#1139588 (C++23) No.772 Dynamic Distance Sum

• 問題: No.772 Dynamic Distance Sum
• ユーザー: imsuck
• 提出日時: 2025-12-09 09:54:11
• 言語: C++23 (gcc 13.3.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 1,289 ms / 5,000 ms
• コード長: 14,269 bytes
• コンパイル時間: 4,107 ms
• コンパイル使用メモリ: 303,552 KB
• 実行使用メモリ: 24,028 KB
• 最終ジャッジ日時: 2025-12-09 09:54:40
• 合計ジャッジ時間: 25,254 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 27

ソースコード

#line 1 "/home/imsuck/Yes/prog-sol/testing.cpp"
#include <bits/stdc++.h>
using namespace std;

#line 1 "/home/imsuck/Yes/cp-library/other/types.hpp"

using i8 = int8_t;
using u8 = uint8_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f32 = float;
using f64 = double;
using f80 = long double;
using str = string;
template<class T> using vec = vector<T>;
template<class E = i32> using graph = vec<vec<E>>;
#line 5 "/home/imsuck/Yes/prog-sol/testing.cpp"
#line 1 "/home/imsuck/Yes/cp-library/tree/top_tree_ecnerwala.hpp"

/**
 * https://github.com/ecnerwala/cp-book/blob/master/src/top_tree.hpp
 * Convenient memo:
 *   Creating vertices:
 *     n->val = ...;
 *     n->set_vert();
 *
 *   Creating edges:
 *     link(e, va, vb);
 *
 *   Updates:
 *     auto cur = get_path(va, vb); // or get_subtree(va, vb)
 *     cur->do_stuff();
 *     cur->pull_all();
 *
 * Node types:
 *   path edges: compress(c[0], self, c[1])
 *     assert(is_path && !is_vert);
 *     assert(c[0] && c[1]);
 *     assert(c[0]->is_path && c[1]->is_path);
 *     assert(!c[2]);
 *   (path) vertices: add_vertex(self, rake(c[0], c[1]))
 *     assert(is_path && is_vert);
 *     assert(!c[2]);
 *     if (c[0]) assert(!c[0]->is_path);
 *     if (c[1]) assert(!c[1]->is_path);
 *   non-path edges: rake(c[0], add_edge(self, c[2]), c[1])
 *     assert(!is_path && !is_vert);
 *     assert(c[2])
 *     assert(c[2]->is_path);
 *     if (c[0]) assert(!c[0]->is_path);
 *     if (c[1]) assert(!c[1]->is_path);
 */
template<class node> struct top_tree_node_base {
    using ptr = node *;

  private:
    ptr as_derived() { return (ptr)this; }
    auto as_derived() const { return (const ptr)this; }

  public:
    bool rev = false;
    ptr p = 0;
    array<ptr, 3> c{0, 0, 0};

    int d() const {
        assert(p);
        if (this == p->c[0]) return 0;
        if (this == p->c[1]) return 1;
        if (this == p->c[2]) return 2;
        assert(false);
    }
    ptr &p_c() { return p->c[d()]; }

    bool is_vert, is_path;
    void set_vert() { is_path = is_vert = true, _pull(); }

    bool r() const { return !p || p->is_path != is_path; }

  // protected:
#define CHECK(a) \
    template<class T, class = void> struct has_##a##_t : false_type {}; \
    template<class T> struct has_##a##_t<T, void_t<decltype(&T::a)>> : true_type {}; \
    template<class T> static constexpr bool has_##a = has_##a##_t<T>::value;
    CHECK(push) CHECK(flip) CHECK(pull)
#undef CHECK
    void _flip() {
        assert(is_path);
        swap(c[0], c[1]), rev ^= 1;
        if constexpr (has_flip<node>) as_derived()->flip();
    }
    void push_rev() {
        if (rev) {
            assert(is_path);
            if (!is_vert) {
                c[0]->_flip();
                c[1]->_flip();
            }
            rev = false;
        }
    }
    void _push() {
        push_rev();
        if constexpr (has_push<node>) as_derived()->push();
    }
    void _pull() {
        if constexpr (has_pull<node>) as_derived()->pull();
    }

  public:
    void push_all() {
        if (p) p->push_all();
        _push();
    }
    void push_flip_all() {
        if (p) p->push_flip_all();
        if (rev) {
            assert(is_path);
            if (!is_vert) {
                c[0]->_flip();
                c[1]->_flip();
            }
            rev = false;
        }
    }
    ptr pull_all() {
        ptr cur = as_derived();
        cur->_push(), cur->_pull();
        for (; cur->p; cur->_pull()) cur = cur->p;
        return cur;
    }

  // private:
    static inline void attach(ptr pa, int c_d, ptr ch) {
        pa->c[c_d] = ch;
        if (ch) ch->p = pa;
    }
    void rot() {
        assert(!is_vert);
        assert(!r());

        ptr pa = p;
        int x = d();
        assert(x != 2);
        ptr ch = c[!x];

        if (pa->p) pa->p_c() = as_derived();
        this->p = pa->p;

        attach(pa, x, ch);
        attach(as_derived(), !x, pa);

        pa->_pull();
    }
    void rot2(int c_d) {
        assert(!is_vert);
        assert(!r());
        assert(c[c_d]);
        assert(!c[c_d]->is_vert);

        if (d() == c_d) return rot();

        ptr pa = p;
        int x = d();
        assert(x != 2);
        ptr ch = c[c_d]->c[!x];

        if (pa->p) pa->p_c() = as_derived();
        this->p = pa->p;

        attach(pa, x, ch);
        attach(c[c_d], !x, pa);

        pa->_pull();
    }

    void splay_dir(int x) {
        for (; !r() && d() == x; rot())
            if (!p->r() && p->d() == x) p->rot();
    }

    void splay() {
        assert(!is_vert);
        for (; !r(); rot())
            if (!p->r()) p->d() == d() ? p->rot() : rot();
    }

    void splay2(int c_d) {
        assert(!is_vert && is_path);
        assert(c[c_d] && !c[c_d]->is_vert);
        for (; !r(); rot2(c_d))
            if (!p->r()) p->d() == d() ? p->rot() : rot2(c_d);
    }

    void splay2() {
        assert(!is_vert && is_path);
        assert(!r());
        p->splay2(d());
    }

    void splay_vert() {
        assert(is_vert);

        if (r()) return;

        p->splay_dir(d());
        if (p->r()) return;
        assert(p->d() != d());

        if (d() == 1) p->rot();
        assert(d() == 0);

        p->splay2();
        assert(d() == 0);
        assert(p->d() == 1);
        assert(p->p->r());
    }

    ptr cut_right() {
        assert(is_vert && is_path);
        splay_vert();

        if (r() || d() == 1) {
            assert(r() || (d() == 1 && p->r()));
            assert(!c[0]);
            return 0;
        }

        ptr pa = p;
        assert(pa->r() || (pa->d() == 1 && pa->p->r()));
        assert(!pa->is_vert);
        assert(pa->is_path);
        assert(pa->c[0] == this);
        assert(!pa->c[2]);

        if (pa->p) pa->p_c() = as_derived();
        this->p = pa->p;

        pa->is_path = false;
        pa->c[2] = pa->c[1];

        attach(pa, 0, c[0]);
        attach(pa, 1, c[1]);

        c[0] = 0;
        attach(as_derived(), 1, pa);
        assert(!c[2]);

        return pa->_pull(), pa;
    }

    ptr splice_non_path() {
        assert(!is_vert);
        assert(!is_path);

        splay();
        assert(p && p->is_vert && p->is_path);
        p->cut_right();

        if (!p->is_path) rot();
        assert(p && p->is_vert && p->is_path);
        assert(p->r() || (p->d() == 1 && p->p->r()));
        assert(p->c[d()] == this && !p->c[!d()]);

        ptr pa = p;

        if (pa->p) pa->p_c() = as_derived();
        this->p = pa->p;

        attach(pa, 0, c[0]);
        attach(pa, 1, c[1]);

        assert(c[2] && c[2]->is_path);
        attach(as_derived(), 0, pa);
        c[1] = c[2], c[2] = 0;

        is_path = true;

        return pa->_pull(), pa;
    }

    ptr splice_all() {
        ptr res = as_derived();
        for (ptr cur = as_derived(); cur; cur = cur->p) {
            if (!cur->is_path) res = cur->splice_non_path();
            assert(cur->is_path);
        }
        return res;
    }

  public:
    ptr expose() {
        assert(is_vert);

        push_all();

        ptr res = splice_all();
        cut_right(), pull_all();

        return res;
    }

    ptr expose_edge() {
        assert(!is_vert);

        push_all();

        ptr v = is_path ? c[1] : c[2];
        for (v->_push(); !v->is_vert; v->_push()) v = v->c[0];

        ptr res = v->splice_all();
        v->cut_right(), v->pull_all();

        assert(!p);
        assert(v == c[1]);

        return res == v ? as_derived() : res;
    }

    ptr meld_path_end() {
        assert(!p);
        ptr rt = as_derived();
        while (true) {
            rt->_push();
            if (rt->is_vert) break;
            rt = rt->c[1];
        }
        rt->splay_vert();
        if (rt->c[0] && rt->c[1]) {
            ptr ch = rt->c[1];
            while (true) {
                ch->_push();
                if (!ch->c[0]) break;
                ch = ch->c[0];
            }
            ch->splay();

            attach(ch, 0, rt->c[0]), rt->c[0] = 0;

            ch->_pull();
        } else if (rt->c[0]) {
            rt->c[1] = rt->c[0], rt->c[0] = 0;
        }
        return rt->pull_all();
    }

    void evert() {
        expose();

        ptr rt = as_derived();
        while (rt->p) {
            assert(rt->d() == 1);
            rt = rt->p;
        }

        rt->_flip();
        rt->meld_path_end();

        expose();

        assert(!p);
    }

    friend void link(ptr e, ptr v, ptr p) {
        assert(e && v && p);
        assert(!e->c[0] && !e->c[1] && !e->c[2]);
        v->evert(), p->expose();
        while (p->p) p = p->p;

        assert(!v->p);

        e->is_path = true, e->is_vert = false;
        attach(e, 0, p);
        attach(e, 1, v);
        e->_pull();
    }
    friend void link(node &e, node &v, node &p) { link(&e, &v, &p); }

    // Link v's root as a child of p with edge e
    // Returns false if they're already in the same subtree
    friend bool link_root(ptr e, ptr v, ptr p) {
        assert(e && v && p);
        assert(!e->c[0] && !e->c[1] && !e->c[2]);
        v->expose();
        p->expose();

        while (v->p) v = v->p;
        while (p->p) p = p->p;
        if (v == p) return false;

        e->is_path = true, e->is_vert = false;
        attach(e, 0, p);
        attach(e, 1, v);
        e->_pull();

        return true;
    }
    friend bool link_root(node &e, node &v, node &p) {
        return link_root(&e, &v, &p);
    }

    friend pair<ptr, ptr> cut(ptr e) {
        assert(!e->is_vert);
        e->expose_edge();

        assert(!e->p);
        assert(e->is_path);

        ptr l = e->c[0], r = e->c[1];
        assert(l && r);
        assert(!e->c[2]);

        e->c[0] = e->c[1] = 0;
        l->p = r->p = 0;

        l->meld_path_end();

        return {l, r};
    }
    friend pair<node &, node &> cut(node &e) {
        auto r = cut(&e);
        return {*r.first, *r.second};
    }

    friend ptr get_path(ptr v) {
        assert(v->is_vert);
        v->expose();
        if (!v->p) return v;
        assert(!v->p->p);
        return v->p;
    }
    friend node &get_path(node &v) { return *get_path(&v); }

    friend ptr get_subtree(ptr v) { return v->expose(), v; }
    friend node &get_subtree(node &v) { return v.expose(), v; }

    friend ptr lca(ptr u, ptr v) {
        if (u == v) return u;
        u->expose();
        auto up = u->p;
        ptr l = v->expose();
        if (u != v && up == u->p && (!up || !up->p)) return 0;
        return l;
    }
    friend ptr lca(node &u, node &v) { return lca(&u, &v); }
};
#line 6 "/home/imsuck/Yes/prog-sol/testing.cpp"

struct node : top_tree_node_base<node> { // subtree sums
    i32 val, sub, max_sub;
    i64 path_len;
    array<i64, 2> ans;

    void flip() { swap(ans[0], ans[1]); }

    void pull() {
        sub = max_sub = path_len = 0;
        ans.fill(0);

        for (i32 z = 0; z <= 2; z++) {
            if (!c[z]) continue;
            sub += c[z]->sub;
            if (z == 2) continue;
            ans[0] += c[z]->ans[0];
            max_sub = max(max_sub, c[z]->max_sub);
        }

        if (is_vert) {
            sub += val;
            ans[1] = ans[0];
        } else if (is_path) {
            path_len = val;
            for (i32 z = 0; z < 2; z++) {
                path_len += c[z]->path_len;
                ans[z] = c[z]->ans[z] + c[!z]->ans[z] +
                         (c[z]->path_len + val) * c[!z]->sub;
            }
        } else {
            ans[0] += c[2]->ans[0] + 1LL * val * c[2]->sub;
            max_sub = max(max_sub, c[2]->sub);
            ans[1] = ans[0];
        }
    }
};

template<class F> node *search(node *p, F select) {
    while (node *nxt = select(p)) {
        assert(p->is_vert);
        while (true) {
            nxt = select(p);
            if (nxt == p->c[2]) break;
            p = nxt;
        }
        p = nxt;
        assert(p->is_path);
        while (!p->is_vert) p = select(p);
    }
    p->evert();
    assert(!select(p));
    return p;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    i32 n, q;
    cin >> n >> q;

    vector<node> vs(n);
    map<pair<i32, i32>, node> edge;
    auto es = [&](i32 u, i32 v) -> node & {
        return edge[minmax(u, v)];
    };
    auto lnk = [&](i32 u, i32 v) {
        if (u > v) swap(u, v);
        link(es(u, v), vs[u], vs[v]);
    };
    auto ct = [&](i32 u, i32 v) {
        if (u > v) swap(u, v);
        auto it = edge.find({u, v});
        assert(it != edge.end());
        cut(it->second);
        edge.erase(it);
    };

    for (i32 i = 0; i < n; i++) {
        vs[i].val = 1;
        vs[i].set_vert();
    }

    i64 sum = 0;

    for (i32 qi = 0; qi < q; qi++) {
        i32 op;
        cin >> op;
        if (op == 1) {
            i32 u, v, w;
            cin >> u >> v >> w;
            u = (u - 1 + sum) % n;
            v = (v - 1 + sum) % n;
            es(u, v).val = w;
            lnk(u, v);
        } else if (op == 2) {
            i32 u, v;
            cin >> u >> v;
            u = (u - 1 + sum) % n;
            v = (v - 1 + sum) % n;
            ct(u, v);
        } else if (op == 3) {
            i32 v;
            cin >> v;
            v = (v - 1 + sum) % n;
            vs[v].evert();
            vs[v].val ^= 1;
            vs[v].pull_all();

            i32 N = vs[v].sub;
            i64 right_sum = 0;
            auto centroid = search(&vs[v], [&](node *p) -> node * {
                p->_push();
                if (p->is_path && !p->is_vert) {
                    assert(p->c[0] && p->c[1]);
                    if (2 * (p->c[1]->sub + right_sum) <= N) {
                        right_sum += p->c[1]->sub;
                        return p->c[0];
                    } else {
                        return p->c[1];
                    }
                } else {
                    right_sum = 0;
                    if (2 * p->max_sub <= N) return 0;
                    if (p->c[0] && 2 * p->c[0]->max_sub > N) return p->c[0];
                    if (p->c[1] && 2 * p->c[1]->max_sub > N) return p->c[1];
                    return p->c[2];
                }
            });

            cout << centroid->ans[0] << "\n";
            sum += centroid->ans[0];
            sum %= n;
        }
    }
}