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Submission #869444

# Submission time Handle Problem Language Result Execution time Memory
869444 2023-11-04T11:07:26 Z makrav Cat Exercise (JOI23_ho_t4) C++14
100 / 100
 772 ms 230064 KB 
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef vector<int> vei;
typedef vector<vei> vevei;

#define all(a) (a).begin(), (a).end()
#define sz(a) (int) a.size()
#define con cout << "NO\n"
#define coe cout << "YES\n";
#define str string
#define pb push_back
#define ff first
#define sc second
#define pii pair<int, int>
#define mxe max_element
#define mne min_element
#define stf shrink_to_fit
#define f(i, l, r) for (int i = (l); i < (r); i++)
#define double ld
#define int ll

const int MAXN = 200010;

vector<int> Log_2(MAXN, 0);
void fill() {
    for (int i = 2; i < MAXN; i++) {
        Log_2[i] = Log_2[i / 2] + 1;
    }
}

struct SparseTable {
    int n;
    vector<int> a;
    vector<vector<int>> mx;

    SparseTable(int n_, vector<int> a_) {
        n = n_;
        a = a_;
        mx.resize(n, vector<int>(Log_2[n] + 1, -1));
        build();
    }

    void build() {
        for (int i = n - 1; i >= 0; i--) {
            mx[i][0] = a[i];
            int st = 1;
            while ((1 << st) + i <= n) {
                mx[i][st] = max(mx[(1 << (st - 1)) + i][st - 1], mx[i][st - 1]);
                st++;
            }
        }
    }

    int req(int l, int r) {
        bool sw = false;
        int sz = r - l + 1;
        int otr1 = mx[l][Log_2[sz]];
        int ot2 = mx[r - (1 << Log_2[sz]) + 1][Log_2[sz]];
        return max(otr1, ot2);
    }
};
mt19937 rnd(time(0));

struct node {
    int val, siz, prior, ind, mn, hg;
    node* l = nullptr, * r = nullptr, * par = nullptr;
    node() = default;
    node(int val_, int H, int ind_) {
        prior = rnd();
        val = val_;
        ind = ind_;
        siz = 1;
        mn = H;
        hg = H;
        l = nullptr;
        r = nullptr;
        par = nullptr;
    }
};

vector<pair<node*, node*>> euler;

struct cartesiantree {
    node* r = nullptr;

    int size(node* root) {
        if (root == nullptr) return 0;
        return root->siz;
    }

    int mn(node* root) {
        if (root == nullptr) return 0;
        return root->mn;
    }

    void upd(node* root) {
        if (root == nullptr) return;
        root->siz = size(root->l) + size(root->r) + 1;
        root->mn = max(root->hg, max(mn(root->l), mn(root->r)));
        if (root->l != nullptr) root->l->par = root;
        if (root->r != nullptr) root->r->par = root;
    }

    pair<node*, node*> split(node* root, int x) {
        if (root == nullptr) return { nullptr, nullptr };
        if (size(root->l) < x) {
            pair<node*, node*> p = split(root->r, x - size(root->l) - 1);
            if (p.ff != nullptr)p.ff->par = nullptr;
            if (p.sc != nullptr)p.sc->par = nullptr;
            root->r = p.ff;
            upd(root);
            return { root, p.sc };
        }
        else {
            pair<node*, node*> p = split(root->l, x);
            if (p.ff != nullptr)p.ff->par = nullptr;
            if (p.sc != nullptr)p.sc->par = nullptr;
            root->l = p.sc;
            upd(root);
            return { p.ff, root };
        }
    }

    node* merge(node* a, node* b) {
        if (a == nullptr) return b;
        if (b == nullptr) return a;
        if (a->prior < b->prior) {
            node* x = merge(a, b->l);
            b->l = x;
            upd(b);
            upd(a);
            return b;
        }
        else {
            node* x = merge(a->r, b);
            a->r = x;
            upd(a);
            upd(b);
            return a;
        }
    }

    int get_pos(node* x) {
        int ps = size(x->l);
        while (x->par != nullptr) {
            if (x->par->r == x) ps += size(x->par->l) + 1;
            x = x->par;
        }
        return ps;
    }

    node* getroot(node* x) {
        while (x->par != nullptr) x = x->par;
        return x;
    }

    int kth(node* root, int k) {
        if (root == nullptr)return -1;
        if (size(root->l) == k) {
            cout << (root->par == nullptr ? -1 : root->par->ind) << ' ';
            return root->val;
        }
        if (size(root->l) > k) {
            return kth(root->l, k);
        }
        else {
            return kth(root->r, k - size(root->l) - 1);
        }
    }

    void SPL(int x) {
        int left = get_pos(euler[x].ff), right = get_pos(euler[x].sc);
        auto p = split(getroot(euler[x].ff), left);
        auto p2 = split(p.sc, right - left + 1);
        merge(p.ff, p2.sc);
    }

    void mrg(int x, int y) {
        int left = 1 + get_pos(euler[y].ff);
        auto p = split(getroot(euler[y].ff), left);
        merge(p.ff, merge(getroot(euler[x].ff), p.sc));
    }
};

vector<unordered_set<int>> g;
vector<int> order, par;

void dfs(int v, int p) {
    par[v] = p;
    order.pb(v);
    for (auto& u : g[v]) {
        if (u != p) {
            dfs(u, v);
        }
    }
    order.pb(v);
}

struct LCA {
    int n;
    vector<unordered_set<int>> g;
    vector<vector<int>> up;
    vector<int> tin, tout, h;
    int timer = 0, l;

    LCA() = default;
    LCA(int n_, vector<unordered_set<int>>& g_) {
        n = n_;
        g = g_;
        l = (int)log2(n) + 1;
        up.assign(n, vector<int>(l, 0));
        tin.assign(n, 0);
        tout.assign(n, 0);
        h.assign(n, 0);
        dfs(0, 0, 0);
    }

    void dfs(int v, int p, int hg) {
        h[v] = hg;
        tin[v] = timer++;
        up[v][0] = p;
        f(i, 1, l) {
            up[v][i] = up[up[v][i - 1]][i - 1];
        }

        for (auto& u : g[v]) {
            if (u != p) {
                dfs(u, v, hg + 1);
            }
        }
        tout[v] = timer++;
    }

    bool parent(int a, int b) {
        return tin[a] <= tin[b] && tout[a] >= tout[b];
    }

    int lca(int a, int b) {
        if (parent(a, b)) return a;
        if (parent(b, a)) return b;

        for (int i = l - 1; i >= 0; i--) {
            if (!parent(up[a][i], b)) {
                a = up[a][i];
            }
        }
        return up[a][0];
    }

    int len(int a, int b) {
        return h[a] + h[b] - 2 * h[lca(a, b)];
    }
};

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    fill();

    int n; cin >> n;
    vector<int> h(n);
    f(i, 0, n) cin >> h[i];
    SparseTable sp(n, h);
    vector<int> pos(n + 1, 0);
    for (int i = 0; i < n; i++) {
        pos[h[i]] = i;
    }

    vector<pair<int, int>> e(n - 1);
    f(i, 0, n - 1) cin >> e[i].ff >> e[i].sc;

    g.resize(n);
    par.assign(n, 0);
    for (auto& u : e) {
        g[u.ff - 1].insert(u.sc - 1);
        g[u.sc - 1].insert(u.ff - 1);
    }
    LCA L(n, g);

    dfs(0, 0);
    cartesiantree ct;
    euler.resize(n);
    for (int i = 0; i < sz(order); i++) {
        node* nw = new node(order[i], h[order[i]], i);
        if (euler[order[i]].ff == nullptr) {
            euler[order[i]].ff = nw;
            ct.r = ct.merge(ct.r, euler[order[i]].ff);
        }
        else {
            euler[order[i]].sc = nw;
            ct.r = ct.merge(ct.r, euler[order[i]].sc);
        }
    }
    int ans = 0;

    vector<pair<node*, int>> roots = { {ct.r, 0} };
    int op = 0;
    while (!roots.empty()) {
        op++;

        auto cur = roots.back();
        roots.pop_back();
        int H = ct.mn(cur.ff);
        int v = pos[H];

        int SZ = ct.size(cur.ff);

        if (SZ == 2) {
            ans = max(ans, cur.sc);
        }

        vector<int> cut;
        for (auto& u : g[v]) {
            if (u != par[v]) {
                cut.pb(u);
            }
        }

        for (auto& u : cut) {
            g[v].erase(u);
            g[u].erase(v);
            ct.SPL(u);
            int v2 = pos[ct.mn(ct.getroot(euler[u].ff))];
            roots.pb({ ct.getroot(euler[u].ff), cur.sc + L.len(v, v2) });
        }
        if (!g[v].empty()) {
            ct.SPL(v);
            int u = *g[v].begin();
            g[v].erase(u);
            g[u].erase(v);
            int v2 = pos[ct.mn(ct.getroot(euler[u].ff))];
            roots.pb({ ct.getroot(euler[u].ff), cur.sc + L.len(v, v2) });
        }
    }
    cout << ans << '\n';

    return 0;
}

Compilation message

Main.cpp: In member function 'll SparseTable::req(ll, ll)':
Main.cpp:60:14: warning: unused variable 'sw' [-Wunused-variable]
   60 |         bool sw = false;
      |              ^~

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1884 KB Output is correct
2 Correct 1 ms 1884 KB Output is correct
3 Correct 1 ms 1884 KB Output is correct
4 Correct 1 ms 2036 KB Output is correct
5 Correct 1 ms 1884 KB Output is correct
6 Correct 1 ms 1884 KB Output is correct
7 Correct 1 ms 1884 KB Output is correct
8 Correct 1 ms 1884 KB Output is correct
9 Correct 1 ms 1884 KB Output is correct
10 Correct 1 ms 1884 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1884 KB Output is correct
2 Correct 1 ms 1884 KB Output is correct
3 Correct 1 ms 1884 KB Output is correct
4 Correct 1 ms 2036 KB Output is correct
5 Correct 1 ms 1884 KB Output is correct
6 Correct 1 ms 1884 KB Output is correct
7 Correct 1 ms 1884 KB Output is correct
8 Correct 1 ms 1884 KB Output is correct
9 Correct 1 ms 1884 KB Output is correct
10 Correct 1 ms 1884 KB Output is correct
11 Correct 1 ms 2140 KB Output is correct
12 Correct 1 ms 2288 KB Output is correct
13 Correct 1 ms 2140 KB Output is correct
14 Correct 2 ms 2140 KB Output is correct
15 Correct 2 ms 2140 KB Output is correct
16 Correct 2 ms 2140 KB Output is correct
17 Correct 2 ms 2296 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1884 KB Output is correct
2 Correct 1 ms 1884 KB Output is correct
3 Correct 1 ms 1884 KB Output is correct
4 Correct 1 ms 2036 KB Output is correct
5 Correct 1 ms 1884 KB Output is correct
6 Correct 1 ms 1884 KB Output is correct
7 Correct 1 ms 1884 KB Output is correct
8 Correct 1 ms 1884 KB Output is correct
9 Correct 1 ms 1884 KB Output is correct
10 Correct 1 ms 1884 KB Output is correct
11 Correct 1 ms 2140 KB Output is correct
12 Correct 1 ms 2288 KB Output is correct
13 Correct 1 ms 2140 KB Output is correct
14 Correct 2 ms 2140 KB Output is correct
15 Correct 2 ms 2140 KB Output is correct
16 Correct 2 ms 2140 KB Output is correct
17 Correct 2 ms 2296 KB Output is correct
18 Correct 9 ms 7004 KB Output is correct
19 Correct 10 ms 7004 KB Output is correct
20 Correct 11 ms 7256 KB Output is correct
21 Correct 10 ms 7004 KB Output is correct
22 Correct 9 ms 7004 KB Output is correct
23 Correct 8 ms 7004 KB Output is correct
24 Correct 9 ms 7180 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1884 KB Output is correct
2 Correct 1 ms 1884 KB Output is correct
3 Correct 1 ms 1884 KB Output is correct
4 Correct 1 ms 2036 KB Output is correct
5 Correct 1 ms 1884 KB Output is correct
6 Correct 1 ms 1884 KB Output is correct
7 Correct 1 ms 1884 KB Output is correct
8 Correct 1 ms 1884 KB Output is correct
9 Correct 1 ms 1884 KB Output is correct
10 Correct 1 ms 1884 KB Output is correct
11 Correct 1 ms 2140 KB Output is correct
12 Correct 1 ms 2288 KB Output is correct
13 Correct 1 ms 2140 KB Output is correct
14 Correct 2 ms 2140 KB Output is correct
15 Correct 2 ms 2140 KB Output is correct
16 Correct 2 ms 2140 KB Output is correct
17 Correct 2 ms 2296 KB Output is correct
18 Correct 9 ms 7004 KB Output is correct
19 Correct 10 ms 7004 KB Output is correct
20 Correct 11 ms 7256 KB Output is correct
21 Correct 10 ms 7004 KB Output is correct
22 Correct 9 ms 7004 KB Output is correct
23 Correct 8 ms 7004 KB Output is correct
24 Correct 9 ms 7180 KB Output is correct
25 Correct 1 ms 1880 KB Output is correct
26 Correct 11 ms 7004 KB Output is correct
27 Correct 10 ms 7004 KB Output is correct
28 Correct 11 ms 7004 KB Output is correct
29 Correct 10 ms 7204 KB Output is correct
30 Correct 10 ms 7020 KB Output is correct
31 Correct 10 ms 7004 KB Output is correct
32 Correct 10 ms 7004 KB Output is correct
33 Correct 11 ms 7020 KB Output is correct

Subtask #5
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1884 KB Output is correct
2 Correct 1 ms 1884 KB Output is correct
3 Correct 1 ms 1884 KB Output is correct
4 Correct 1 ms 2036 KB Output is correct
5 Correct 1 ms 1884 KB Output is correct
6 Correct 1 ms 1884 KB Output is correct
7 Correct 1 ms 1884 KB Output is correct
8 Correct 1 ms 1884 KB Output is correct
9 Correct 1 ms 1884 KB Output is correct
10 Correct 1 ms 1884 KB Output is correct
11 Correct 1 ms 2140 KB Output is correct
12 Correct 1 ms 2288 KB Output is correct
13 Correct 1 ms 2140 KB Output is correct
14 Correct 2 ms 2140 KB Output is correct
15 Correct 2 ms 2140 KB Output is correct
16 Correct 2 ms 2140 KB Output is correct
17 Correct 2 ms 2296 KB Output is correct
18 Correct 9 ms 7004 KB Output is correct
19 Correct 10 ms 7004 KB Output is correct
20 Correct 11 ms 7256 KB Output is correct
21 Correct 10 ms 7004 KB Output is correct
22 Correct 9 ms 7004 KB Output is correct
23 Correct 8 ms 7004 KB Output is correct
24 Correct 9 ms 7180 KB Output is correct
25 Correct 418 ms 230044 KB Output is correct
26 Correct 396 ms 229896 KB Output is correct
27 Correct 414 ms 230064 KB Output is correct
28 Correct 388 ms 230060 KB Output is correct
29 Correct 390 ms 229468 KB Output is correct
30 Correct 382 ms 229940 KB Output is correct
31 Correct 379 ms 229700 KB Output is correct

Subtask #6
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1884 KB Output is correct
2 Correct 1 ms 2140 KB Output is correct
3 Correct 482 ms 220704 KB Output is correct
4 Correct 477 ms 221328 KB Output is correct
5 Correct 454 ms 220832 KB Output is correct

Subtask #7
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1884 KB Output is correct
2 Correct 1 ms 1884 KB Output is correct
3 Correct 1 ms 1884 KB Output is correct
4 Correct 1 ms 2036 KB Output is correct
5 Correct 1 ms 1884 KB Output is correct
6 Correct 1 ms 1884 KB Output is correct
7 Correct 1 ms 1884 KB Output is correct
8 Correct 1 ms 1884 KB Output is correct
9 Correct 1 ms 1884 KB Output is correct
10 Correct 1 ms 1884 KB Output is correct
11 Correct 1 ms 2140 KB Output is correct
12 Correct 1 ms 2288 KB Output is correct
13 Correct 1 ms 2140 KB Output is correct
14 Correct 2 ms 2140 KB Output is correct
15 Correct 2 ms 2140 KB Output is correct
16 Correct 2 ms 2140 KB Output is correct
17 Correct 2 ms 2296 KB Output is correct
18 Correct 9 ms 7004 KB Output is correct
19 Correct 10 ms 7004 KB Output is correct
20 Correct 11 ms 7256 KB Output is correct
21 Correct 10 ms 7004 KB Output is correct
22 Correct 9 ms 7004 KB Output is correct
23 Correct 8 ms 7004 KB Output is correct
24 Correct 9 ms 7180 KB Output is correct
25 Correct 1 ms 1880 KB Output is correct
26 Correct 11 ms 7004 KB Output is correct
27 Correct 10 ms 7004 KB Output is correct
28 Correct 11 ms 7004 KB Output is correct
29 Correct 10 ms 7204 KB Output is correct
30 Correct 10 ms 7020 KB Output is correct
31 Correct 10 ms 7004 KB Output is correct
32 Correct 10 ms 7004 KB Output is correct
33 Correct 11 ms 7020 KB Output is correct
34 Correct 418 ms 230044 KB Output is correct
35 Correct 396 ms 229896 KB Output is correct
36 Correct 414 ms 230064 KB Output is correct
37 Correct 388 ms 230060 KB Output is correct
38 Correct 390 ms 229468 KB Output is correct
39 Correct 382 ms 229940 KB Output is correct
40 Correct 379 ms 229700 KB Output is correct
41 Correct 1 ms 1884 KB Output is correct
42 Correct 1 ms 2140 KB Output is correct
43 Correct 482 ms 220704 KB Output is correct
44 Correct 477 ms 221328 KB Output is correct
45 Correct 454 ms 220832 KB Output is correct
46 Correct 768 ms 226544 KB Output is correct
47 Correct 768 ms 226328 KB Output is correct
48 Correct 752 ms 227668 KB Output is correct
49 Correct 772 ms 226052 KB Output is correct
50 Correct 755 ms 220420 KB Output is correct
51 Correct 735 ms 220468 KB Output is correct
52 Correct 727 ms 220412 KB Output is correct
53 Correct 742 ms 220816 KB Output is correct