沉迷Link-Cut tree无法自拔之：[BZOJ3669][Noi2014] 魔法森林

//made by Hero_of_Someone
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#define N (50040)
#define M (100010)
#define RG register
using namespace std;
inline int gi(){ RG int x=0,q=1; RG char ch=getchar(); while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
  if(ch=='-') q=-1,ch=getchar(); while('0'<=ch&&ch<='9') x=x*10+ch-'0',ch=getchar(); return q*x; }
void File(){freopen(".in","r",stdin);freopen(".out","w",stdout);}

int n,m;
struct Edge{ 
  int u,v,a,b; 
  bool operator<(const Edge& x)const{ return a<x.a; }
}e[M];

inline void init(){
  n=gi(),m=gi();
  for(RG int i=1;i<=m;i++){
    e[i].u=gi(),e[i].v=gi();
    e[i].a=gi(),e[i].b=gi();
  }
  sort(e+1,e+m+1);
}

int Max[N+M],val[N+M];
int ch[N+M][2],fa[N+M],rev[N+M];

inline void cur(int x,int y){ val[x]=Max[x]=y; }

inline bool cnm(int x,int y){ return e[x].b<e[y].b; }

inline void up(int x){
  Max[x]=max(Max[ch[x][0]],Max[ch[x][1]],cnm);
  Max[x]=max(Max[x],val[x],cnm);
}

inline void reverse(int x){
  swap(ch[x][0],ch[x][1]);
  rev[x]^=1;
}

inline void down(int x){
  if(!rev[x]) return ;
  reverse(ch[x][0]);
  reverse(ch[x][1]);
  rev[x]=0;
}

inline bool is_root(int x){ return ch[fa[x]][0]!=x && x!=ch[fa[x]][1]; }

inline bool lr(int x){ return x==ch[fa[x]][1]; }

inline void rotate(int x){
  RG int y=fa[x],z=fa[y],k=lr(x);
  if(!is_root(y)) ch[z][lr(y)]=x;
  fa[x]=z; fa[ch[x][k^1]]=y; fa[y]=x;
  ch[y][k]=ch[x][k^1]; ch[x][k^1]=y;
  up(y); up(x);
}

int st[N+M];
inline void splay(int x){
  RG int y=x,top=0;
  while(1){
    st[++top]=y;
    if(is_root(y)) break;
    y=fa[y];
  }
  for(RG int i=top;i;i--) down(st[i]);
  while(!is_root(x)){
    if(!is_root(fa[x])) rotate(lr(x)^lr(fa[x])?x:fa[x]);
    rotate(x);
  }
}

inline void access(int x){
  RG int y=0;
  while(x){ splay(x);
    ch[x][1]=y; fa[y]=x;
    up(x); y=x; x=fa[x];
  }
}

inline void make_root(int x){
  access(x); splay(x); reverse(x);
}

inline int find(int x){
  while(fa[x]) x=fa[x];
  return x;
}

inline void link(int x,int y){
  if(find(x)==find(y)) return ;
  make_root(x); fa[x]=y;
}

inline void cut(int x,int y){
  make_root(x); access(y); splay(y);
  if(ch[y][0]==x) ch[y][0]=0,fa[x]=0,up(y);
}

inline int query(int x,int y){
  make_root(x); access(y); splay(y);
  return Max[y];
}

inline void Insert(int id){
  RG int x=e[id].u,y=e[id].v;
  if(x==y) return ;
  if(find(x)==find(y)){
    RG int tmp=query(x,y);
    if(e[tmp].b<=e[id].b) return ;
    cut(n+tmp,e[tmp].u);
    cut(n+tmp,e[tmp].v);
  }
  cur(n+id,id);
  link(x,n+id);
  link(y,n+id);
}

inline void work(){
  RG int ans=1<<30;
  for(RG int i=1;i<=m;i++){ 
    Insert(i);
    if(find(1)!=find(n)) continue;
    ans=min(ans,e[i].a+e[query(1,n)].b);
  }
  if(ans==1<<30) ans=-1;
  printf("%d\n",ans);
}

int main(){ init(); work(); return 0; }