[GCD最小生成树 LCT] HDU5398 .GCD TREE

可以发现只要保留边 (i,j) 其中 i 整除 j 的边就行了

用LCT来维护最大生成树就可以了

#include <cstdio>#include <iostream>#include <algorithm>using namespace std;typedef long long ll;const int N=1500010;int n,cnt,m;struct iedge{    int x,y;    friend bool operator <(iedge a,iedge b){        return a.x<b.x;    }}e[N];struct inode{    inode *ch[2],*f;    int v,imax;    bool rev;}a[N];int lst;ll cur,ans[100010];void PutAns(ll x){    if(x>=10) PutAns(x/10); putchar(x%10+'0');}int fa[N];int find(int x){    return fa[x]==x?x:fa[x]=find(fa[x]);}inline int isr(inode *x){    return x->f && x->f->ch[1]==x;}inline int isl(inode *x){    return !x->f || (x->f->ch[0]!=x && x->f->ch[1]!=x);}inline void Up(inode *x){    if(!x) return ;    x->imax=x->v;    if(x->ch[0] && e[x->ch[0]->imax].y<e[x->imax].y)        x->imax=x->ch[0]->imax;    if(x->ch[1] && e[x->ch[1]->imax].y<e[x->imax].y)        x->imax=x->ch[1]->imax;}inline void Push(inode *x){    if(!x || !x->rev) return ;    swap(x->ch[0],x->ch[1]);    if(x->ch[0]) x->ch[0]->rev^=1;    if(x->ch[1]) x->ch[1]->rev^=1;    x->rev=0;}inline void rot(inode *x){    inode *y=x->f,*z=y->f; int wh=isr(x);    if(!isl(y)) z->ch[isr(y)]=x; x->f=z;    if(y->ch[wh]=x->ch[wh^1]) y->ch[wh]->f=y;    (x->ch[wh^1]=y)->f=x; Up(y); Up(x);}void PushTop(inode *x){    if(!isl(x)) PushTop(x->f); Push(x);}inline void splay(inode *x){    PushTop(x);    for(;!isl(x);rot(x)) if(!isl(x->f)) rot(isr(x)^isr(x->f)?x:x->f);}inline void access(inode *x){    for(inode *t=0;x;x=x->f)        splay(x),x->ch[0]=t,t=x,Up(x);}inline void reverse(inode *x){    access(x); splay(x); x->rev^=1;}inline void link(inode *x,inode *y){    reverse(x); x->f=y; access(x);}inline void cut(inode *x,inode *y){    reverse(x); access(y); splay(y); x->f=y->ch[0]=0; Up(y);}inline int Query(inode *x,inode *y){    reverse(x); access(y); splay(y);    return y->imax;}inline void Addedge(iedge c,int x){    a[m+x].imax=a[m+x].v=x;    if(find(c.x)!=find(c.y)){        fa[find(c.x)]=find(c.y);         link(a+c.x,a+m+x); link(a+c.y,a+m+x);        cur+=e[x].y;        return ;    }    int imin=Query(a+c.x,a+c.y);    if(e[imin].y>=e[x].y) return ;    cur+=e[x].y-e[imin].y;    cut(a+e[imin].x,a+m+imin); cut(a+e[imin].y,a+m+imin);    link(a+c.x,a+m+x); link(a+c.y,a+m+x);}int main(){    m=100000; e[0].y=1<<30;    for(int i=1;i<=m;i++)        for(int j=i+i;j<=m;j+=i) e[++cnt]=(iedge){j,i};    sort(e+1,e+1+cnt); int j=0;    for(int i=1;i<=m;i++) fa[i]=i;    while(~scanf("%d",&n)){        for(int i=lst+1;i<=n;i++){            while(e[j+1].x<=i && j<cnt)                 Addedge(e[j+1],j+1),j++;            ans[i]=cur;        }        lst=max(lst,n);        PutAns(ans[n]); putchar('\n');    }    return 0;}