[WC2014]紫荆花之恋(动态点分治+替罪羊思想)

#include<iostream>
#include<cstdio>
#include<vector>
#include<cstdlib>
#define ls tr[p].l
#define rs tr[p].r
#define N 100002
using namespace std;
typedef long long ll;
int topp,q[N*32],cnt,head[N],tot,p[N][20],dep[N],size[N],siz[N],dp[N],sum,root,rt[N],n,st[N],top,T[N];
ll deep[N],dis[N],r[N],ans;
bool vis[N],tag[N];
vector<int>vec[N],E[N];
struct edge{int n,to;ll l;}e[N<<1];
inline void add(int u,int v,ll l){e[++tot].n=head[u];e[tot].to=v;head[u]=tot;e[tot].l=l;}
const double pha=0.75;
const int mod=1e9;
struct node{int size,cnt,l,r,rd;ll val;}tr[N*32];
inline void pushup(int p){tr[p].size=tr[ls].size+tr[rs].size+tr[p].cnt;}
inline int newnode(ll x){
    int y=topp?q[topp--]:++cnt;
    tr[y].l=tr[y].r=0;tr[y].val=x;tr[y].rd=rand();tr[y].size=tr[y].cnt=1;
    return y;
}
inline void re(int x){q[++topp]=x;}
inline void lturn(int &p){
    int x=tr[p].r;tr[p].r=tr[x].l;tr[x].l=p;
    tr[x].size=tr[p].size;pushup(p);p=x;
}
inline void rturn(int &p){
    int x=tr[p].l;tr[p].l=tr[x].r;tr[x].r=p;
    tr[x].size=tr[p].size;pushup(p);p=x;
}
inline void ins(int &p,ll x){
    if(!p){p=newnode(x);return;}
    tr[p].size++; 
    if(tr[p].val==x){tr[p].cnt++;return;}
    if(x>tr[p].val){
        ins(rs,x);
        if(tr[p].rd>tr[rs].rd)lturn(p);
    }
    else{
        ins(ls,x);
        if(tr[p].rd>tr[ls].rd)rturn(p);
    }
} 
inline ll get_rank(int p,ll x){
    if(!p)return 0;
    if(tr[p].val<=x)return tr[ls].size+tr[p].cnt+get_rank(rs,x);
    return get_rank(ls,x);
}
void bl(int p){if(ls)bl(ls);printf("%lld ",tr[p].val);if(rs)bl(rs);}
inline ll rd(){
    int x=0;char c=getchar();bool f=0;
    while(!isdigit(c)){if(c==‘-‘)f=1;c=getchar();}
    while(isdigit(c)){x=(x<<1)+(x<<3)+(c^48);c=getchar();} 
    return f?-x:x;
}
inline int getlca(int a,int b){
    if(dep[a]<dep[b])swap(a,b);
    for(int i=18;i>=0;--i)if(dep[a]-(1<<i)>=dep[b])a=p[a][i];
    if(a==b)return a;
    for(int i=18;i>=0;--i)if(p[a][i]!=p[b][i])a=p[a][i],b=p[b][i];
    return p[a][0];
}
inline ll dist(int a,int b){return dis[a]+dis[b]-2*dis[getlca(a,b)];}
void getsize(int u,int fa){
    siz[u]=1;
    for(int i=head[u];i;i=e[i].n)if(e[i].to!=fa&&vis[e[i].to]&&!tag[e[i].to]){
        int v=e[i].to;getsize(v,u);siz[u]+=siz[v]; 
    }
}
void getroot(int u,int fa){
    dp[u]=0;siz[u]=1;
    for(int i=head[u];i;i=e[i].n)if(vis[e[i].to]&&e[i].to!=fa&&!tag[e[i].to]){
        int v=e[i].to;getroot(v,u);
        siz[u]+=siz[v];dp[u]=max(dp[u],siz[v]);
    } 
    dp[u]=max(sum-siz[u],dp[u]);
    if(dp[u]<dp[root])root=u;
}
void getdeep(int u,int fa,int top,int tt){
    ins(rt[top],deep[u]-r[u]);E[top].push_back(u);
    ins(T[tt],deep[u]-r[u]);vec[u].push_back(top);
    size[top]++;
    for(int i=head[u];i;i=e[i].n)if(e[i].to!=fa&&vis[e[i].to]&&!tag[e[i].to]){
        int v=e[i].to;deep[v]=deep[u]+e[i].l;
        getdeep(v,u,top,tt);
    }
}
void solve(int u){
    tag[u]=1;
    size[u]=1;E[u].push_back(u);
    ins(rt[u],-r[u]);
    for(int i=head[u];i;i=e[i].n)if(vis[e[i].to]&&!tag[e[i].to]){
        int v=e[i].to;
        sum=siz[v];root=n+1;
        getroot(v,u);getsize(root,0);
        deep[v]=e[i].l;getdeep(v,u,u,root);
        solve(root);
    }
}
void efs(int p){if(!p)return;if(ls)efs(ls);if(rs)efs(rs);re(p);}
inline void rebuild(int u){
    int ma=E[u].size();
    for(int i=0;i<ma;++i){
        int v=E[u][i];
        st[++top]=v;vis[v]=1;
    }
    ma=vec[u].size();
    int king=ma?vec[u].back():0;
    for(int i=1;i<=top;++i){
        int x=st[i];size[x]=0;
        E[x].clear();
        while(vec[x].size()&&vec[x].back()!=king)vec[x].pop_back();
        efs(rt[x]);efs(T[x]);rt[x]=T[x]=0;
    }
    root=n+1;sum=top;dp[root]=n+1;
    getroot(u,0);getsize(root,0);int haha=root;
    solve(root);
    if(king){
        for(int i=1;i<=top;++i){
          int x=st[i];
          ll d=dist(x,king);
          ins(T[haha],d-r[x]);
        }
    }
    while(top){
        int x=st[top];
        vis[st[top]]=0;
        tag[st[top]]=0;
        top--;
    }
}
inline void check(int u){
    int ma=vec[u].size();
    for(int i=1;i<ma;++i){
        int v=vec[u][i],v1=vec[u][i-1];
        if(size[v1]*pha<size[v]){
            rebuild(v1);
            break;
        }
    }
}
inline void work(int u,int fa){
    int ma=vec[fa].size();
    for(int i=0;i<ma;++i)vec[u].push_back(vec[fa][i]);
    vec[u].push_back(fa);    
    ins(rt[u],-r[u]);size[u]=1;E[u].push_back(u);
    ma++;
    for(int i=ma-1;i>=0;--i){
        int v=vec[u][i];ll d=dist(u,v);
        size[v]++;E[v].push_back(u);
        int nex=i==ma-1?u:vec[u][i+1];
        ins(rt[v],d-r[u]);ins(T[nex],d-r[u]);
        ans+=get_rank(rt[v],r[u]-d)-get_rank(T[nex],r[u]-d);
    }
    check(u);
} 
int main(){
    srand(3783252);
    n=rd();n=rd();
    ll a=rd(),c=rd();r[1]=rd();
    size[1]=1;ins(rt[1],-r[1]);
    E[1].push_back(1);
    printf("%lld\n",ans);
    for(int i=2;i<=n;++i){
        a=rd();c=rd();r[i]=rd();
        a=a^(ans%mod);    
        add(i,a,c);add(a,i,c);
        dep[i]=dep[a]+1;dis[i]=dis[a]+c;p[i][0]=a;
        for(int j=1;(1<<j)<=dep[i];++j)p[i][j]=p[p[i][j-1]][j-1];
        work(i,a);
        printf("%lld\n",ans);
    } 
    return 0;
}