS(v,x), sz[x]+=sz[v], tmp+=sum[v];
	sum[x]=(int)((tmp+sz[x])%mod);
	tmp=0;
	for(int v,i=H[x]; i; i=nxt[i])
		if((v=to[i])!=f) tmp+=1ll*(sz[x]-sz[v])*sum[v]%mod;
	Ans+=tmp%mod;
}
void DFS2(int x,int f)
{
	LL tmp=0,size=sz3[x]+1;
	for(int v,i=H[x]; i; i=nxt[i])
		if((v=to[i])!=f) DFS(v,x), size+=sz[v], tmp+=sum[v];
	sz[x]=(int)(size%mod);
	sum[x]=(int)((tmp+sz[x]+sum3[x])%mod);
	tmp=0;
	for(int v,i=H[x]; i; i=nxt[i])
		if((v=to[i])!=f) tmp+=1ll*(sz[x]-sz[v])*sum[v]%mod;
	Ans+=tmp%mod;
}

int main()
{
	freopen("c3.in","r",stdin);
//	freopen(".out","w",stdout);

	n=read(), m=read();
	if(1ll*n*m<=4e6) {Subtask1::Main(); return 0;}
	for(int i=1; i<n; ++i) AddEdge(read(),read());
	DFS(1,1), Ans=Ans*(m-1)%mod;
	sum2[1]=sum[1], sz2[1]=sz[1];
	for(int i=1,a,b,u,v; i<m; ++i)
	{
		a=read(), b=read(), u=read(), v=read();
		if(!sz2[v]) DFS(v,v);
		sz3[u]+=sz2[v], sz3[u]>=mod&&(sz3[u]-=mod);
		sum3[u]+=(sum2[v]+sz2[v])%mod, sum3[u]>=mod&&(sum3[u]-=mod);
	}
	DFS2(1,1);
	printf("%lld\n",Ans%mod);

	return 0;
}