BZOJ 3091: 城市旅行 LCT

维护 $\sum_{}v[i]\times dep[i]$ 与 $\sum_{} v[i]\times dep[i]^2$

其中 $dep[i]$ 表示 $i$ 点在该点所在 $LCT$ 的 $splay$ 中的中序遍历序.

然后正着维护一个，反着维护一个就行了.              

#include <cstdio>  
#include <cstring> 
#include <string>
#include <map>
#include <algorithm>   
#define N 50005  
#define ll long long   
#define siz size       
#define ts tag
#define lson s[x].ch[0] 
#define rson s[x].ch[1]    
#define get(x) (s[s[x].f].ch[1]==x) 
#define Isr(x) (!(s[s[x].f].ch[0]==x||s[s[x].f].ch[1]==x))        
using namespace std;   

ll sqr(ll x) { return x*x;  }   
ll calc1(ll x) { return x*(x+1ll)/2; }   
ll calc2(ll x) { return x*(x+1ll)*(2ll*x+1ll)/6; }   
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;  }

namespace IO {      

    void setIO(string s) 
    {
        string in=s+".in"; 
        string out=s+".out"; 
        freopen(in.c_str(),"r",stdin); 
        freopen(out.c_str(),"w",stdout); 
    }     

};          
 
int sta[N]; 
map<int,int>con[N];        

struct node { 
    int ch[2],rev,f; 
    ll s0[2],s1[2],s2[2],tag,v,size; 
}s[N];          

void Pushup(int x) 
{           
    s[x].size=s[lson].size+s[rson].size+1;  
    s[x].s0[0]=s[lson].s0[0]+s[rson].s0[0]+s[x].v;     
    s[x].s1[0]=s[lson].s1[0]+s[rson].s1[0]+(s[rson].s0[0]+s[x].v)*(s[lson].size+1);        
    s[x].s2[0]=s[s[x].ch[0]].s2[0]+s[s[x].ch[1]].s2[0]+(s[s[x].ch[1]].s0[0]+s[x].v)*(s[s[x].ch[0]].size+1)*(s[s[x].ch[0]].size+1)+2ll*s[s[x].ch[1]].s1[0]*(s[s[x].ch[0]].size+1);      
    s[x].s0[1]=s[lson].s0[1]+s[rson].s0[1]+s[x].v;   
    s[x].s1[1]=s[rson].s1[1]+s[lson].s1[1]+(s[lson].s0[1]+s[x].v)*(s[rson].size+1);        
    s[x].s2[1]=s[s[x].ch[1]].s2[1]+s[s[x].ch[0]].s2[1]+(s[s[x].ch[0]].s0[1]+s[x].v)*(s[s[x].ch[1]].size+1)*(s[s[x].ch[1]].size+1)+2ll*s[s[x].ch[0]].s1[1]*(s[s[x].ch[1]].size+1);       
} 

void Up_tag(int x,ll v) 
{      
    s[x].v+=v;      
    s[x].tag+=v;  
    s[x].s0[0]+=s[x].size*v;        
    s[x].s0[1]+=s[x].size*v;          
    s[x].s1[0]+=calc1(s[x].size)*v; 
    s[x].s1[1]+=calc1(s[x].size)*v;        
    s[x].s2[0]+=calc2(s[x].size)*v;   
    s[x].s2[1]+=calc2(s[x].size)*v;   
}  

void Up_rev(int x) 
{  
    s[x].rev^=1; 
    swap(lson,rson); 
    swap(s[x].s0[0],s[x].s0[1]); 
    swap(s[x].s1[0],s[x].s1[1]),swap(s[x].s2[0],s[x].s2[1]);   
}  

void Pushdown(int x) 
{ 
    if(s[x].tag) 
    {
        if(lson) Up_tag(lson,s[x].tag); 
        if(rson) Up_tag(rson,s[x].tag); 
        s[x].tag=0; 
    }
    if(s[x].rev) 
    {
        if(lson) Up_rev(lson); 
        if(rson) Up_rev(rson);    
        s[x].rev=0;        
    }
}  

 
void rotate(int x) 
{    
    int old=s[x].f,fold=s[old].f,which=get(x);   
    if(!Isr(old)) s[fold].ch[s[fold].ch[1]==old]=x;     
    s[old].ch[which]=s[x].ch[which^1]; 
    if(s[old].ch[which]) s[s[old].ch[which]].f=old; 
    s[x].ch[which^1]=old,s[old].f=x,s[x].f=fold; 
    Pushup(old),Pushup(x); 
}

void Splay(int x) 
{     
    int v=0,u=x,fa; 
    for(sta[++v]=u;!Isr(u);u=s[u].f)  sta[++v]=s[u].f;  
    for(;v;--v)  Pushdown(sta[v]);   
    for(u=s[u].f;(fa=s[x].f)!=u;rotate(x))   
    {   
        if(s[fa].f!=u) 
            rotate(get(fa)==get(x)?fa:x);
    }
}           

void Access(int x) 
{
    for(int y=0;x;y=x,x=s[x].f)  
    {
        Splay(x);     
        rson=y; 
        Pushup(x);  
    }
}

void Make_Root(int x) 
{
    Access(x); 
    Splay(x); 
    Up_rev(x);   
}

void Link_Edge(int x,int y) 
{    
    Access(x),Splay(x); 
    Make_Root(y);   
    s[y].f=x;   
}    

void Cut_Edge(int x,int y) 
{     
    Make_Root(x),Access(y),Splay(y);    
    if(!s[x].ch[1]&&s[y].ch[0]==x)   s[y].ch[0]=s[x].f=0;            
    Pushup(y);           
}

void Split(int x,int y) 
{
    Make_Root(x),Access(y),Splay(y);      
}

int Find_Root(int x) 
{   
    while(s[x].f) x=s[x].f;  
    return x;   
}       

int main() 
{ 
    // IO::setIO("input"); 
    int i,j,n,m; 
    scanf("%d%d",&n,&m);       
    for(i=1;i<=n;++i)  scanf("%lld",&s[i].v),Pushup(i); 
    for(i=1;i<n;++i) 
    {
        int x,y; 
        scanf("%d%d",&x,&y); 
        Link_Edge(x,y); 
        con[x][y]=con[y][x]=1; 
    }
    for(i=1;i<=m;++i) 
    {
        int op,x,y,z; 
        scanf("%d",&op); 
        if(op==1) 
        {    
            scanf("%d%d",&x,&y);           
            if(!con[x][y])  continue;   
            else 
            {
                Cut_Edge(x,y);    
                con[x][y]=con[y][x]=0; 
            }
        }
        if(op==2) 
        {    
            scanf("%d%d",&x,&y); 
            if(Find_Root(x)==Find_Root(y))  continue;        
            else 
            {
                con[x][y]=con[y][x]=1;    
                Link_Edge(x,y);            
            }
        }
        if(op==3) 
        {
            scanf("%d%d%d",&x,&y,&z);   
            if(Find_Root(x)!=Find_Root(y)) continue;        
            Split(x,y);      
            Up_tag(y,(ll)z);                       
        }
        if(op==4)                          
        {
            scanf("%d%d",&x,&y);     
            if(Find_Root(x)!=Find_Root(y)) printf("-1\n"); 
            else 
            {
                Split(x,y);                    
                ll dn=s[y].size*(s[y].size+1)/2;                               
                ll up=(s[y].size+1ll)*s[y].s1[0]-s[y].s2[0];  
                ll g=gcd(up,dn); 
                printf("%lld/%lld\n",up/g,dn/g);    
            }   
        }
    }
    return 0;
}