E、阔力梯的树

#include<bits/stdc++.h>
using namespace std;
#define pb push_back
typedef long long ll;
const ll INF=0x3f3f3f3f;
set<int>s;
const int M=1e5+5;
int sz[M],son[M],vis[M];
vector<int>g[M];
ll ans[M],tmp[M];
ll sum;
void dfs1(int u){
    sz[u]=1;
    for(int i=0;i<g[u].size();i++){
        int v=g[u][i];
        dfs1(v);
        sz[u]+=sz[v];
        if(sz[v]>sz[son[u]])
            son[u]=v;
    }
}
void update(int u,int k){
    if(k==-1);
        s.erase(u);        
    set<int>::iterator it=s.lower_bound(u);
    
    ll r=*it;
    it--;
    ll l=*it;
    if(k==1)
        s.insert(u);
    if(l!=-INF&&r!=INF)///当插入/删除的值在中间 
        sum-=(r-l)*(r-l)*k;

    if(l!=-INF)//当插入/删除的值左边有数 
        sum+=(u-l)*(u-l)*k;

    if(r!=INF)///当插入/删除的值右边有数 
        sum+=(r-u)*(r-u)*k;

    for(int i=0;i<g[u].size();i++)
        if(!vis[g[u][i]])
            update(g[u][i],k);
}
void dfs2(int u,int sign){
    //cout<<u<<endl;
    ///
    for(int i=0;i<g[u].size();i++){
        int v=g[u][i];
        if(v!=son[u])
            dfs2(v,0);
    }
    if(son[u])
        dfs2(son[u],1),vis[son[u]]=1;
    update(u,1);
    
    ans[u]=sum;
    vis[son[u]]=0;
    if(!sign)
        update(u,-1);
}
int main(){
    int n;
    s.insert(INF);
    s.insert(-INF);
    scanf("%d",&n);
    for(int u,i=2;i<=n;i++){
        scanf("%d",&u);
        g[u].pb(i);
    }    
    dfs1(1);
    dfs2(1,0);
    for(int i=1;i<=n;i++)
        printf("%lld\n",ans[i]);
    return 0;
}