oj.uz

Submission #898819

# Submission time Handle Problem Language Result Execution time Memory
898819 2024-01-05T07:06:21 Z juliany2 Capital City (JOI20_capital_city) C++17
41 / 100
 3000 ms 70228 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], reach[N];
bool vis[N], done[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;

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

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

    memset(reach, -1, sizeof(reach));

    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 3 ms 19036 KB Output is correct
2 Correct 3 ms 19032 KB Output is correct
3 Correct 3 ms 19180 KB Output is correct
4 Correct 4 ms 19176 KB Output is correct
5 Correct 4 ms 19032 KB Output is correct
6 Correct 4 ms 19036 KB Output is correct
7 Correct 4 ms 19200 KB Output is correct
8 Correct 3 ms 19036 KB Output is correct
9 Correct 3 ms 19036 KB Output is correct
10 Correct 3 ms 19032 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 19036 KB Output is correct
2 Correct 3 ms 19032 KB Output is correct
3 Correct 3 ms 19180 KB Output is correct
4 Correct 4 ms 19176 KB Output is correct
5 Correct 4 ms 19032 KB Output is correct
6 Correct 4 ms 19036 KB Output is correct
7 Correct 4 ms 19200 KB Output is correct
8 Correct 3 ms 19036 KB Output is correct
9 Correct 3 ms 19036 KB Output is correct
10 Correct 3 ms 19032 KB Output is correct
11 Correct 6 ms 19292 KB Output is correct
12 Correct 6 ms 19288 KB Output is correct
13 Correct 6 ms 19544 KB Output is correct
14 Correct 6 ms 19292 KB Output is correct
15 Correct 6 ms 19292 KB Output is correct
16 Correct 8 ms 19292 KB Output is correct
17 Correct 5 ms 19292 KB Output is correct
18 Correct 6 ms 19292 KB Output is correct
19 Correct 6 ms 19292 KB Output is correct
20 Correct 5 ms 19292 KB Output is correct
21 Correct 5 ms 19288 KB Output is correct
22 Correct 6 ms 19548 KB Output is correct
23 Correct 5 ms 19376 KB Output is correct
24 Correct 6 ms 19464 KB Output is correct
25 Correct 6 ms 19292 KB Output is correct
26 Correct 6 ms 19412 KB Output is correct
27 Correct 6 ms 19292 KB Output is correct
28 Correct 6 ms 19292 KB Output is correct
29 Correct 6 ms 19288 KB Output is correct
30 Correct 6 ms 19288 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 467 ms 69604 KB Output is correct
2 Correct 266 ms 70112 KB Output is correct
3 Correct 436 ms 69284 KB Output is correct
4 Correct 277 ms 70228 KB Output is correct
5 Correct 423 ms 66128 KB Output is correct
6 Correct 273 ms 69996 KB Output is correct
7 Correct 477 ms 66464 KB Output is correct
8 Correct 257 ms 69564 KB Output is correct
9 Correct 438 ms 67824 KB Output is correct
10 Correct 439 ms 62100 KB Output is correct
11 Correct 450 ms 64996 KB Output is correct
12 Correct 438 ms 67668 KB Output is correct
13 Correct 417 ms 61828 KB Output is correct
14 Correct 432 ms 68152 KB Output is correct
15 Correct 439 ms 67812 KB Output is correct
16 Correct 407 ms 62820 KB Output is correct
17 Correct 454 ms 63312 KB Output is correct
18 Correct 443 ms 63332 KB Output is correct
19 Correct 425 ms 66744 KB Output is correct
20 Correct 419 ms 68948 KB Output is correct
21 Correct 3 ms 19036 KB Output is correct

Subtask #4
0 / 59.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 19036 KB Output is correct
2 Correct 3 ms 19032 KB Output is correct
3 Correct 3 ms 19180 KB Output is correct
4 Correct 4 ms 19176 KB Output is correct
5 Correct 4 ms 19032 KB Output is correct
6 Correct 4 ms 19036 KB Output is correct
7 Correct 4 ms 19200 KB Output is correct
8 Correct 3 ms 19036 KB Output is correct
9 Correct 3 ms 19036 KB Output is correct
10 Correct 3 ms 19032 KB Output is correct
11 Correct 6 ms 19292 KB Output is correct
12 Correct 6 ms 19288 KB Output is correct
13 Correct 6 ms 19544 KB Output is correct
14 Correct 6 ms 19292 KB Output is correct
15 Correct 6 ms 19292 KB Output is correct
16 Correct 8 ms 19292 KB Output is correct
17 Correct 5 ms 19292 KB Output is correct
18 Correct 6 ms 19292 KB Output is correct
19 Correct 6 ms 19292 KB Output is correct
20 Correct 5 ms 19292 KB Output is correct
21 Correct 5 ms 19288 KB Output is correct
22 Correct 6 ms 19548 KB Output is correct
23 Correct 5 ms 19376 KB Output is correct
24 Correct 6 ms 19464 KB Output is correct
25 Correct 6 ms 19292 KB Output is correct
26 Correct 6 ms 19412 KB Output is correct
27 Correct 6 ms 19292 KB Output is correct
28 Correct 6 ms 19292 KB Output is correct
29 Correct 6 ms 19288 KB Output is correct
30 Correct 6 ms 19288 KB Output is correct
31 Correct 467 ms 69604 KB Output is correct
32 Correct 266 ms 70112 KB Output is correct
33 Correct 436 ms 69284 KB Output is correct
34 Correct 277 ms 70228 KB Output is correct
35 Correct 423 ms 66128 KB Output is correct
36 Correct 273 ms 69996 KB Output is correct
37 Correct 477 ms 66464 KB Output is correct
38 Correct 257 ms 69564 KB Output is correct
39 Correct 438 ms 67824 KB Output is correct
40 Correct 439 ms 62100 KB Output is correct
41 Correct 450 ms 64996 KB Output is correct
42 Correct 438 ms 67668 KB Output is correct
43 Correct 417 ms 61828 KB Output is correct
44 Correct 432 ms 68152 KB Output is correct
45 Correct 439 ms 67812 KB Output is correct
46 Correct 407 ms 62820 KB Output is correct
47 Correct 454 ms 63312 KB Output is correct
48 Correct 443 ms 63332 KB Output is correct
49 Correct 425 ms 66744 KB Output is correct
50 Correct 419 ms 68948 KB Output is correct
51 Correct 3 ms 19036 KB Output is correct
52 Correct 592 ms 56004 KB Output is correct
53 Correct 549 ms 55900 KB Output is correct
54 Correct 539 ms 56096 KB Output is correct
55 Correct 522 ms 55892 KB Output is correct
56 Correct 539 ms 55852 KB Output is correct
57 Correct 571 ms 55856 KB Output is correct
58 Execution timed out 3008 ms 56144 KB Time limit exceeded
59 Halted 0 ms 0 KB -