oj.uz

Submission #898787

# Submission time Handle Problem Language Result Execution time Memory
898787 2024-01-05T06:14:05 Z juliany2 Capital City (JOI20_capital_city) C++17
41 / 100
 3000 ms 70924 KB 
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define all(x) (x).begin(), (x).end()

template<class T> struct ST {
    static constexpr T ID = {(int) 1e9, 0}; // or whatever ID
    inline T comb(T a, T b) { return min(a, b); } // or whatever function

    int sz;
    vector<T> t;

    void init(int _sz, T val = ID) {
        t.assign((sz = _sz) * 2, ID);
    }
    void init(vector<T> &v) {
        t.resize((sz = v.size()) * 2);
        for (int i = 0; i < sz; ++i)
            t[i + sz] = v[i];
        for (int i = sz - 1; i; --i)
            t[i] = comb(t[i * 2], t[(i * 2) | 1]);
    }
    void upd(int i, T x) {
        for (t[i += sz] = x; i > 1; i >>= 1)
            t[i >> 1] = comb(t[i], t[i ^ 1]);
    }
    T query(int l, int r) {
        T ql = ID, qr = ID;
        for (l += sz, r += sz + 1; l < r; l >>= 1, r >>= 1) {
            if (l & 1) ql = comb(ql, t[l++]);
            if (r & 1) qr = comb(t[--r], qr);
        }
        return comb(ql, qr);
    }
};

struct DSU {
    vector<int> e;
    DSU(int sz) { e = vector<int>(sz + 1, -1); }

    int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }

    bool same_set(int a, int b) { return get(a) == get(b); }

    int size(int x) { return -e[get(x)]; }

    bool unite(int x, int y) {
        x = get(x), y = get(y);
        if (x == y) return false;
        if (e[x] > e[y]) swap(x, y);
        e[x] += e[y]; e[y] = x;
        return true;
    }
};

const int N = 2e5 + 7, L = 20;
int n, k;
vector<int> adj[N], col[N], topo, comp;
set<int> active;
ST<array<int, 2>> st;
int c[N], lift[N][L], dep[N], sz[N], head[N], pos[N], start[N], who[N], timer;
int tin[N], tout[N];
bool vis[N];

void dfs(int v = 1, int p = 0) {
    tin[v] = ++timer;
    sz[v] = 1;
    lift[v][0] = p;
    for (int i = 1; i < L; i++)
        lift[v][i] = lift[lift[v][i - 1]][i - 1];

    for (int &u : adj[v]) {
        if (u != p) {
            dep[u] = dep[v] + 1;
            dfs(u, v);
            sz[v] += sz[u];
            if (adj[v][0] == p || sz[v] > sz[adj[v][0]])
                swap(u, adj[v][0]);
        }
    }

    tout[v] = timer;
}

void dfs_hld(int v = 1, int p = 0) {
    pos[v] = timer++;
    for (int u : adj[v]) {
        if (u != p) {
            head[u] = (u == adj[v][0] ? head[v] : u);
            dfs_hld(u, v);
        }
    }
}

int lca(int u, int v) {
    if (dep[u] > dep[v])
        swap(u, v);

    for (int i = L - 1; ~i; --i)
        if (dep[v] - (1 << i) >= dep[u])
            v = lift[v][i];

    if (u == v)
        return u;

    for (int i = L - 1; ~i; --i)
        if (lift[v][i] != lift[u][i])
            v = lift[v][i], u = lift[u][i];
    return lift[u][0];
}

void dfs1(int a);

void process(int a, int b) {
    while (active.lower_bound(a) != active.end()) {
        int x = *active.lower_bound(a);
        if (x > b)
            break;

        if (!vis[who[x]])
            dfs1(who[x]);
        active.erase(x);
    }
}

void query(int a, int b) {
    for (; head[a] != head[b]; b = lift[head[b]][0])
        process(pos[head[b]], pos[b]);

    process(pos[a], pos[b]);
}

void dfs1(int a) {
    vis[a] = 1;
    for (int v : col[a])
        query(start[a], v);

    topo.push_back(a);
}

void dfs2(int a) {
    vis[a] = 1;
    comp.push_back(a);
    for (int v : col[a]) {
        while (st.query(tin[v], tout[v])[0] <= dep[v]) {
            int x = st.query(tin[v], tout[v])[1];
            st.upd(tin[x], {(int) 1e9, 0});
            if (!vis[c[x]])
                dfs2(c[x]);
        }
    }
}

int main() {
    cin.tie(0)->sync_with_stdio(false);

    cin >> n >> k;

    for (int i = 1; i < n; i++) {
        int u, v;
        cin >> u >> v;

        adj[u].push_back(v);
        adj[v].push_back(u);
    }

    for (int i = 1; i <= n; i++) {
        cin >> c[i];
        col[c[i]].push_back(i);
    }

    timer = 0;
    dfs();

    for (int i = 1; i <= k; i++) {
        start[i] = col[i][0];
        for (int x : col[i]) {
            start[i] = lca(start[i], x);
        }
    }


    timer = 1;
    head[1] = 1;
    dfs_hld();

    for (int i = 1; i <= n; i++)
        who[pos[i]] = c[i];

    for (int i = 1; i <= n; i++)
        active.insert(i);

    for (int i = 1; i <= k; i++)
        if (!vis[i])
            dfs1(i);

    reverse(all(topo));

    st.init(n + 1);
    memset(vis, 0, sizeof(vis));
    memset(head, 0, sizeof(head));

    for (int i = 1; i <= n; i++)
        st.upd(tin[i], {dep[start[c[i]]], i});

    DSU dsu(n + 1);

    int ans = k - 1;
    for (int v : topo) {
        if (!vis[v]) {
            comp.clear();
            dfs2(v);

            int cnt = 0;
            for (int x : comp)
                for (int u : col[x])
                    head[u] = v, cnt++;

            for (int x : comp)
                for (int s : col[x])
                    for (int t : adj[s])
                        if (head[t] == v)
                            dsu.unite(s, t);

            if (dsu.size(col[comp[0]][0]) == cnt)
                ans = min(ans, (int) comp.size() - 1);
        }
    }

    cout << ans << '\n';

    return 0;
}

Subtask #1
1.0 / 1.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 20316 KB Output is correct
2 Correct 4 ms 20316 KB Output is correct
3 Correct 4 ms 20316 KB Output is correct
4 Correct 4 ms 20316 KB Output is correct
5 Correct 4 ms 20316 KB Output is correct
6 Correct 4 ms 20316 KB Output is correct
7 Correct 4 ms 20316 KB Output is correct
8 Correct 4 ms 20316 KB Output is correct
9 Correct 4 ms 20316 KB Output is correct
10 Correct 4 ms 20316 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 20316 KB Output is correct
2 Correct 4 ms 20316 KB Output is correct
3 Correct 4 ms 20316 KB Output is correct
4 Correct 4 ms 20316 KB Output is correct
5 Correct 4 ms 20316 KB Output is correct
6 Correct 4 ms 20316 KB Output is correct
7 Correct 4 ms 20316 KB Output is correct
8 Correct 4 ms 20316 KB Output is correct
9 Correct 4 ms 20316 KB Output is correct
10 Correct 4 ms 20316 KB Output is correct
11 Correct 6 ms 20572 KB Output is correct
12 Correct 7 ms 20568 KB Output is correct
13 Correct 7 ms 20512 KB Output is correct
14 Correct 7 ms 20572 KB Output is correct
15 Correct 8 ms 20572 KB Output is correct
16 Correct 9 ms 20824 KB Output is correct
17 Correct 6 ms 20568 KB Output is correct
18 Correct 6 ms 20728 KB Output is correct
19 Correct 7 ms 20572 KB Output is correct
20 Correct 6 ms 20512 KB Output is correct
21 Correct 6 ms 20568 KB Output is correct
22 Correct 7 ms 20572 KB Output is correct
23 Correct 6 ms 20640 KB Output is correct
24 Correct 6 ms 20512 KB Output is correct
25 Correct 6 ms 20572 KB Output is correct
26 Correct 6 ms 20772 KB Output is correct
27 Correct 6 ms 20572 KB Output is correct
28 Correct 8 ms 20572 KB Output is correct
29 Correct 8 ms 20692 KB Output is correct
30 Correct 8 ms 20568 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 431 ms 66688 KB Output is correct
2 Correct 270 ms 70924 KB Output is correct
3 Correct 424 ms 69720 KB Output is correct
4 Correct 256 ms 70676 KB Output is correct
5 Correct 413 ms 66892 KB Output is correct
6 Correct 267 ms 70804 KB Output is correct
7 Correct 402 ms 67152 KB Output is correct
8 Correct 259 ms 70356 KB Output is correct
9 Correct 459 ms 68432 KB Output is correct
10 Correct 405 ms 63344 KB Output is correct
11 Correct 408 ms 65956 KB Output is correct
12 Correct 441 ms 68432 KB Output is correct
13 Correct 408 ms 62804 KB Output is correct
14 Correct 407 ms 68688 KB Output is correct
15 Correct 419 ms 68468 KB Output is correct
16 Correct 426 ms 63520 KB Output is correct
17 Correct 420 ms 64080 KB Output is correct
18 Correct 423 ms 64336 KB Output is correct
19 Correct 417 ms 67508 KB Output is correct
20 Correct 450 ms 69952 KB Output is correct
21 Correct 4 ms 20316 KB Output is correct

Subtask #4
0 / 59.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 20316 KB Output is correct
2 Correct 4 ms 20316 KB Output is correct
3 Correct 4 ms 20316 KB Output is correct
4 Correct 4 ms 20316 KB Output is correct
5 Correct 4 ms 20316 KB Output is correct
6 Correct 4 ms 20316 KB Output is correct
7 Correct 4 ms 20316 KB Output is correct
8 Correct 4 ms 20316 KB Output is correct
9 Correct 4 ms 20316 KB Output is correct
10 Correct 4 ms 20316 KB Output is correct
11 Correct 6 ms 20572 KB Output is correct
12 Correct 7 ms 20568 KB Output is correct
13 Correct 7 ms 20512 KB Output is correct
14 Correct 7 ms 20572 KB Output is correct
15 Correct 8 ms 20572 KB Output is correct
16 Correct 9 ms 20824 KB Output is correct
17 Correct 6 ms 20568 KB Output is correct
18 Correct 6 ms 20728 KB Output is correct
19 Correct 7 ms 20572 KB Output is correct
20 Correct 6 ms 20512 KB Output is correct
21 Correct 6 ms 20568 KB Output is correct
22 Correct 7 ms 20572 KB Output is correct
23 Correct 6 ms 20640 KB Output is correct
24 Correct 6 ms 20512 KB Output is correct
25 Correct 6 ms 20572 KB Output is correct
26 Correct 6 ms 20772 KB Output is correct
27 Correct 6 ms 20572 KB Output is correct
28 Correct 8 ms 20572 KB Output is correct
29 Correct 8 ms 20692 KB Output is correct
30 Correct 8 ms 20568 KB Output is correct
31 Correct 431 ms 66688 KB Output is correct
32 Correct 270 ms 70924 KB Output is correct
33 Correct 424 ms 69720 KB Output is correct
34 Correct 256 ms 70676 KB Output is correct
35 Correct 413 ms 66892 KB Output is correct
36 Correct 267 ms 70804 KB Output is correct
37 Correct 402 ms 67152 KB Output is correct
38 Correct 259 ms 70356 KB Output is correct
39 Correct 459 ms 68432 KB Output is correct
40 Correct 405 ms 63344 KB Output is correct
41 Correct 408 ms 65956 KB Output is correct
42 Correct 441 ms 68432 KB Output is correct
43 Correct 408 ms 62804 KB Output is correct
44 Correct 407 ms 68688 KB Output is correct
45 Correct 419 ms 68468 KB Output is correct
46 Correct 426 ms 63520 KB Output is correct
47 Correct 420 ms 64080 KB Output is correct
48 Correct 423 ms 64336 KB Output is correct
49 Correct 417 ms 67508 KB Output is correct
50 Correct 450 ms 69952 KB Output is correct
51 Correct 4 ms 20316 KB Output is correct
52 Correct 784 ms 56564 KB Output is correct
53 Correct 768 ms 56400 KB Output is correct
54 Correct 738 ms 56276 KB Output is correct
55 Correct 781 ms 56144 KB Output is correct
56 Correct 731 ms 56300 KB Output is correct
57 Correct 783 ms 56048 KB Output is correct
58 Execution timed out 3011 ms 56652 KB Time limit exceeded
59 Halted 0 ms 0 KB -