結果

問題 No.650 行列木クエリ
ユーザー finefine
提出日時 2020-05-12 03:03:13
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 277 ms / 2,000 ms
コード長 10,371 bytes
コンパイル時間 2,883 ms
コンパイル使用メモリ 199,344 KB
実行使用メモリ 60,904 KB
最終ジャッジ日時 2024-07-19 15:44:20
合計ジャッジ時間 4,891 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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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 2 ms
5,248 KB
testcase_01 AC 135 ms
15,744 KB
testcase_02 AC 277 ms
56,024 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 138 ms
15,872 KB
testcase_05 AC 272 ms
55,936 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 143 ms
16,768 KB
testcase_09 AC 268 ms
60,904 KB
testcase_10 AC 2 ms
5,376 KB
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ソースコード

diff # 

#include <bits/stdc++.h>

using namespace std;

using ll = long long;

constexpr char newl = '\n';

// https://noshi91.hatenablog.com/entry/2019/03/31/174006
template <std::uint_fast64_t Modulus>
struct ModInt {
    using u64 = std::uint_fast64_t;

    static constexpr u64 MOD = Modulus;

    u64 val;

    constexpr ModInt(const u64 x = 0) noexcept : val(x % MOD) {}

    constexpr ModInt operator+() const noexcept { return ModInt(*this); }
    constexpr ModInt operator-() const noexcept {
        ModInt res(*this);
        if (res.val != 0) res.val = MOD - res.val;
        return res;
    }

    constexpr bool operator==(const ModInt& rhs) const noexcept { return val == rhs.val; }
    constexpr bool operator!=(const ModInt& rhs) const noexcept { return val != rhs.val; }

    // prefix increment/decrement
    constexpr ModInt& operator++() noexcept { return *this += ModInt(1); }
    constexpr ModInt& operator--() noexcept { return *this -= ModInt(1); }

    // postfix increment/decrement
    constexpr ModInt& operator++(int) noexcept {
        ModInt tmp(*this);
        ++*this;
        return tmp;
    }
    constexpr ModInt& operator--(int) noexcept {
        ModInt tmp(*this);
        --*this;
        return tmp;
    }

    constexpr ModInt operator+(const ModInt& rhs) const noexcept {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt& rhs) const noexcept {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt& rhs) const noexcept {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt& rhs) const noexcept {
        return ModInt(*this) /= rhs;
    }

    constexpr ModInt& operator+=(const ModInt& rhs) noexcept {
        val += rhs.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr ModInt& operator-=(const ModInt& rhs) noexcept {
        if (val < rhs.val) val += MOD;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt& operator*=(const ModInt& rhs) noexcept {
        val = val * rhs.val % MOD;
        return *this;
    }

    // prime Modulus only
    constexpr ModInt& operator/=(const ModInt& rhs) noexcept {
        return *this *= rhs.inv();
    }

    // prime Modulus only
    constexpr ModInt inv() const noexcept {
        return pow(*this, MOD - 2);
    }
};

template<std::uint_fast64_t Modulus>
constexpr ModInt<Modulus> pow(ModInt<Modulus> x, std::uint_fast64_t n) {
    ModInt<Modulus> res(1);
    while (n) {
        if (n & 1) res *= x;
        x *= x;
        n >>= 1;
    }
    return res;
}

template<std::uint_fast64_t Modulus>
istream& operator>>(istream& is, ModInt<Modulus>& x) {
    std::uint_fast64_t val;
    is >> val;
    x = ModInt<Modulus>(val);
    return is;
}

template<std::uint_fast64_t Modulus>
ostream& operator<<(ostream& os, const ModInt<Modulus>& x) {
    return os << x.val;
}

using mint = ModInt<1000000007>;

// https://qiita.com/ageprocpp/items/8dfe768218da83314989
// http://codeforces.com/blog/entry/53170
// https://github.com/ningenMe/compro-library/blob/master/lib/graph/Tree.cpp#L220
// https://beet-aizu.github.io/library/library/tree/heavylightdecomposition.cpp.html
// https://ei1333.github.io/luzhiled/snippets/tree/heavy-light-decomposition.html
class HLD {
public:
    using Graph = vector< vector<int> >;
    using Segment = pair<int, int>;

private:
    void dfs_size(int cur, int par) {
        // if g[cur][0] == par, always sub_size[nex] < sub_size[par]
        // and this will be broken...
        if (!g[cur].empty() && g[cur][0] == par) swap(g[cur][0], g[cur].back());

        for (int& nex : g[cur]) {
            if (nex == par) continue;
            parent[nex] = cur;

            dfs_size(nex, cur);
            sub_size[cur] += sub_size[nex];

            if (sub_size[nex] > sub_size[g[cur][0]]) {
                swap(nex, g[cur][0]);
            }
        }
    }

    // head: HLD
    // in, out: Euler Tour
    void dfs_hld(int cur, int par, int& times) {
        in[cur] = times++;
        for (int nex : g[cur]) {
            if (nex == par) continue;

            // if nex == g[cur][0]: heavy edge
            // else: light edge
            head[nex] = (nex == g[cur][0] ? head[cur] : nex);

            dfs_hld(nex, cur, times);
        }
        out[cur] = times;
    }

    // convert node/edge path to segments
    // segment: [l, r)
    // is_edge_path ? edge path : node path
    vector<Segment> to_segments(int u, int v, bool is_edge_path) {
        vector<Segment> segments;
        while (true) {
            if (in[u] > in[v]) swap(u, v);
            if (head[u] == head[v]) {
                if (u != v || !is_edge_path) {
                    segments.emplace_back(in[u] + is_edge_path, in[v] + 1);
                }
                break;
            }
            segments.emplace_back(in[head[v]], in[v] + 1);
            v = parent[head[v]];
        }
        return segments;
    }

public:

    Graph g;
    vector<int> sub_size, parent, in, out, head;

    HLD(const Graph& tree, const int root = 0)
    : g(tree), sub_size(tree.size(), 1), parent(tree.size(), -1),
      in(tree.size()), out(tree.size()), head(tree.size(), root) {
        dfs_size(root, -1);
        int times = 0;
        dfs_hld(root, -1, times);
    }

    int lca(int u, int v) {
        while (true) {
            if (in[u] > in[v]) swap(u, v);
            if (head[u] == head[v]) return u;
            v = parent[head[v]];
        }
    }

    inline vector<Segment> node_path_to_segments(int u, int v) {
        return to_segments(u, v, false);
    }

    // you have to convert edge cost to node cost
    // see: https://www.hamayanhamayan.com/entry/2017/04/10/172636
    inline vector<Segment> edge_path_to_segments(int u, int v) {
        return to_segments(u, v, true);
    }

    Segment subtree_to_segment(int v) {
        return {in[v], out[v]};
    }
};

using vec = vector<mint>;
using mat = vector<vec>;

mat mul(const mat& A, const mat& B) {
    mat C(A.size(), vec(B[0].size(), 0));
    for (int i = 0; i < A.size(); i++) {
        for (int k = 0; k < B.size(); k++) {
            for (int j = 0; j < B[0].size(); j++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    return C;
}

mat pow(mat A, ll n) {
    mat B(A.size(), vec(A.size(), 0));
    for (int i = 0; i < A.size(); i++) {
        B[i][i] = 1;
    }
    while (n > 0) {
        if (n & 1) B = mul(B, A);
        A = mul(A, A);
        n >>= 1;
    }
    return B;
}

template <class Monoid>
struct SegmentTree {
    using T = typename Monoid::T;

    int n;
    vector<T> data;

    SegmentTree() {}

    SegmentTree(int size, T initial_value = Monoid::unit()) {
        n = 1;
        while (n < size) n <<= 1;
        data.assign(2 * n - 1, initial_value);

        if (initial_value != Monoid::unit()) {
            for (int i = n - 2; i >= 0; i--) data[i] = Monoid::merge(data[i * 2 + 1], data[i * 2 + 2]);
        }
    }

    SegmentTree(const vector<T>& v) {
        int size = v.size();
        n = 1;
        while (n < size) n <<= 1;
        data.assign(2 * n - 1, Monoid::unit());

        for (int i = 0; i < size; i++) data[i + n - 1] = v[i];
        for (int i = n - 2; i >= 0; i--) data[i] = Monoid::merge(data[i * 2 + 1], data[i * 2 + 2]);
    }

    T getLeaf(int k) {
        return data[k + n - 1];
    }

    void update(int k, T x) {
        k += n - 1; //葉の節点
        Monoid::update(data[k], x);
        while (k > 0) {
            k = (k - 1) / 2;
            data[k] = Monoid::merge(data[k * 2 + 1], data[k * 2 + 2]);
        }
    }

    //区間[a, b)に対するクエリに答える
    //k:節点番号, [l, r):節点に対応する区間
    T query(int a, int b, int k, int l, int r) {
        //[a, b)と[l, r)が交差しない場合
        if (r <= a || b <= l) return Monoid::unit();
        //[a, b)が[l, r)を含む場合、節点の値
        if (a <= l && r <= b) return data[k];
        else {
            //二つの子をマージ
            T vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
            T vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
            return Monoid::merge(vl, vr);
        }
    }

    //外から呼ぶ用
    T query(int a, int b) {
        return query(a, b, 0, 0, n);
    }

    //非再帰版: バグってるかもしれないので定数倍高速化する時以外使わないで
    //区間[a, b)に対するクエリに答える
    T query_fast(int a, int b) {
        T vl = Monoid::unit(), vr = Monoid::unit();
        for (int l = a + n, r = b + n; l != r; l >>= 1, r >>= 1) {
            if (l & 1) vl = Monoid::merge(vl, data[l++ - 1]);
            if (r & 1) vr = Monoid::merge(data[--r - 1], vr);
        }
        return Monoid::merge(vl, vr);
    }
};

template <class U = mat>
struct RangeMul {
    using T = U;
    static T merge(T x, T y) { return mul(x, y); }
    static void update(T& target, T x) { target = x; }
    static constexpr T unit() { return T({{1, 0}, {0, 1}}); }
};

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

    int n;
    cin >> n;

    HLD::Graph g(n);
    vector<int> a(n - 1), b(n - 1);
    for (int i = 0; i < n - 1; i++) {
        cin >> a[i] >> b[i];
        g[a[i]].push_back(b[i]);
        g[b[i]].push_back(a[i]);
    }

    HLD hld(g);
    SegmentTree< RangeMul<> > st(n);

    int q;
    cin >> q;

    for (int i = 0; i < q; i++) {
        char command;
        cin >> command;

        if (command == 'x') {
            int j;
            cin >> j;

            mat x(2, vec(2));
            for (int k = 0; k < 2; k++) {
                for (int l = 0; l < 2; l++) {
                    cin >> x[k][l];
                }
            }

            for (auto& seg : hld.edge_path_to_segments(a[j], b[j])) {
                st.update(seg.first, x);
            }
        } else {
            int j, k;
            cin >> j >> k;

            mat ans = RangeMul<>::unit();
            for (auto& seg : hld.edge_path_to_segments(j, k)) {
                ans = mul(st.query_fast(seg.first, seg.second), ans);
            }

            for (int l = 0; l < 2; l++) {
                for (int m = 0; m < 2; m++) {
                    cout << ans[l][m] << " \n"[l == 1 && m == 1];
                }
            }
        }
    }

    return 0;
}
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