Submission #670788

#	Time	Username	Problem	Language	Result	Execution time	Memory
670788		Kahou	Capital City (JOI20_capital_city)	C++14	11 / 100	3139 ms	514492 KiB

capital_city

/* In the name of God, aka Allah */
// let this be mytemp.cpp
#include<bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define endl '\n'
#define mk make_pair
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int N = 2e5 + 50, LG = 18, M = 4e6 + 50;
int n, k, c[N], h[N], m, id[LG][N], par[LG][N];
bool mark[M];
bool vis[M];
int scc[M], cnt[M];
vector<int> topol;
vector<int> adj[N], adj2[2][M];
vector<int> vc[N];
int t;

void dfs(int u, int p) {
        h[u] = h[p]+1;
        par[0][u] = p;
        adj2[0][id[0][u]].push_back(c[u]);
        adj2[1][c[u]].push_back(id[0][u]);
        for (int v:adj[u]) {
                if (v == p) continue;
                dfs(v, u);
        }
}
int LCA(int u, int v) {
        if (h[u] > h[v]) swap(u, v);
        for (int x = LG-1; x >= 0; x--) {
                if ((h[v]-h[u])>>x&1) v = par[x][v];
        }
        for (int x = LG-1; x >= 0; x--) {
                if (par[x][u] != par[x][v]) u = par[x][u], v= par[x][v];
        }
        if (u == v) return u;
        return par[0][u];
}
void add_edge(int u, int v) {
        int x = c[u];
        for (int t = LG-1; t >= 0; t--) {
                if ((h[u]-h[v]+1)>>t&1) {
                        adj2[0][x].push_back(id[t][u]);
                        adj2[1][id[t][u]].push_back(x);
                        u = par[t][u];
                }
        }
}
void dfs2(int u) {
        vis[u] = 1;
        for (int v:adj2[1][u]){
                if (vis[v]) continue;
                dfs2(v);
        }
        topol.push_back(u);
}
void sfd(int u) {
        scc[u] = t;
        for (int v:adj2[0][u]) {
                if (scc[v]) {
                        mark[t] = mark[t] || (scc[v] != t);
                        continue;
                }
                sfd(v);
        }
}

void solve() {
        cin >> n >> k;
        for (int i = 1; i <= n-1; i++) {
                int u, v;
                cin >> u >> v;
                adj[u].push_back(v), adj[v].push_back(u);
        }
        for (int u = 1; u <= n; u++) {
                cin >> c[u];
                vc[c[u]].push_back(u);
        }
        m = k;
        for (int x = 0; x < LG; x++) {
                for (int u = 1; u <= n; u++) {
                        id[x][u] = ++m;
                }
        }
        dfs(1, 0);
        for (int x = 1; x < LG; x++) {
                for (int u = 1; u <= n; u++) {
                        par[x][u] = par[x-1][par[x-1][u]];
                        adj2[0][id[x][u]].push_back(id[x-1][u]);
                        adj2[0][id[x][u]].push_back(id[x-1][par[x-1][u]]);
                        adj2[1][id[x-1][u]].push_back(id[x][u]);
                        adj2[1][id[x-1][par[x-1][u]]].push_back(id[x][u]);
                }
        }
        for (int x = 1; x <= k; x++) {
                int r = vc[x][0];
                for (int u : vc[x]) {
                        r = LCA(r, u);
                }
                for (int u : vc[x]) {
                        add_edge(u, r);
                }
        }

        for (int u = 1; u <= m; u++) {
                if (!vis[u]) dfs2(u);
        }
        reverse(topol.begin(), topol.end());
        for (int u:topol) {
                if (!scc[u]) {
                        t++;
                        sfd(u);
                }
        }
        for (int x = 1; x <= k; x++) {
                cnt[scc[x]]++;
        }

        int ans = N;
        for (int x = 1; x <= t; x++) {
                if (mark[x]) continue;
                ans = min(ans, cnt[x]);
        }
        cout << ans-1 << endl;
}

int main() {
        ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        solve();
        return 0;
}

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