#include "beechtree.h"
#include <bits/stdc++.h>
#define all(x) (x).begin(), (x).end()
#define xx first
#define yy second
using namespace std;
typedef pair<int, int> pii;
const int N = 2e5 + 1;
struct Graph
{
int cnt[N];
bool con[N];
set<pii> srt[N];
map<int, vector<int>> col[N];
} graph;
bool check(int v, int u)
{
for (auto &pr : graph.col[v])
{
auto &[col, vec] = pr;
auto it = graph.col[u].find(col);
if (it == graph.col[u].end() || graph.cnt[vec[0]] > graph.cnt[it->yy[0]])
{
return false;
}
}
return true;
}
bool insertAndCheck(set<pii> &srt, pii p)
{
auto [it, st] = srt.insert(p);
bool result = true;
if (it != srt.begin())
{
result &= check(prev(it)->yy, it->yy);
}
if (next(it) != srt.end())
{
result &= check(it->yy, next(it)->yy);
}
return result;
}
int dfs(int u)
{
graph.cnt[u] = 1;
graph.con[u] = true;
for (auto &pr : graph.col[u])
{
auto &[col, vec] = pr;
graph.con[u] &= vec.size() == 1;
for (int v : vec)
{
int cnv = dfs(v);
if (cnv == -1)
{
graph.con[u] = false;
}
else
{
graph.cnt[u] += cnv;
}
if (graph.con[u])
{
if (graph.srt[v].size() > graph.srt[u].size())
{
graph.srt[u].swap(graph.srt[v]);
}
for (pii p : graph.srt[v])
{
graph.con[u] &= insertAndCheck(graph.srt[u], p);
}
}
}
}
graph.con[u] &= insertAndCheck(graph.srt[u], {graph.cnt[u], u});
return graph.con[u] ? graph.cnt[u] : -1;
}
vector<int> beechtree(int n, int m, vector<int> P, vector<int> C)
{
for (int i = 1; i < n; ++i)
{
int p = P[i];
int c = C[i];
if (!graph.col[p].count(c))
{
graph.col[p][c] = vector<int>();
}
graph.col[p][c].push_back(i);
}
dfs(0);
vector<int> ans;
for (int i = 0; i < n; ++i)
ans.push_back(graph.con[i]);
return ans;
}
