[LCT 动态最大生成树] HDU 5398 GCD Tree

一个数肯定是和自己约数连更优

那么就是动态维护最大生成树

两个log

#include<cstdio>  #include<cstdlib>  #include<cstring>  #include<vector>#include<stack>#include<algorithm>  using namespace std;  typedef pair<int,int> abcd;typedef long long ll;  inline char nc(){    static char buf[100000],*p1=buf,*p2=buf;    if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }    return *p1++;  }    inline bool read(int &x){    char c=nc(),b=1;    for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1; else if (c==EOF) return 0;   for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;  return 1;}const int N=300005;struct Splay{    struct node{      int size,idx,rev;      int val,minimum;      node *p,*ch[2],*fat,*mpos;      void setc(node *c,int d) { ch[d]=c; c->p=this; }      bool dir() { return p->ch[1]==this; }      void update() {        size=ch[0]->size+ch[1]->size+1;        minimum=val; mpos=this;        if (ch[0]->minimum<minimum)  minimum=ch[0]->minimum,mpos=ch[0]->mpos;        if (ch[1]->minimum<minimum)  minimum=ch[1]->minimum,mpos=ch[1]->mpos;      }      void reverse() { rev^=1; swap(ch[0],ch[1]); }      void pushdown(node *null){        if (rev){  if (ch[0]!=null) ch[0]->reverse();  if (ch[1]!=null) ch[1]->reverse();  rev=0;        }      }    }*null,Mem[N];    Splay() { null=Mem; null->p=null->ch[0]=null->ch[1]=null->fat=null; null->size=0; null->minimum=(1<<30)+(1<<29); null->mpos=null; }    void rot(node *x){      if (x==null || x->p==null) return ;      bool d=x->dir(); node *p=x->p;      if (p->p!=null) p->p->setc(x,p->dir()); else x->p=null;      p->setc(x->ch[d^1],d); x->setc(p,d^1); p->update(); x->update(); swap(x->fat,p->fat);    }    node *sta[N];    void splay(node *x){      int pnt=0; node *y=x;      while (y!=null) sta[++pnt]=y,y=y->p;      for (int i=pnt;i;i--) sta[i]->pushdown(null);      while (x->p!=null)        if (x->p->p==null)  rot(x);        else  x->dir()==x->p->dir()?(rot(x->p),rot(x)):(rot(x),rot(x));    }    node *Access(node *x){      node *y=null;      while (x!=null){        splay(x);        x->ch[1]->p=null; x->ch[1]->fat=x;        x->setc(y,1); y->fat=null;        x->update();        y=x; x=x->fat;      }      return y;    }    void Link(node *x,node *y){      if (Jud(x,y)) return;      Access(x)->reverse(); splay(x); x->fat=y; Access(x);    }    void Cut(node *x){      Access(x); splay(x); x->ch[0]->p=null; x->ch[0]=null; x->fat=null; x->update();    }    void Cut(node *x,node *y){      Access(x)->reverse(); Cut(y);    }    node *Root(node *x){      Access(x); splay(x);      node *y=x;      while (y->ch[0]!=null) y->pushdown(null),y=y->ch[0];      return y;    }    bool Jud(node *x,node *y){      return Root(x)==Root(y);    }    int Query(node *x,node *y){      Access(x)->reverse();      return Access(y)->minimum;    }    node *Road(node *x,node *y){      Access(x)->reverse();      return Access(y)->mpos;    }  }LCT;    Splay::node *pos[N];    inline void Init(){    for (int i=1;i<=N-5;i++){      pos[i]=LCT.Mem+i;       pos[i]->p=pos[i]->ch[0]=pos[i]->ch[1]=pos[i]->fat=LCT.null;       pos[i]->val=1<<30; pos[i]->minimum=1<<30; pos[i]->mpos=pos[i];      pos[i]->idx=i; pos[i]->size=1;    }  }const int MAXN=1e5;vector<int> d[MAXN+5];ll Ans[MAXN+5];int n=MAXN,m;int icnt;int u[N],v[N];stack<int> S;inline void Memery(){  for (int i=100000;i;i--) S.push(i);}inline int New(){  int i=S.top(); S.pop(); i+=n;  pos[i]->p=pos[i]->ch[0]=pos[i]->ch[1]=pos[i]->fat=LCT.null;     pos[i]->val=1<<30; pos[i]->minimum=1<<30; pos[i]->mpos=pos[i]; pos[i]->size=1;  return i-n;}inline void Del(int x){  S.push(x);}int main(){  freopen("t.in","r",stdin);  freopen("t.out","w",stdout);  Init(); Memery();  for (int i=2;i<=n;i++) for (int j=i+i;j<=n;j+=i) d[j].push_back(i);  ll ret=0;  Ans[1]=ret;  for (int i=2;i<=n;i++){    icnt=New(); u[icnt]=1; v[icnt]=i;    pos[n+icnt]->val=1; pos[n+icnt]->update();    LCT.Link(pos[n+icnt],pos[i]);      LCT.Link(pos[n+icnt],pos[1]);    ret+=1;    for (int j=0;j<(signed)d[i].size();j++){      int d=::d[i][j];        Splay::node *road=LCT.Road(pos[d],pos[i]);        if (road->val<d){icnt=New(); u[icnt]=d; v[icnt]=i;pos[n+icnt]->val=d; pos[n+icnt]->update();LCT.Cut(road,pos[u[road->idx-n]]);  LCT.Cut(road,pos[v[road->idx-n]]);  LCT.Link(pos[n+icnt],pos[i]);  LCT.Link(pos[n+icnt],pos[d]);ret+=d-road->val;Del(road->idx-n);      }    }    Ans[i]=ret;  }  int _n;  while (read(_n))    printf("%lld\n",Ans[_n]);  return 0;}