uoj#274. 【清华集训2016】温暖会指引我们前行（LCT）

传送门

不难发现肯定是在温度的最大生成树上走是最优的

于是用\(LCT\)维护最大生成树，每一次加边时如果已经连通，就判断一下路径上的最小温度是否小于当前温度，是的话就断掉那条边，加入新边

//minamoto
#include<bits/stdc++.h>
#define R register
#define fi first
#define se second
#define pi pair<int,int>
#define fp(i,a,b) for(R int i=a,I=b+1;i<I;++i)
#define fd(i,a,b) for(R int i=a,I=b-1;i>I;--i)
#define go(u) for(int i=head[u],v=e[i].v;i;i=e[i].nx,v=e[i].v)
using namespace std;
char buf[1<<21],*p1=buf,*p2=buf;
inline char getc(){return p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++;}
int read(){
    R int res,f=1;R char ch;
    while((ch=getc())>'9'||ch<'0')(ch=='-')&&(f=-1);
    for(res=ch-'0';(ch=getc())>='0'&&ch<='9';res=res*10+ch-'0');
    return res*f;
}
inline char getop(){char ch;while((ch=getc())!='f'&&ch!='m'&&ch!='c');return ch;}
char sr[1<<21],z[20];int C=-1,Z=0;
inline void Ot(){fwrite(sr,1,C+1,stdout),C=-1;}
void print(R int x){
    if(C>1<<20)Ot();if(x<0)sr[++C]='-',x=-x;
    while(z[++Z]=x%10+48,x/=10);
    while(sr[++C]=z[Z],--Z);sr[++C]='\n';
}
const int N=4e5+5;
int ch[N][2],fa[N],v[N],sum[N],f[N],w[N],px[N],py[N];bool rev[N];pi mn[N];
int n,m,id,x,y,t,l,zz;char op;
int find(int x){return f[x]==x?x:f[x]=find(f[x]);}
inline bool is(R int x){return ch[fa[x]][0]!=x&&ch[fa[x]][1]!=x;}
void upd(R int x){
	sum[x]=sum[ch[x][0]]+sum[ch[x][1]]+w[x];
	mn[x]=min(pi(v[x],x),min(mn[ch[x][0]],mn[ch[x][1]]));
}
inline void ppd(R int x){swap(ch[x][0],ch[x][1]),rev[x]^=1;}
inline void pd(R int x){if(rev[x])ppd(ch[x][0]),ppd(ch[x][1]),rev[x]=0;}
void update(R int x){if(!is(x))update(fa[x]);pd(x);}
void rotate(int x){
	int y=fa[x],z=fa[y],d=ch[y][1]==x;
	if(!is(y))ch[z][ch[z][1]==y]=x;
	fa[x]=z,fa[ch[x][d^1]]=y,ch[y][d]=ch[x][d^1],ch[x][d^1]=y,fa[y]=x,upd(y);
}
void splay(int x){
	update(x);
	for(R int y=fa[x],z=fa[y];!is(x);y=fa[x],z=fa[y]){
		if(!is(y))(ch[y][1]==x)^(ch[z][1]==y)?rotate(x):rotate(y);
		rotate(x);
	}upd(x);
}
inline void access(int x){
	int t=0;
	while(x)splay(x),ch[x][1]=t,upd(x),t=x,x=fa[x];
}
inline void makert(int x){
	access(x),splay(x),ppd(x);
}
inline void split(int x,int y){
	makert(x),access(y),splay(y);
}
inline void link(int x,int y){
	makert(x),fa[x]=y;
}
inline void cut(int x,int y){
	split(x,y),fa[x]=ch[y][0]=0,upd(y);
}
int main(){
//	freopen("testdata.in","r",stdin);
	n=read(),m=read();
	mn[0]=pi(1<<30,0);
	fp(i,1,n)f[i]=i,v[i]=1<<30,mn[i]=pi(v[i],i);
	while(m--){
		op=getop();
		switch(op){
			case 'f':{
				id=read()+1,x=read()+1,y=read()+1,t=read(),l=read();
				v[id+n]=t,sum[id+n]=w[id+n]=l,mn[id+n]=pi(v[id+n],id+n);
				px[id]=x,py[id]=y;
				if(find(x)!=find(y))link(id+n,x),link(id+n,y),f[f[x]]=f[y];
				else{
					split(x,y);
					if(mn[y].fi<t){
						zz=mn[y].se-n,cut(zz+n,px[zz]),cut(zz+n,py[zz]);
						link(id+n,x),link(id+n,y);
					}
				}
				break;
			}
			case 'm':{
				x=read()+1,y=read()+1;
				if(find(x)!=find(y))print(-1);
				else split(x,y),print(sum[y]);
				break;
			}
			case 'c':{
				id=read()+1,l=read();
				splay(id+n),w[id+n]=l,upd(id+n);
				break;
			}
		}
	}return Ot(),0;
}