#826751 (C++17) No.2163 LCA Sum Query

提出ソース

結果

問題	No.2163 LCA Sum Query
ユーザー	to-omer
提出日時	2022-12-18 22:01:46
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	736 ms / 6,000 ms
コード長	10,071 bytes
コンパイル時間	1,489 ms
コンパイル使用メモリ	98,776 KB
実行使用メモリ	18,920 KB
最終ジャッジ日時	2023-08-11 09:12:21
合計ジャッジ時間	21,051 ms
ジャッジサーバーID （参考情報）	judge12 / judge15

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 4,380 KB
testcase_01	AC	1 ms 4,380 KB
testcase_02	AC	3 ms 4,380 KB
testcase_03	AC	2 ms 4,384 KB
testcase_04	AC	3 ms 4,384 KB
testcase_05	AC	3 ms 4,384 KB
testcase_06	AC	2 ms 4,384 KB
testcase_07	AC	2 ms 4,384 KB
testcase_08	AC	2 ms 4,380 KB
testcase_09	AC	3 ms 4,384 KB
testcase_10	AC	3 ms 4,384 KB
testcase_11	AC	2 ms 4,380 KB
testcase_12	AC	314 ms 4,972 KB
testcase_13	AC	445 ms 14,916 KB
testcase_14	AC	333 ms 16,816 KB
testcase_15	AC	157 ms 4,380 KB
testcase_16	AC	274 ms 15,184 KB
testcase_17	AC	235 ms 8,648 KB
testcase_18	AC	183 ms 4,600 KB
testcase_19	AC	141 ms 4,384 KB
testcase_20	AC	31 ms 9,440 KB
testcase_21	AC	126 ms 8,804 KB
testcase_22	AC	417 ms 17,384 KB
testcase_23	AC	614 ms 17,432 KB
testcase_24	AC	415 ms 17,328 KB
testcase_25	AC	606 ms 17,320 KB
testcase_26	AC	436 ms 17,584 KB
testcase_27	AC	656 ms 17,472 KB
testcase_28	AC	433 ms 17,528 KB
testcase_29	AC	650 ms 17,480 KB
testcase_30	AC	391 ms 18,512 KB
testcase_31	AC	724 ms 18,648 KB
testcase_32	AC	399 ms 17,960 KB
testcase_33	AC	736 ms 18,432 KB
testcase_34	AC	128 ms 18,900 KB
testcase_35	AC	156 ms 18,920 KB
testcase_36	AC	132 ms 18,884 KB
testcase_37	AC	158 ms 18,832 KB
testcase_38	AC	395 ms 18,296 KB
testcase_39	AC	636 ms 18,236 KB
testcase_40	AC	390 ms 18,056 KB
testcase_41	AC	646 ms 18,312 KB

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ソースコード

raw source code

#include <algorithm>
#include <array>
#include <cassert>
#include <iostream>
#include <set>
#include <vector>
using ll = long long;
using namespace std;
#define rep(i, n) for (int i = 0, _rep_ub = (n); i < _rep_ub; i++)
#define fastio                                                                 \
    cin.tie(0);                                                                \
    ios::sync_with_stdio(0);

// BEGIN: [structure/lct/link-cut-tree-subtree]
// https://ei1333.github.io/library/structure/lct/link-cut-tree-subtree.hpp
template <typename SUM, typename KEY> struct LinkCutTreeSubtree {

    struct Node {
        Node *l, *r, *p;

        KEY key;
        SUM sum;

        bool rev;
        int sz;

        bool is_root() const { return !p || (p->l != this && p->r != this); }

        Node(const KEY &key, const SUM &sum)
            : l(nullptr), r(nullptr), p(nullptr), key(key), sum(sum),
              rev(false), sz(1) {}
    };

    const SUM ident;

    LinkCutTreeSubtree(const SUM &ident) : ident(ident) {}

    Node *make_node(const KEY &key) {
        auto ret = new Node(key, ident);
        update(ret);
        return ret;
    }

    Node *set_key(Node *t, const KEY &key) {
        expose(t);
        t->key = key;
        update(t);
        return t;
    }

    void toggle(Node *t) {
        swap(t->l, t->r);
        t->sum.toggle();
        t->rev ^= true;
    }

    void push(Node *t) {
        if (t->rev) {
            if (t->l) toggle(t->l);
            if (t->r) toggle(t->r);
            t->rev = false;
        }
    }

    void update(Node *t) {
        t->sz = 1;
        if (t->l) t->sz += t->l->sz;
        if (t->r) t->sz += t->r->sz;
        t->sum.merge(t->key, t->l ? t->l->sum : ident,
                     t->r ? t->r->sum : ident);
    }

    void rotr(Node *t) {
        auto *x = t->p, *y = x->p;
        if ((x->l = t->r)) t->r->p = x;
        t->r = x, x->p = t;
        update(x), update(t);
        if ((t->p = y)) {
            if (y->l == x) y->l = t;
            if (y->r == x) y->r = t;
            update(y);
        }
    }

    void rotl(Node *t) {
        auto *x = t->p, *y = x->p;
        if ((x->r = t->l)) t->l->p = x;
        t->l = x, x->p = t;
        update(x), update(t);
        if ((t->p = y)) {
            if (y->l == x) y->l = t;
            if (y->r == x) y->r = t;
            update(y);
        }
    }

    void splay(Node *t) {
        push(t);
        while (!t->is_root()) {
            auto *q = t->p;
            if (q->is_root()) {
                push(q), push(t);
                if (q->l == t)
                    rotr(t);
                else
                    rotl(t);
            } else {
                auto *r = q->p;
                push(r), push(q), push(t);
                if (r->l == q) {
                    if (q->l == t)
                        rotr(q), rotr(t);
                    else
                        rotl(t), rotr(t);
                } else {
                    if (q->r == t)
                        rotl(q), rotl(t);
                    else
                        rotr(t), rotl(t);
                }
            }
        }
    }

    Node *expose(Node *t) {
        Node *rp = nullptr;
        for (auto *cur = t; cur; cur = cur->p) {
            splay(cur);
            if (cur->r) cur->sum.add(cur->r->sum);
            cur->r = rp;
            if (cur->r) cur->sum.erase(cur->r->sum);
            update(cur);
            rp = cur;
        }
        splay(t);
        return rp;
    }

    void link(Node *child, Node *parent) {
        expose(child);
        expose(parent);
        child->p = parent;
        parent->r = child;
        update(parent);
    }

    Node *cut(Node *child) {
        expose(child);
        auto *parent = child->l;
        child->l = nullptr;
        parent->p = nullptr;
        update(child);
        return parent;
    }

    void evert(Node *t) {
        expose(t);
        toggle(t);
        push(t);
    }

    Node *lca(Node *u, Node *v) {
        if (get_root(u) != get_root(v)) return nullptr;
        expose(u);
        return expose(v);
    }

    Node *get_kth(Node *x, int k) {
        expose(x);
        while (x) {
            push(x);
            if (x->r && x->r->sz > k) {
                x = x->r;
            } else {
                if (x->r) k -= x->r->sz;
                if (k == 0) return x;
                k -= 1;
                x = x->l;
            }
        }
        return nullptr;
    }

    Node *get_root(Node *x) {
        expose(x);
        while (x->l) {
            push(x);
            x = x->l;
        }
        return x;
    }

    SUM &query(Node *t) {
        expose(t);
        return t->sum;
    }
};
// END: [structure/lct/link-cut-tree-subtree]

// BEGIN: [tree/levelancestor]
// (https://beet-aizu.github.io/library/tree/levelancestor.cpp)
struct LevelAncestor {
    vector<vector<int>> G, par, lad;
    vector<int> dep, nxt, len, pth, ord, hs;
    LevelAncestor(int n)
        : G(n), dep(n), nxt(n, -1), len(n), pth(n), ord(n), hs(n + 1, 0) {
        int h = 1;
        while ((1 << h) <= n) h++;
        par.assign(h, vector<int>(n, -1));
        for (int i = 2; i <= n; i++) hs[i] = hs[i >> 1] + 1;
    }

    void add_edge(int u, int v) {
        G[u].emplace_back(v);
        G[v].emplace_back(u);
    }

    void dfs(int v, int p, int d, int f) {
        if (nxt[v] < 0) {
            par[0][nxt[v] = v] = p;
            len[v] = dep[v] = d;
            for (int u : G[v]) {
                if (u == p) continue;
                dfs(u, v, d + 1, 0);
                if (len[v] < len[u]) nxt[v] = u, len[v] = len[u];
            }
        }
        if (!f) return;
        pth[v] = lad.size();
        lad.emplace_back();
        for (int k = v;; k = nxt[k]) {
            lad.back().emplace_back(k);
            pth[k] = pth[v];
            if (k == nxt[k]) break;
        }
        for (;; p = v, v = nxt[v]) {
            for (int u : G[v])
                if (u != p and u != nxt[v]) dfs(u, v, d + 1, 1);
            if (v == nxt[v]) break;
        }
    }

    void build(int r = 0) {
        int n = G.size();
        dfs(r, -1, 0, 1);
        for (int k = 0; k + 1 < (int)par.size(); k++) {
            for (int v = 0; v < n; v++) {
                if (par[k][v] < 0)
                    par[k + 1][v] = -1;
                else
                    par[k + 1][v] = par[k][par[k][v]];
            }
        }
        for (int i = 0; i < (int)lad.size(); i++) {
            int v = lad[i][0], p = par[0][v];
            if (~p) {
                int k = pth[p], l = min(ord[p] + 1, (int)lad[i].size());
                lad[i].resize(l + lad[i].size());
                for (int j = 0, m = lad[i].size(); j + l < m; j++)
                    lad[i][m - (j + 1)] = lad[i][m - (j + l + 1)];
                for (int j = 0; j < l; j++)
                    lad[i][j] = lad[k][ord[p] - l + j + 1];
            }
            for (int j = 0; j < (int)lad[i].size(); j++)
                if (pth[lad[i][j]] == i) ord[lad[i][j]] = j;
        }
    }

    int lca(int u, int v) {
        int h = par.size();

        if (dep[u] > dep[v]) swap(u, v);
        for (int k = 0; k < h; k++)
            if ((dep[v] - dep[u]) >> k & 1) v = par[k][v];

        if (u == v) return u;
        for (int k = h - 1; k >= 0; k--) {
            if (par[k][u] == par[k][v]) continue;
            u = par[k][u];
            v = par[k][v];
        }
        return par[0][u];
    }

    int distance(int u, int v) { return dep[u] + dep[v] - dep[lca(u, v)] * 2; }

    int up(int v, int d) {
        if (d == 0) return v;
        v = par[hs[d]][v];
        d -= 1 << hs[d];
        return lad[pth[v]][ord[v] - d];
    }

    // from u to v
    int next(int u, int v) {
        if (dep[u] >= dep[v]) return par[0][u];
        int l = up(v, dep[v] - dep[u] - 1);
        return par[0][l] == u ? l : par[0][u];
    }
};
// END: [tree/levelancestor]

struct LcaSum {
    ll psum, csum, cnt, weight;
    ll lsum, lcnt, lcnt2;

    LcaSum()
        : psum(0), csum(0), cnt(0), weight(0), lsum(0), lcnt(0), lcnt2(0) {}

    void toggle() { swap(psum, csum); }

    void merge(pair<ll, ll> cost, const LcaSum &parent, const LcaSum &child) {
        auto [c, id] = cost;
        cnt = parent.cnt + child.cnt + (c > 0) + lcnt;
        weight = parent.weight + child.weight + id * lcnt + c;
        ll pcnt = parent.cnt + lcnt;
        ll pcnt2 = parent.cnt * parent.cnt + lcnt2;
        psum = parent.psum + child.psum + lsum;
        ll ccnt = child.cnt + lcnt;
        ll ccnt2 = child.cnt * child.cnt + lcnt2;
        csum = parent.csum + child.csum + lsum;

        psum += c * pcnt + id * (pcnt * pcnt - pcnt2) / 2;
        csum += c * ccnt + id * (ccnt * ccnt - ccnt2) / 2;
        csum += parent.weight * (ccnt + (c > 0));
        psum += child.weight * (pcnt + (c > 0));
    }

    void add(const LcaSum &chsum) {
        lsum += chsum.csum;
        lcnt += chsum.cnt;
        lcnt2 += chsum.cnt * chsum.cnt;
    }

    void erase(const LcaSum &chsum) {
        lsum -= chsum.csum;
        lcnt -= chsum.cnt;
        lcnt2 -= chsum.cnt * chsum.cnt;
    }
} e;

const int MAX = 50050;
using LCT = LinkCutTreeSubtree<LcaSum, pair<ll, ll>>;
LCT::Node *vs[MAX] = {};

int main() {
    fastio;
    int n, q;
    cin >> n >> q;

    LCT lct(e);
    LevelAncestor la(n + 1);

    rep(i, n + 1) vs[i] = lct.make_node({0, i});
    la.add_edge(0, 1);
    rep(_i, n - 1) {
        int a, b;
        cin >> a >> b;
        lct.evert(vs[b]);
        lct.link(vs[b], vs[a]);
        la.add_edge(a, b);
    }
    la.build();

    rep(_i, q) {
        int u, r, v;
        cin >> u >> r >> v;
        lct.set_key(vs[u], {u - vs[u]->key.first, u});
        lct.evert(vs[r]);
        ll p = v != r ? la.next(v, r) : 0;
        if (p) {
            lct.evert(vs[p]);
            lct.cut(vs[v]);
        }
        LcaSum res = lct.query(vs[v]);
        cout << res.csum << '\n';
        if (p) {
            lct.evert(vs[v]);
            lct.link(vs[v], vs[p]);
        }
    }

    return 0;
}

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結果

テストケース

ソースコード