HDU6393(环套树)

题解:　很显然的是这个图必然是一个树上套一个简单环　我们考虑到只有树的情况　那么直接树链剖分+线段树就好了　如果多加一条边　qko告诉我可以类似基环树那样　取出这个环　那么我们可以对于一个询问分类　如果在一颗子树上我们可以直接查询即可　如果绕过环相连　那么可以取两点对应环上的点取min 加上两个点在不同子树中的路径长度即可

#include <bits/stdc++.h>
#define ll long long
#define link(x) for(edge *j=h[x];j;j=j->next)
const int MAXN=1e5+10;
const int inf=1e9;
using namespace std;
struct FastIO
{
    static const int S=200;
    int wpos;
    char wbuf[S];
    FastIO():wpos(0){}
    inline int xchar()
    {
        static char buf[S];
        static int len=0,pos=0;
        if(pos==len) pos=0,len=fread(buf,1,S,stdin);
        if(pos==len) exit(0);
        return buf[pos++];
    }
    inline int read()
    {
        int s=1,c=xchar(),x=0;
        while(c<=32) c=xchar();
        if(c=='-') s=-1,c=xchar();
        for(;'0'<=c&&c<='9';c=xchar()) x=x*10+c-'0';
        return x*s;
    }
    ~FastIO()
    {
        if(wpos) fwrite(wbuf,1,wpos,stdout),wpos=0;
    }
}io;
int n,m;
int F[MAXN],f[MAXN],b[MAXN];
int dep[MAXN],fa[MAXN],son[MAXN],num[MAXN],pos[MAXN],key[MAXN];
bool vis[MAXN],vi[MAXN];
int v1[MAXN];
struct edge{int t,id;ll v;bool f;edge*next,*rev;}e[MAXN<<2],*h[MAXN],*o=e;
void add(int x,int y,ll v,int p){o->v=v;o->t=y;o->id=p;o->next=h[x];h[x]=o++;}
int __v[MAXN];
int find1(int x){
    if(x==F[x])return x;
    else return F[x]=find1(F[x]);
}
int _x,tot,c[MAXN],_t;
void _dfs(int x){
    __v[x]++;
    link(x)if(!j->f){
    j->f=j->rev->f=true;
    if(__v[j->t]){_t=j->t;c[++tot]=x;vis[x]=1;return;}
    else _dfs(j->t);
    if(_t){c[++tot]=x;vis[x]=1;break;}
    }
    if(_t==x)_t=0;
}
void dfs(int v,int pre,int deep){
    dep[v]=deep+1;fa[v]=pre;num[v]=1;
    link(v)if(j->t!=pre&&!vis[j->t]){
        F[j->t]=v;
        key[j->t]=j->v;
        pos[j->id]=j->t;
        dfs(j->t,v,deep+1);
        num[v]+=num[j->t];
        if(son[v]==-1||num[j->t]>num[son[v]])son[v]=j->t;        
    }
}
int p[MAXN],fp[MAXN],tp[MAXN],cnt;
void dfs1(int v,int td){
    p[v]=++cnt;fp[p[v]]=v;tp[v]=td;
    if(son[v]!=-1)dfs1(son[v],td);
    link(v)if(j->t!=fa[v]&&j->t!=son[v]&&!vis[j->t])dfs1(j->t,j->t);
}
ll sum[MAXN<<2];
void built(int rt,int l,int r){
    if(l==r){sum[rt]=key[fp[l]];return ;}
    int mid=(l+r)>>1;
    built(rt<<1,l,mid);
    built(rt<<1|1,mid+1,r);
    sum[rt]=sum[rt<<1]+sum[rt<<1|1];
}
ll ans;
void querty(int rt,int l,int r,int ql,int qr){
    if(ql<=l&&r<=qr){ans+=sum[rt];return ;}
    int mid=(l+r)>>1;
    if(ql<=mid)querty(rt<<1,l,mid,ql,qr);
    if(qr>mid)querty(rt<<1|1,mid+1,r,ql,qr);
}
void update(int rt,int l,int r,int t,int vul){
    if(l==r){sum[rt]=vul;return ;}
    int mid=(l+r)>>1;
    if(t<=mid)update(rt<<1,l,mid,t,vul);
    else update(rt<<1|1,mid+1,r,t,vul);
    sum[rt]=sum[rt<<1]+sum[rt<<1|1];
}
ll Sum(int u,int v){
    int uu=tp[u];int vv=tp[v];
    ll ans1=0;
    while(uu!=vv){
        if(dep[uu]<dep[vv]){swap(uu,vv);swap(u,v);}
        ans=0;querty(1,1,n,p[uu],p[u]);ans1+=ans;
        u=fa[uu];uu=tp[u];
    }
    if(dep[u]>dep[v])swap(u,v);
    //cout<<son[u]<<" "<<u<<" "<<v<<" "<<p[son[u]]<<" "<<p[v]<<" "<<ans1<<endl;
    if(u!=v)ans=0,querty(1,1,n,p[son[u]],p[v]),ans1+=ans;
    return ans1;
}
ll sum1[MAXN<<2];
int get_id(int x){return x&(-x);}
void update1(int x,int vul){
    //cout<<x<<" "<<vul<<endl;
    for(int i=x;i<=2*n;i+=get_id(i))sum1[i]+=vul;
}
ll querty1(int x){
    ll ans1=0;
    for(int i=x;i>0;i-=get_id(i))ans1+=sum1[i];
    return ans1;
}
int main(){
    //freopen("k.out","w",stdout);
    int _=io.read();//scanf("%d",&_);
    while(_--){
        n=io.read();m=io.read();memset(e,0,sizeof(e));memset(h,0,sizeof(h));o=e;
        memset(vis,0,sizeof(vis));memset(sum1,0,sizeof(sum1));memset(sum,0,sizeof(sum));
        memset(vi,0,sizeof(vi));
        memset(__v,0,sizeof(__v));
        for(int i=1;i<=n;i++)F[i]=i,son[i]=-1,pos[i]=n+1;
        int u,v,vul;tot=0;cnt=0;
        for(int i=1;i<=n;i++)u=io.read(),v=io.read(),vul=io.read(),add(u,v,vul,i),add(v,u,vul,i),h[u]->rev=h[v],h[v]->rev=h[u];
        for(int i=1;i<=n;i++)if(!__v[i])_dfs(i);
        for(int i=1;i<=tot;i++)v1[c[i]]=i;
        for(int i=1;i<=tot;i++)c[i+tot]=c[i],v1[c[i+tot]]=v1[c[i]];
        tot*=2;
        for(int k=1;k<=tot-1;k++)
            link(c[k])if(j->t==c[k+1])b[k+1]=j->v,pos[j->id]=min(pos[j->id],k+1),vi[j->id]=1;
        for(int k=1;k<=tot;k++)update1(k,b[k]);
        tot/=2;
        for(int i=1;i<=tot;i++){dfs(c[i],0,0);dfs1(c[i],c[i]);}
        //for(int i=1;i<=n;i++)cout<<key[i]<<" ";
        //    cout<<endl;
        built(1,1,n);
        int op,x,y;
        for(int i=1;i<=m;i++){
            op=io.read();x=io.read();y=io.read();
            if(op==0){
                if(vi[x]){
                    x=pos[x];
                    update1(x,-1*b[x]);update1(x,y);
                    update1(x+tot,-1*b[x]);update1(x+tot,y);
                    b[x]=y;
                }
                else update(1,1,n,p[pos[x]],y);
            }
            else{
                int t1=find1(x);int t2=find1(y);
                if(t1==t2)printf("%lld\n",Sum(x,y));
                else{
                    ll ans1=Sum(x,t1);ans1+=Sum(y,t2);
                    t1=v1[t1];t2=v1[t2];
                    if(t1>t2)swap(t1,t2);
                    ans1+=min(querty1(t2)-querty1(t1),querty1(t1+tot)-querty1(t2));
                    printf("%lld\n",ans1);
                } 
            }
        }
    }
    return 0;
}