oj.uz

Submission #898837

# Submission time Handle Problem Language Result Execution time Memory
898837 2024-01-05T07:43:02 Z juliany2 Capital City (JOI20_capital_city) C++17
41 / 100
 3000 ms 67920 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) {
    int it = 0;
    while (active.lower_bound(a) != active.end()) {
        int x = *active.lower_bound(a);
        if (x > b)
            break;

        assert(it++ <= n);
        active.erase(x);
        if (!vis[who[x]])
            dfs1(who[x]);
    }
}

void query(int a, int b) {
    int it = 0;
    for (; head[a] != head[b]; b = lift[head[b]][0]) {
        assert(it++ <= n);
        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]) {
        int it = 0;
        while (st.query(tin[v], tout[v])[0] <= dep[v]) {
            assert(it++ <= n);
            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 4 ms 19032 KB Output is correct
2 Correct 3 ms 19036 KB Output is correct
3 Correct 3 ms 19036 KB Output is correct
4 Correct 3 ms 19124 KB Output is correct
5 Correct 3 ms 19036 KB Output is correct
6 Correct 3 ms 19036 KB Output is correct
7 Correct 3 ms 19196 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 19036 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 19032 KB Output is correct
2 Correct 3 ms 19036 KB Output is correct
3 Correct 3 ms 19036 KB Output is correct
4 Correct 3 ms 19124 KB Output is correct
5 Correct 3 ms 19036 KB Output is correct
6 Correct 3 ms 19036 KB Output is correct
7 Correct 3 ms 19196 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 19036 KB Output is correct
11 Correct 5 ms 19292 KB Output is correct
12 Correct 7 ms 19292 KB Output is correct
13 Correct 6 ms 19384 KB Output is correct
14 Correct 6 ms 19544 KB Output is correct
15 Correct 6 ms 19292 KB Output is correct
16 Correct 6 ms 19292 KB Output is correct
17 Correct 5 ms 19288 KB Output is correct
18 Correct 5 ms 19292 KB Output is correct
19 Correct 5 ms 19288 KB Output is correct
20 Correct 5 ms 19292 KB Output is correct
21 Correct 5 ms 19292 KB Output is correct
22 Correct 5 ms 19292 KB Output is correct
23 Correct 5 ms 19292 KB Output is correct
24 Correct 6 ms 19292 KB Output is correct
25 Correct 6 ms 19292 KB Output is correct
26 Correct 6 ms 19340 KB Output is correct
27 Correct 6 ms 19296 KB Output is correct
28 Correct 6 ms 19288 KB Output is correct
29 Correct 6 ms 19444 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 440 ms 67504 KB Output is correct
2 Correct 268 ms 67768 KB Output is correct
3 Correct 442 ms 67152 KB Output is correct
4 Correct 262 ms 67920 KB Output is correct
5 Correct 423 ms 64080 KB Output is correct
6 Correct 256 ms 67876 KB Output is correct
7 Correct 390 ms 64712 KB Output is correct
8 Correct 258 ms 67532 KB Output is correct
9 Correct 455 ms 65872 KB Output is correct
10 Correct 443 ms 60208 KB Output is correct
11 Correct 499 ms 63060 KB Output is correct
12 Correct 482 ms 65744 KB Output is correct
13 Correct 469 ms 59728 KB Output is correct
14 Correct 480 ms 66104 KB Output is correct
15 Correct 480 ms 65748 KB Output is correct
16 Correct 493 ms 60752 KB Output is correct
17 Correct 477 ms 61120 KB Output is correct
18 Correct 450 ms 61472 KB Output is correct
19 Correct 468 ms 64528 KB Output is correct
20 Correct 411 ms 66708 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 4 ms 19032 KB Output is correct
2 Correct 3 ms 19036 KB Output is correct
3 Correct 3 ms 19036 KB Output is correct
4 Correct 3 ms 19124 KB Output is correct
5 Correct 3 ms 19036 KB Output is correct
6 Correct 3 ms 19036 KB Output is correct
7 Correct 3 ms 19196 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 19036 KB Output is correct
11 Correct 5 ms 19292 KB Output is correct
12 Correct 7 ms 19292 KB Output is correct
13 Correct 6 ms 19384 KB Output is correct
14 Correct 6 ms 19544 KB Output is correct
15 Correct 6 ms 19292 KB Output is correct
16 Correct 6 ms 19292 KB Output is correct
17 Correct 5 ms 19288 KB Output is correct
18 Correct 5 ms 19292 KB Output is correct
19 Correct 5 ms 19288 KB Output is correct
20 Correct 5 ms 19292 KB Output is correct
21 Correct 5 ms 19292 KB Output is correct
22 Correct 5 ms 19292 KB Output is correct
23 Correct 5 ms 19292 KB Output is correct
24 Correct 6 ms 19292 KB Output is correct
25 Correct 6 ms 19292 KB Output is correct
26 Correct 6 ms 19340 KB Output is correct
27 Correct 6 ms 19296 KB Output is correct
28 Correct 6 ms 19288 KB Output is correct
29 Correct 6 ms 19444 KB Output is correct
30 Correct 6 ms 19288 KB Output is correct
31 Correct 440 ms 67504 KB Output is correct
32 Correct 268 ms 67768 KB Output is correct
33 Correct 442 ms 67152 KB Output is correct
34 Correct 262 ms 67920 KB Output is correct
35 Correct 423 ms 64080 KB Output is correct
36 Correct 256 ms 67876 KB Output is correct
37 Correct 390 ms 64712 KB Output is correct
38 Correct 258 ms 67532 KB Output is correct
39 Correct 455 ms 65872 KB Output is correct
40 Correct 443 ms 60208 KB Output is correct
41 Correct 499 ms 63060 KB Output is correct
42 Correct 482 ms 65744 KB Output is correct
43 Correct 469 ms 59728 KB Output is correct
44 Correct 480 ms 66104 KB Output is correct
45 Correct 480 ms 65748 KB Output is correct
46 Correct 493 ms 60752 KB Output is correct
47 Correct 477 ms 61120 KB Output is correct
48 Correct 450 ms 61472 KB Output is correct
49 Correct 468 ms 64528 KB Output is correct
50 Correct 411 ms 66708 KB Output is correct
51 Correct 3 ms 19036 KB Output is correct
52 Correct 501 ms 53868 KB Output is correct
53 Correct 541 ms 54100 KB Output is correct
54 Correct 566 ms 53860 KB Output is correct
55 Correct 519 ms 54124 KB Output is correct
56 Correct 546 ms 53888 KB Output is correct
57 Correct 503 ms 53736 KB Output is correct
58 Execution timed out 3025 ms 54352 KB Time limit exceeded
59 Halted 0 ms 0 KB -