#include "beechtree.h"
#include<bits/stdc++.h>
#define int long long
#define f0r(i,n) for(int i = 0; i<n; i++)
#define pb push_back
#define mp make_pair
#define vi vector<int>
#define mii map<int,int>
#define pii pair<int,int>
#define vpii vector<pii>
#define FOR(i, k, n) for(int i = k; i<n; i++)
#define vb vector<bool>
using namespace std;
vector<vi>adj, colset;
vi dep, sts, die, diesum;
int dfs(int node){
int cur = 1;
for(auto u : adj[node]){
dep[u] = dep[node] + 1;
cur += dfs(u);
}
sts[node] = cur;
return cur;
}
int d2(int node){
int cur = die[node];
for(auto u : adj[node]){
cur += d2(u);
}
diesum[node] = cur;
return cur;
}
std::vector<signed> beechtree(signed N, signed M, std::vector<signed> P, std::vector<signed> C)
{
vector<signed>ans(N);
FOR(i, 1, N)ans[i] = 1;
colset.clear(); colset.resize(N); adj.clear(); adj.resize(N);
dep.clear(); dep.resize(N); sts.clear(); sts.resize(N); die.clear(); die.resize(N); diesum.clear(); diesum.resize(N);
FOR(i, 1, N){
adj[P[i]].pb(i);
}
f0r(i, N){
set<int>tmp;
for(auto u : adj[i]){
tmp.insert(u); colset[i].pb(u);
}
if(tmp.size() != colset[i].size()){
die[i] = 1;
}
}
dfs(0);
d2(0);
vpii w;
f0r(i, N){
w.pb(mp(colset[i].size(), i));
}
sort(w.rbegin(), w.rend());
bool ok = 1;
if(w[0].second != 0)ok = 0;
set<int>vis;
f0r(i, N){
set<int>ne;
for(auto u : colset[i]){
if(!vis.count(u))ok = 0;
ne.insert(u);
}
if(!ok)break;
vis = ne;
}
if(ok)ans[0] = 1;
f0r(i, N){
if(diesum[i] != 0)ans[i] = 0;
}
return ans;
}
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