#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>
#define vout(v) for(auto u : v)cout<<u<<' '; cout<<endl;
using namespace std;
vector<vi>adj, colset, su, cha;
vi dep, sts, die, diesum, tp;
vector<signed>ans; int M;
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;
}
void d3(int node){
if(sts[node] == 1){
su[node][tp[node]]++; return;
}
for(auto u : adj[node]){
d3(u);
f0r(j, 4){
su[node][j] += su[u][j];
}
}
su[node][tp[node]]++;
}
void d4(int node){
if(sts[node] == 1){
cha[node] = {0};
return;
}
vector<pair<vi, int>>w;
for(auto u : adj[node]){
d4(u);
w.pb(mp(cha[u], u));
}
sort(w.rbegin(), w.rend());
adj[node].clear();
for(auto u : w){
adj[node].pb(u.second);
}
queue<int>q;
vi seq;
q.push(node); seq.pb(adj[node].size());
while(!q.empty()){
int node = q.front(); q.pop();
for(auto u : adj[node]){
q.push(u); seq.pb(adj[u].size());
}
}
cha[node] = seq;
}
void solve(int node){
if(sts[node] == 1){
ans[node] = 1; return;
}
for(auto u : adj[node]){
solve(u);
}
if(diesum[node] != 0){
ans[node] = 0; return;
}
//test if including the next for loop preserves correct ans
for(auto u : adj[node]){
if(ans[u] == 0){
ans[node] = 0; return;
}
}
/*
vi w = su[node];
//vout(w);
if(tp[node] == 1 && w[3] != 0){
ans[node] = 0; return;
}
if(tp[node] == 2 && w[3] != 0){
ans[node] = 0; return;
}
if(w[1] != 0 && w[2] != 0){
ans[node] = 0; return;
}
ans[node] = 1; return;
*/
queue<int>q;
vi seq;
q.push(node); seq.pb(node);
while(!q.empty()){
int node = q.front(); q.pop();
for(auto u : adj[node]){
q.push(u); seq.pb(u);
}
}
set<int>vis;
f0r(i, M){
vis.insert(i + 1);
}
bool ok = 1;
f0r(i, seq.size()){
set<int>ne;
for(auto u : colset[seq[i]]){
if(!vis.count(u))ok = 0;
ne.insert(u);
}
if(node == 0){
for(auto u : vis)cout<<u<<' ';
cout<<'\n';
for(auto u : ne)cout<<u<<' ';
cout<<'\n';
cout<<'\n';
}
if(!ok)break;
vis = ne;
}
ans[node] = ok;
}
std::vector<signed> beechtree(signed N, signed M, std::vector<signed> P, std::vector<signed> C)
{
::M = M;
ans.resize(N);
FOR(i, 1, N)ans[i] = 0;
colset.clear(); colset.resize(N); adj.clear(); adj.resize(N); tp.clear(); tp.resize(N);
dep.clear(); dep.resize(N); sts.clear(); sts.resize(N); die.clear(); die.resize(N); diesum.clear(); diesum.resize(N);
cha.resize(N);
FOR(i, 1, N){
adj[P[i]].pb(i);
}
f0r(i, N){
set<int>tmp;
for(auto u : adj[i]){
tmp.insert(C[u]); colset[i].pb(C[u]);
}
if(tmp.size() != colset[i].size()){
die[i] = 1;
}
int sum = 0;
for(auto u : tmp){
sum += u;
}
tp[i] = sum;
}
dfs(0);
d2(0);
if(N <= 8){
f0r(i, N){
vi st;
queue<int>q; q.push(i); st.pb(i);
while(!q.empty()){
int node = q.front(); q.pop();
for(auto u : adj[node]){
q.push(u); st.pb(u);
}
}
sort(st.begin(), st.end());
bool okk = 0;
do{
vi f;
f.pb(0);
mii m;
FOR(j, 1, st.size()){
if(m.count(C[st[j]]))f.pb(m[C[st[j]]]);
else f.pb(0);
m[C[st[j]]]++;
}
bool ok = 1;
if(st[0] != i)ok = 0;
FOR(j,1, st.size()){
if(P[st[j]] != st[f[j]])ok = 0;
}
if(ok)okk = 1;
}while(next_permutation(st.begin(), st.end()));
ans[i] = okk;
}
f0r(i, N){
if(diesum[i] != 0)ans[i] = 0;
}
return ans;
}
else{
vb realfather(N);
f0r(i, N){
bool ok = 1;
for(auto u : adj[i]){
if(sts[u] != 1)ok = 0;
}
realfather[i] = ok;
}
f0r(i, N){
int cnt = 0; int sp = 0;
for(auto u : adj[i]){
if(sts[u] != 1){
cnt++; sp = u;
}
}
if(cnt == 1){
if(realfather[sp]){
set<int>thing;
for(auto u : colset[i])thing.insert(u);
bool ok = 1;
for(auto u : colset[sp]){
if(!thing.count(u))ok = 0;
}
ans[i] = ok;
}
}
else if(cnt == 0){
ans[i] = 1;
}
}
f0r(i, N){
if(diesum[i] != 0)ans[i] = 0;
}
//for adj of each node, sort them by size of colset
/*
f0r(i,N){
vpii w;
for(auto u : adj[i]){
w.pb(mp(colset[u].size(), u));
sort(w.rbegin(), w.rend());
}
adj[i].clear();
for(auto u : w){
adj[i].pb(u.second);
}
}
*/
/*
d4(0);
f0r(i, N){
vout(cha[i]);
}
*/
/*
su.resize(N);
f0r(i, N){
su[i].resize(4);
}
d3(0);
solve(0);
*/
// solve(0);
return ans;
}
}
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