P2387 [NOI2014]魔法森林（LCT）

P2387 [NOI2014]魔法森林

LCT边权维护经典题

咋维护呢？边化为点，边权变点权。

本题中我们把边对关键字A进行排序，动态维护关键字B的最小生成树

加边后出现环咋办？

splay维护最大边的编号，找到最大边删除再加新边就ok辣

#include<cstdio>

#include<algorithm>

using namespace std;

inline void Swap(int &a,int &b){a^=b^=a^=b;}

inline int Min(int a,int b){return a<b?a:b;}

void read(int &x){

    static char c=getchar();x=;

    while(c<''||c>'') c=getchar();

    while(''<=c&&c<='') x=x*+(c^),c=getchar();

}

#define N 200005

struct edge{int f,t,A,B;}a[N];

int n,m,ans=2e9,ch[N][],fa[N],val[N],s[N],rev[N],dad[N];

#define lc ch[x][0]

#define rc ch[x][1]

inline bool cmp(edge P,edge Q){return P.A<Q.A;}

int find(int x){return dad[x]==x?x:dad[x]=find(dad[x]);}

inline bool nrt(int x){return ch[fa[x]][]==x||ch[fa[x]][]==x;}

void up(int x){//维护平衡树上最大点权的点的编号（就是边化为的点）

    s[x]=x;

    if(val[s[lc]]>val[s[x]]) s[x]=s[lc];

    if(val[s[rc]]>val[s[x]]) s[x]=s[rc];

}

void Rev(int x){Swap(lc,rc); rev[x]^=;}

void down(int x){if(rev[x]) Rev(lc),Rev(rc),rev[x]=;}

void Pre(int x){if(nrt(x))Pre(fa[x]); down(x);}

void turn(int x){

    int y=fa[x],z=fa[y],l=(ch[y][]==x),r=l^;

    if(nrt(y)) ch[z][ch[z][]==y]=x;

    fa[ch[x][r]]=y; fa[y]=x; fa[x]=z;

    ch[y][l]=ch[x][r]; ch[x][r]=y;

    up(y); up(x);

}

void splay(int x){

    Pre(x);

    for(;nrt(x);turn(x)){

        int y=fa[x],z=fa[y];

        if(nrt(y)) turn(((ch[z][]==y)^(ch[y][]==x))?x:y);

    }

}

void access(int x){for(int y=;x;y=x,x=fa[x]) splay(x),rc=y,up(x);}

void makert(int x){access(x);splay(x);Rev(x);}

int findrt(int x){

    access(x);splay(x);down(x);

    while(lc) x=lc,down(x);

    splay(x); return x;

}

void link(int x,int y){makert(x); if(findrt(y)!=x)fa[x]=y;}

void cut(int x,int y){

    makert(x);

    if(findrt(y)==x&&fa[y]==x&&!ch[y][]) fa[y]=rc=,up(x);

}

void split(int x,int y){makert(x);access(y);splay(y);}

int main(){

    read(n);read(m); register int i;

    for(i=;i<=n+m;++i) dad[i]=i;

    for(i=;i<=m;++i)

        read(a[i].f),read(a[i].t),read(a[i].A),read(a[i].B);

    sort(a+,a+m+,cmp);

    for(i=;i<=m;++i) val[n+i]=a[i].B;

    for(i=;i<=m;++i){

        int r1=find(a[i].f),r2=find(a[i].t),e;//并查集维护是否连通

        if(r1==r2){

            split(a[i].f,a[i].t); e=s[a[i].t];

            if(val[e]<=a[i].B) continue;

            cut(a[e-n].f,e); cut(e,a[e-n].t);//删掉最大边

        }else dad[r1]=r2;

        link(a[i].f,i+n); link(i+n,a[i].t);

        if(find()==find(n)) split(n,),ans=Min(ans,a[i].A+val[s[]]);

    }

    if(ans>=2e9) puts("-1");

    else printf("%d",ans);

    return ;

}