This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define endl "\n"
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
using namespace std;
using lld = long long;
using pii = pair<int, int>;
using pll = pair<lld, lld>;
////////////////////////////////////////////////////////////////
const int MN = 303030;
int K, N1, N2;
struct Tree {
int root, cnt[MN], rep[MN];
vector<int> adj[MN];
void set_parent(int u, int p) {
if (p == 0) root = u;
else adj[p].push_back(u);
}
void dfs(int u) {
if (u <= K) cnt[u] = 1, rep[u] = u;
for (auto v: adj[u]) {
dfs(v);
cnt[u] += cnt[v];
rep[u] = rep[v];
}
}
};
Tree T1, T2;
// dsu
int par[MN], siz[MN];
void init(int N) {
for (int i=1; i<=N; i++) par[i] = i, siz[i] = 1;
}
int find(int x) {
if (par[x] == x) return x;
return par[x] = find(par[x]);
}
void merge(int x, int y) {
x = find(x), y = find(y);
if (x == y) return;
par[y] = x;
siz[x] += siz[y];
}
int size(int x) {
return siz[find(x)];
}
// end dsu
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
////////////////////////////////
cin >> N1 >> N2 >> K;
for (int u=1, p; u<=N1; u++) { cin >> p; T1.set_parent(u, p); }
for (int u=1, p; u<=N2; u++) { cin >> p; T2.set_parent(u, p); }
T1.dfs(T1.root);
T2.dfs(T2.root);
vector<array<int, 3>> E;
for (int u=K+1; u<=N1; u++) if (T1.adj[u].size() > 0) E.push_back({T1.cnt[u], 1, u});
for (int u=K+1; u<=N2; u++) if (T2.adj[u].size() > 0) E.push_back({T2.cnt[u], 2, u});
sort(all(E));
init(K);
bool ok = 1;
for (auto [c, t, u]: E) {
Tree &T = t == 1 ? T1 : T2;
for (auto v: T.adj[u]) merge(T.rep[u], T.rep[v]);
if (size(T.rep[u]) != c) ok = 0;
}
cout << (ok ? "YES" : "NO") << endl;
////////////////////////////////
return 0;
}
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