[GCD最小生成树 LCT] HDU5398 .GCD TREE

#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
;

struct inode{
inode *ch[2],*f;
int v,imax;
bool rev;
}a
;

int lst;

ll cur,ans[100010];

void PutAns(ll x){
if(x>=10) PutAns(x/10); putchar(x%10+'0');
}

int fa
;

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
); putchar('\n');
}
return 0;
}