Submission #930394

#	Time	Username	Problem	Language	Result	Execution time	Memory
930394		ParsaS	Capital City (JOI20_capital_city)	C++17	0 / 100	73 ms	26116 KiB

capital_city

// In the name of God
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define mp make_pair
typedef long long ll;
const int N = 2e5 + 5, lg = 20;
int n, k, a[N];
vector<int> adj[N], vec[N];
int up[N][lg], tin[N], tout[N], T, h[N];
int f[N], par[N];

void dfs(int v, int p) {
	up[v][0] = p;
	par[v] = p;
	for (int i = 1; i < lg; i++) {
		up[v][i] = up[up[v][i - 1]][i - 1];
	}
	tin[v] = ++T;
	for (auto u : adj[v]) {
		if (u != p) {
			h[u] = h[v] + 1;
			dfs(u, v);
		}
	}
	tout[v] = ++T;
}

bool anc(int v, int u) {
	return tin[v] <= tin[u] && tout[v] >= tout[u];
}

int lca(int v, int u) {
	if (tin[v] > tin[u]) swap(v, u);
	if (anc(v, u)) return v;

	for (int i = lg - 1; i >= 0; i--) {
		if (!anc(up[u][i], v)) {
			u = up[u][i];
		}
	}
	return up[u][0];
}

vector<int> V;
int out[N];

void dfs2(int v, int p) {
	vector<int> dat;
	while (!V.empty() && h[f[V.back()]] >= h[f[v]]) {
		dat.pb(V.back());
		V.pop_back();
	}
	V.pb(v);

	int l = -1, r = V.size() - 1;
	while (r - l > 1) {
		int mid = (l + r) >> 1;
		if (h[V[mid]] >= h[f[v]])
			r = mid;
		else l = mid;
	}
	if (a[v] != a[V[r]]) {
		out[a[v]]++;
	}
	for (auto u : adj[v]) {
		if (u != p)
			dfs2(u, v);
	}
	V.pop_back();
	while (!dat.empty()) {
		V.pb(dat.back());
		dat.pop_back();
	}
}

bool vis[N];


int col[N];


void solve() {
	cin >> n >> k;
	for (int i = 0; i < n - 1; i++) {
		int v, u; cin >> v >> u;
		adj[v].pb(u), adj[u].pb(v);
	}
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		vec[a[i]].pb(i);
	}
	if (n > 20) return;

	dfs(1, 1);

	for (int i = 1; i <= k; i++) {
		int u = vec[i].back();
		for (auto v : vec[i]) {
			u = lca(u, v);
		}
		for (auto v : vec[i])
			f[v] = u;
	}

	dfs2(1, 0);
	for (int v = 1; v <= n; v++) {
		int u = par[v], mx = v;
		while (u != f[v] && v != f[v]) {
			if (h[f[u]] < h[f[mx]]) {
				mx = u;
			}
			u = par[u];
		}
		u = mx;
		if (a[v] != a[u]) {
			out[a[v]]++;
		}
	}
	vector<pair<int, int> > ver;
	for (int i = 1; i <= k; i++) {
		if (out[i] == 0) {
			ver.pb(mp(h[f[vec[i].back()]], f[vec[i].back()]));
		}
	}

	sort(ver.begin(), ver.end(), greater<pair<int, int> >());
	int ans = 1e9;
	for (auto [x, v] : ver) {
		queue<int> q;
		q.push(a[v]);
		if (col[a[v]]) continue;
		col[a[v]] = a[v];
		bool ok = true;
		int cnt = 0;
		
		while (!q.empty()) {
			int c = q.front();
			q.pop();

			if (col[c] != a[v]) {
				ok = false;
				break;
			}
			

			for (auto w : vec[c]) {
				if (w == v) continue;
				int u = par[w];
				if (col[a[u]] == 0) {
					col[a[u]] = a[v];
					cnt++;
					q.push(a[u]);
				}
				else if (col[a[u]] != a[v]) ok = false;
			}
		}
		if (ok)
			ans = min(ans, cnt);
	}
	cout << ans << '\n';
}

int32_t main() {
	ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);

	int tc = 1; // cin >> tc;
	while (tc--) {
		solve();
	}

	return 0;
}

• Subtask 1: 0 / 1
• Subtask 2: 0 / 10
• Subtask 3: 0 / 30
• Subtask 4: 0 / 59