BZOJ4912 SDOI2017天才黑客（最短路+虚树）

　　容易想到把边当成点重建图跑最短路。将每条边拆成入边和出边，作为新图中的两个点，由出边向入边连边权为原费用的边。对于原图中的每个点，考虑由其入边向出边连边。直接暴力两两连边当然会被卡掉，注意到其边权是trie上lca的深度，由lca转rmq的做法可知，两点lca即为欧拉序区间中它们之间深度最小的点，于是跑出欧拉序后对入边出边的前后缀建虚点连边即可。当然每次连边时都需要将trie上有用的点提取出来，建虚树即可。

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
#define ll long long
#define N 50010
#define inf 2000000000
#define in(i) (i*2+n)
#define out(i) (i*2+n-1)
char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<'0'||c>'9')) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{
	int 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<<1)+(x<<3)+(c^48),c=getchar();
	return x*f;
}
int T,n,m,k,p[N],t;
struct data{int to,nxt,len,s;
}edge[N];
vector<int> in_edge[N];
namespace trie
{
	int p[N],t,fa[N][18],deep[N],dfn[N],cnt;
	struct data{int to,nxt;}edge[N];
	void clear(){memset(p,0,sizeof(p));cnt=t=0;}
	void addedge(int x,int y){t++;edge[t].to=y,edge[t].nxt=p[x],p[x]=t;}
	void dfs(int k)
	{
		dfn[k]=++cnt;
		for (int i=p[k];i;i=edge[i].nxt)
		{
			deep[edge[i].to]=deep[k]+1;
			fa[edge[i].to][0]=k;
			dfs(edge[i].to);
		}
	}
	void build()
	{
		fa[1][0]=1;dfs(1);
		for (int j=1;j<18;j++)
			for (int i=1;i<=k;i++)
			fa[i][j]=fa[fa[i][j-1]][j-1];
	}
	int lca(int x,int y)
	{
		if (deep[x]<deep[y]) swap(x,y);
		for (int j=17;~j;j--) if (deep[fa[x][j]]>=deep[y]) x=fa[x][j];
		if (x==y) return x;
		for (int j=17;~j;j--) if (fa[x][j]!=fa[y][j]) x=fa[x][j],y=fa[y][j];
		return fa[x][0];
	}
}
namespace graph
{
	int p[N<<6],t,cnt,dis[N<<6];
	bool flag[N<<6];
	struct data{int to,nxt,len;}edge[N<<7];
	struct data2
	{
		int x,d;
		bool operator <(const data2&a) const
		{
			return d>a.d;
		}
	};
	priority_queue<data2> q;
	void addedge(int x,int y,int z){t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].len=z,p[x]=t;}
	void clear(){cnt=n+m*2;t=0;memset(p,0,sizeof(p));}
	void dijkstra()
	{
		for (int i=1;i<=cnt;i++) dis[i]=inf;dis[1]=0;
		memset(flag,0,sizeof(flag));
		q.push((data2){1,0});
		for (;;)
		{
			while (!q.empty()&&flag[q.top().x]) q.pop();
			if (q.empty()) break;
			data2 x=q.top();q.pop();
			flag[x.x]=1;
			for (int i=p[x.x];i;i=edge[i].nxt)
			if (dis[x.x]+edge[i].len<dis[edge[i].to])
			{
				dis[edge[i].to]=dis[x.x]+edge[i].len;
				q.push((data2){edge[i].to,dis[edge[i].to]});
			}
		}
	}
}
namespace virtual_tree
{
	int a[N],tot,stk[N],id[N<<1],top,p[N],x[N],y[N],idin[N<<1],idout[N<<1],pre[N<<1],suf[N<<1],t,cnt;
	struct data{int to,nxt;}edge[N<<1];
	void addedge(int u,int v){t++;x[t]=u,y[t]=v;}
	void clear(){tot=top=t=cnt=0;}
	void push(int x){a[++tot]=x;}
	bool cmp(const int&a,const int&b)
	{
		return trie::dfn[a]<trie::dfn[b];
	}
	void dfs(int k)
	{
		id[++cnt]=k;idin[k]=graph::cnt+cnt;
		for (int i=p[k];i;i=edge[i].nxt)
		{
			dfs(edge[i].to);
			id[++cnt]=k;
		}
	}
	void build()
	{
		if (tot==0) return;
		sort(a+1,a+tot+1,cmp);
		tot=unique(a+1,a+tot+1)-a-1;
		stk[++top]=1;
		for (int i=1+(a[1]==1);i<=tot;i++)
		{
			int l=trie::lca(a[i],stk[top]);
			if (stk[top]!=l)
			{
				while (top>1&&trie::deep[stk[top-1]]>=trie::deep[l]) addedge(stk[top-1],stk[top]),top--;
				if (stk[top]!=l) addedge(l,stk[top]);
				stk[top]=l;
			}
			stk[++top]=a[i];
		}
		while (top>1) addedge(stk[top-1],stk[top]),top--;
		for (int i=1;i<=t;i++) p[x[i]]=p[y[i]]=0;
		for (int i=1;i<=t;i++) edge[i].to=y[i],edge[i].nxt=p[x[i]],p[x[i]]=i;
		dfs(1);for (int i=1;i<=cnt;i++) idout[id[i]]=idin[id[i]]+cnt;graph::cnt+=cnt<<1;
		for (int i=1;i<=cnt;i++)
		{
			pre[i]=++graph::cnt;
			graph::addedge(idin[id[i]],pre[i],0);
			if (i>1) graph::addedge(pre[i-1],pre[i],0);
		}
		for (int i=cnt;i>=1;i--)
		{
			suf[i]=++graph::cnt;
			graph::addedge(suf[i],idout[id[i]],0);
			if (i<cnt) graph::addedge(suf[i],suf[i+1],0);
		}
		for (int i=1;i<=cnt;i++) graph::addedge(pre[i],suf[i],trie::deep[id[i]]);
		for (int i=1;i<=cnt;i++)
		{
			pre[i]=++graph::cnt;
			graph::addedge(pre[i],idout[id[i]],0);
			if (i>1) graph::addedge(pre[i],pre[i-1],0);
		}
		for (int i=cnt;i>=1;i--)
		{
			suf[i]=++graph::cnt;
			graph::addedge(idin[id[i]],suf[i],0);
			if (i<cnt) graph::addedge(suf[i+1],suf[i],0);
		}
		for (int i=1;i<=cnt;i++) graph::addedge(suf[i],pre[i],trie::deep[id[i]]);
	}
}
int main()
{
#ifndef ONLINE_JUDGE
	freopen("bzoj4912.in","r",stdin);
	freopen("bzoj4912.out","w",stdout);
	const char LL[]="%I64d\n";
#else
	const char LL[]="%lld\n";
#endif
	T=read();
	while (T--)
	{
		n=read(),m=read(),k=read();
		memset(p,0,sizeof(p));t=0;
		for (int i=1;i<=n;i++) in_edge[i].clear();
		for (int i=1;i<=m;i++)
		{
			int x=read(),y=read(),len=read(),s=read();
			t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].len=len,edge[t].s=s,p[x]=t;
		}
		trie::clear();
		for (int i=1;i<k;i++)
		{
			int x=read(),y=read(),z=read();
			trie::addedge(x,y);
		}
		trie::build();
		graph::clear();
		for (int i=p[1];i;i=edge[i].nxt)
		graph::addedge(1,out(i),0);
		for (int i=1;i<=m;i++) if (edge[i].to!=1) graph::addedge(in(i),edge[i].to,0);
		for (int i=1;i<=m;i++) graph::addedge(out(i),in(i),edge[i].len);
		for (int i=1;i<=m;i++) in_edge[edge[i].to].push_back(i);
		for (int i=1;i<=n;i++)
		{
			virtual_tree::clear();
			for (int j=0;j<in_edge[i].size();j++) virtual_tree::push(edge[in_edge[i][j]].s);
			for (int j=p[i];j;j=edge[j].nxt) virtual_tree::push(edge[j].s);
			virtual_tree::build();
			for (int j=0;j<in_edge[i].size();j++) graph::addedge(in(in_edge[i][j]),virtual_tree::idin[edge[in_edge[i][j]].s],0);
			for (int j=p[i];j;j=edge[j].nxt) graph::addedge(virtual_tree::idout[edge[j].s],out(j),0);
		}
		graph::dijkstra();
		for (int i=2;i<=n;i++) printf("%d\n",graph::dis[i]);
	}
	return 0;
}