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zc
2020-02-01 00:38:00
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可以发现按dfs序排序后路径是a_1,a_2,a_3,...,a_k,a_1

那答案就是dist(a_1,a_2)+dist(a_2,a_3)+...+dist(a_k,a_1)

设现在要插入x,y,zx的前驱后继(dfs序上)

那么ans+=dist(y,x)+dist(x,z),ans-=dist(y,z)

删去x同理

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i(x);i<=y;++i)
    #define Fdr(i,x,y) for(int i(x);i>=y;--i)
    #define fl(i,x) for(int i(head[x]),to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) ((int)(log2(n)))
    #define inf 2122219134
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const int str=1<<20;static char in_buf[str],*in_s,*in_t;bool __=0;il char gc(){return (in_s==in_t)&&(in_t=(in_s=in_buf)+fread(in_buf,1,str,stdin)),in_s==in_t?__=1,EOF:*in_s++;}il void in(string &ch){ch.clear();if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)__=1;}il void in(char &ch){if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)__=1;else ch=c;}il void in(char *ch){*ch='\0';if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)__=1;*ch='\0';}template<typename T>il void in(T &x){if(__)return;char c=gc();bool f=0;while(c!=EOF&&(c<'0'||c>'9'))f^=(c=='-'),c=gc();if(c==EOF){__=1;return;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=x*10+c-48,c=gc();if(c==EOF)__=1;if(f)x=-x;}template<typename T,typename ... arr>il void in(T &x,arr & ... y){in(x),in(y...);}const char ln='\n';static char out_buf[str],*out_s=out_buf,*out_t=out_buf+str;il void flush(){fwrite(out_buf,1,out_s-out_buf,stdout);out_s=out_buf;}il void pt(char c){(out_s==out_t)?(fwrite(out_s=out_buf,1,str,stdout),*out_s++=c):(*out_s++=c);}il void out(const char* s){while(*s)pt(*s++);}il void out(char* s){while(*s)pt(*s++);}il void out(char c){pt(c);}il void out(string s){for(int i=0;s[i];i++)pt(s[i]);}template<typename T>il void out(T x){if(!x){pt('0');return;}if(x<0)pt('-'),x=-x;char a[50],t=0;while(x)a[t++]=x%10,x/= 10;while(t--)pt(a[t]+'0');}template<typename T,typename ... arr>il void out(T x,arr & ... y){out(x),out(y...);}}using namespace IO;
const int N=200011;
int n,cnt=0,q,head[N],b[N];
struct edge{
    int to,nxt,w;
}e[N<<1];
il void add(int x,int y,int w){e[++cnt].to=y;e[cnt].nxt=head[x];head[x]=cnt;e[cnt].w=w;}
int d[N],dfn[N],sz=0,siz[N],top[N],f[N];
ll dep[N];
void dfs(int x){
    b[dfn[x]=++sz]=x;
    siz[x]=1;
    fl(i,x)if(to!=f[x]){
        dep[to]=dep[x]+e[i].w;
        d[to]=d[x]+1;
        f[to]=x;
        dfs(to);
        siz[x]+=siz[to];
    }
}
void bt(int x,int tp){
    top[x]=tp;int k=0;
    fl(i,x)if(to!=f[x]&&siz[to]>siz[k])k=to;
    if(k)bt(k,tp);
    fl(i,x)if(!top[to])bt(to,to);
}
il ll gd(int x,int y){
    int ox=x,oy=y;
    while(top[x]!=top[y])
        d[top[x]]>d[top[y]]?x=f[top[x]]:y=f[top[y]];
    return dep[ox]+dep[oy]-2ll*dep[d[x]<d[y]?x:y];
}
bool v[N];
set<int>T;
il int pre(int x){
    set<int>::iterator p=T.lower_bound(dfn[x]);
    if(p==T.begin())p=T.end();
    return b[*(--p)];
}
il int nxt(int x){
    set<int>::iterator p=T.upper_bound(dfn[x]);
    if(p==T.end())p=T.begin();
    return b[*p];
}
int main(){
    in(n,q);
    int x,y,z,w;
    ll s=0;
    Fur(i,1,n-1)in(x,y,w),add(x,y,w),add(y,x,w);
    dfs(1);bt(1,1);
    while(q--){
        in(x);
        if(v[x]){
            if(T.size()>1)
                y=pre(x),z=nxt(x),
                s+=gd(y,z),
                s-=gd(x,y)+gd(x,z);
            T.erase(dfn[x]);
        }
        else{
            T.insert(dfn[x]);
            if(T.size()>1)
                y=pre(x),z=nxt(x),
                s-=gd(y,z),
                s+=gd(x,y)+gd(x,z);
        }
        v[x]^=1;
        out(s,ln);
    }
    flush();
}
LG 3320 [SDOI2015]寻宝游戏
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