#include "beechtree.h"
#include <bits/stdc++.h>
#define all(x) (x).begin(),(x).end()
using namespace std;
using ll = long long;
using ld = long double;
//#define int ll
#define sz(x) ((int)(x).size())
using pii = pair<int,int>;
using tii = tuple<int,int,int>;
const int nmax = 1e5 + 5;
vector<pii> g[nmax];
vector<int> P, C;
unordered_set<int> colors[nmax], play[nmax];
bool isanc(unordered_set<int>& A, unordered_set<int>& B) {
if(sz(A) < sz(B)) return 0;
for(auto &x : B)
if(!A.count(x)) return 0;
return 1;
}
vector<int> sol;
int h[nmax];
vector<int> dfs(int node) {
//cerr << node << '\n';
vector<int> here;
sol[node] = 1;
h[node] = 0;
for(auto [x, e] : g[node]) {
auto T = dfs(x);
//cerr << x << ": " << sol[x] << '\n';
sol[node] &= sol[x];
copy(all(T), back_inserter(here));
h[node] = max(h[node], h[x] + 1);
}
here.emplace_back(node);
if(sol[node] == 0 || sz(g[node]) != sz(colors[node])) { sol[node] = 0; return here; }
sort(all(here), [&](int a, int b) { return sz(colors[a]) > sz(colors[b]); });
for(int i = 1; i < sz(here); i++) {
if(!isanc(colors[here[i - 1]], colors[here[i]])) { sol[node] = 0; return here; }
}
vector<vector<int>> ts(h[node] + 1);
for(auto x : here) ts[h[x]].emplace_back(x);
for(auto x : here) play[x] = colors[x];
for(int i = 0; i < h[node]; i++) {
//if(node == 0) {
//cerr << "niveaux " << i << '\n';
//}
for(auto x : here) {
if(x == node) continue;
if(h[x] < i) continue;
//if(node == 0) {
//cerr << x << '\n';
//for(auto x : play)
//}
if(!isanc(play[P[x]], play[x])) { sol[node] = 0; return here; }
}
for(auto a : ts[i]) {
if(a == node) continue;
play[P[a]].erase(C[a]);
}
}
for(auto x : here) {
for(auto y : here) {
if(sz(colors[x]) > sz(colors[y])) {
if(h[x] < h[y]) { sol[node] = 0; return here; }
}
}
}
return here;
}
std::vector<int> beechtree(int N, int M, std::vector<int> P_, std::vector<int> C_) {
P = P_;
C = C_;
for(int i = 1; i < N; i++) {
g[P[i]].emplace_back(i, C[i]);
colors[P[i]].emplace(C[i]);
}
sol.assign(N, 0);
dfs(0);
return sol;
}
/**
Töte es durch genaue Untersuchung\Töte es kann es nur noch schlimmer machen\Es lässt es irgendwie atmen
--
*/
