verify/yuki-650.test.cpp

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• Last update: 2023-09-23 21:29:16+09:00
• Problem: https://yukicoder.me/problems/no/650

Depends on

• library/graph/tree/HLD.cpp
• library/math/Matrix.cpp
• library/mod/modint.cpp
• Segment Tree (library/structure/segtree/SegmentTree.cpp)
• library/template/template.cpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/650"
#include "library/template/template.cpp"
// library
#include "library/graph/tree/HLD.cpp"
#include "library/math/Matrix.cpp"
#include "library/mod/modint.cpp"
#include "library/structure/segtree/SegmentTree.cpp"
using mint = modint<1000000007>;
using mmat = Matrix<mint>;
int main() {
    int n, q;
    cin >> n;
    HLD hld(n);
    vector<Pi> etov(n - 1);
    rep(i, n - 1) {
        int a, b;
        cin >> a >> b;
        hld.add_edge(a, b);
        etov[i] = mp(a, b);
    }
    cin >> q;
    SegmentTree<mmat> seg(
        n, [&](mmat a, mmat b) { return a * b; }, mmat::I(2));
    hld.build();
    rep(_, q) {
        char t;
        cin >> t;
        if (t == 'g') {
            int u, v;
            cin >> u >> v;
            mmat res = hld.query_edge(
                u, v, mmat::I(2),
                [&](int a, int b) { return seg.query(a, b + 1); },
                [&](mmat a, mmat b) { return a * b; });
            cout << res[0][0] << " " << res[0][1] << " " << res[1][0] << " "
                 << res[1][1] << "\n";
        } else {
            int i, a, b, c, d;
            cin >> i >> a >> b >> c >> d;
            int u = etov[i].first, v = etov[i].second;
            hld.update_edge(u, v, [&](int l, int r) {
                return seg.update(l, mmat({{a, b}, {c, d}}));
            });
        }
    }
}

#line 1 "verify/yuki-650.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/650"
#line 2 "library/template/template.cpp"
/* #region header */
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (auto &e : v)
        cout << e << " ";
    cout << endl;
    return os;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &a)
{
    for (auto &i : a)
        scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n)
{
    T ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod)
{
    ll ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}
ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; }
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a)
{
    int n = a.size();
    vector<int> id(n);
    iota(all(id), 0);
    sort(all(id), [&](int i, int j)
         { return a[i] < a[j]; });
    return id;
}
long long xor64(long long range) {
    static uint64_t x = 88172645463325252ULL;
    x ^= x << 13;
    x ^= x >> 7;
    return (x ^= x << 17) % range;
}
struct Timer
{
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap()
    {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
template <typename T = int>
struct Edge
{
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph
{
    vector<vector<Edge<T>>> g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    void add_directed_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es++);
    }

    void add_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }

    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false)
    {
        for (int i = 0; i < M; i++)
        {
            int a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted)
                cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }
};

/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 3 "verify/yuki-650.test.cpp"
// library
#line 1 "library/graph/tree/HLD.cpp"
struct HLD {
    vector<vector<int>> G;
    vector<int> parent, depth, sub_size, v_id, id_to_v, head;
    HLD(int n)
        : G(n),
          v_id(n, -1),
          head(n),
          sub_size(n, 1),
          parent(n, -1),
          depth(n, 0),
          id_to_v(n) {}

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

    void build(int root = 0) {
        int pos = 0;
        dfs_size(root);
        head[root] = root;
        dfs_hld(root, pos);
    }

    void dfs_size(int v) {
        for (int& nv : G[v]) {
            if (nv == parent[v]) {
                nv = G[v].back();
                G[v].pop_back();
            }
        }
        for (int& nv : G[v]) {
            parent[nv] = v;
            depth[nv] = depth[v] + 1;
            dfs_size(nv);
            sub_size[v] += sub_size[nv];
            if (sub_size[nv] > sub_size[G[v][0]]) swap(nv, G[v][0]);
        }
    }

    void dfs_hld(int v, int& pos) {
        v_id[v] = pos;
        id_to_v[pos++] = v;
        for (int nv : G[v]) {
            head[nv] = (nv == G[v][0] ? head[v] : nv);
            dfs_hld(nv, pos);
        }
    }

    int lca(int u, int v) {
        while (1) {
            if (v_id[u] > v_id[v]) swap(u, v);
            if (head[u] == head[v]) return u;
            v = parent[head[v]];
        }
    }

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

    // update vertexes in [u, v] with f
    template <typename F>
    void update(int u, int v, const F& f) {
        while (1) {
            if (v_id[u] > v_id[v]) swap(u, v);
            f(max(v_id[head[v]], v_id[u]), v_id[v]);
            if (head[u] != head[v])
                v = parent[head[v]];
            else
                break;
        }
    }

    // get res for [u, v] with query q and merge each value with f
    // root->leaf
    template <typename T, typename Q, typename F>
    T query(int u, int v, T id, const Q& q, const F& f) {
        T l = id, r = id;
        while (1) {
            if (v_id[u] > v_id[v]) {
                swap(u, v);
                swap(l, r);
            }
            l = f(q(max(v_id[head[v]], v_id[u]), v_id[v]), l);
            if (head[u] != head[v])
                v = parent[head[v]];
            else
                break;
        }
        return f(r, l);
    }

    // update edges between u, v inclusive with func f
    template <typename F>
    void update_edge(int u, int v, const F& f) {
        while (1) {
            if (v_id[u] > v_id[v]) swap(u, v);
            if (head[u] != head[v]) {
                f(v_id[head[v]], v_id[v]);
                v = parent[head[v]];
            } else {
                if (u != v) f(v_id[u] + 1, v_id[v]);
                break;
            }
        }
    }

    // query for edges between u, v inclusive with query q and merge func f
    // root->leaf
    template <typename T, typename Q, typename F>
    T query_edge(int u, int v, T id, const Q& q, const F& f) {
        T l = id, r = id;
        while (1) {
            if (v_id[u] > v_id[v]) {
                swap(u, v);
                swap(l, r);
            }
            if (head[u] != head[v]) {
                l = f(q(v_id[head[v]], v_id[v]), l);
                v = parent[head[v]];
            } else {
                if (u != v) l = f(q(v_id[u] + 1, v_id[v]), l);
                break;
            }
        }
        return f(r, l);
    }
};
#line 1 "library/math/Matrix.cpp"
template <class T>
struct Matrix {
    vector<vector<T>> A;

    Matrix() {}

    Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}

    Matrix(size_t n) : A(n, vector<T>(n, 0)){};

    Matrix(vector<vector<T>> a) { A = a; }

    size_t height() const { return (A.size()); }

    size_t width() const { return (A[0].size()); }

    inline const vector<T>& operator[](int k) const { return (A.at(k)); }

    inline vector<T>& operator[](int k) { return (A.at(k)); }

    static Matrix I(size_t n) {
        Matrix mat(n);
        for (int i = 0; i < n; i++) mat[i][i] = 1;
        return (mat);
    }

    Matrix& operator+=(const Matrix& B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
        return (*this);
    }

    Matrix& operator-=(const Matrix& B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
        return (*this);
    }

    Matrix& operator*=(const Matrix& B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        vector<vector<T>> C(n, vector<T>(m, 0));
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                for (int k = 0; k < p; k++)
                    C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        A.swap(C);
        return (*this);
    }

    Matrix& operator^=(long long k) {
        Matrix B = Matrix::I(height());
        while (k > 0) {
            if (k & 1) B *= *this;
            *this *= *this;
            k >>= 1LL;
        }
        A.swap(B.A);
        return (*this);
    }

    Matrix operator+(const Matrix& B) const { return (Matrix(*this) += B); }

    Matrix operator-(const Matrix& B) const { return (Matrix(*this) -= B); }

    Matrix operator*(const Matrix& B) const { return (Matrix(*this) *= B); }

    Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }

    Matrix pow(long long n) {
        Matrix ret = I(height());
        Matrix x = Matrix(*this);
        while (n > 0) {
            if (n & 1) (ret *= x);
            (x *= x);
            n >>= 1;
        }
        return ret;
    }

    friend ostream& operator<<(ostream& os, Matrix& p) {
        size_t n = p.height(), m = p.width();
        for (int i = 0; i < n; i++) {
            os << "[";
            for (int j = 0; j < m; j++) {
                os << p[i][j] << (j + 1 == m ? "]\n" : ",");
            }
        }
        return (os);
    }

    T determinant() {
        Matrix B(*this);
        assert(width() == height());
        T ret = 1;
        for (int i = 0; i < width(); i++) {
            int idx = -1;
            for (int j = i; j < width(); j++) {
                if (B[j][i] != 0) idx = j;
            }
            if (idx == -1) return (0);
            if (i != idx) {
                ret *= -1;
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T vv = B[i][i];
            for (int j = 0; j < width(); j++) {
                B[i][j] /= vv;
            }
            for (int j = i + 1; j < width(); j++) {
                T a = B[j][i];
                for (int k = 0; k < width(); k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return (ret);
    }

    Matrix transpose() {
        Matrix ret(width(), height());
        rep(i, height()) { rep(j, width()) ret[j][i] = A[i][j]; }
        return ret;
    }
};
#line 2 "library/mod/modint.cpp"
template <int Mod>
struct modint
{
    int x;

    modint() : x(0) {}

    modint(long long y) : x(y >= 0 ? y % Mod : (Mod - (-y) % Mod) % Mod) {}

    modint &operator+=(const modint &p)
    {
        if ((x += p.x) >= Mod)
            x -= Mod;
        return *this;
    }

    modint &operator-=(const modint &p)
    {
        if ((x += Mod - p.x) >= Mod)
            x -= Mod;
        return *this;
    }

    modint &operator*=(const modint &p)
    {
        x = (int)(1LL * x * p.x % Mod);
        return *this;
    }

    modint &operator/=(const modint &p)
    {
        *this *= p.inverse();
        return *this;
    }

    modint operator-() const { return modint(-x); }

    modint operator+(const modint &p) const { return modint(*this) += p; }

    modint operator-(const modint &p) const { return modint(*this) -= p; }

    modint operator*(const modint &p) const { return modint(*this) *= p; }

    modint operator/(const modint &p) const { return modint(*this) /= p; }

    bool operator==(const modint &p) const { return x == p.x; }

    bool operator!=(const modint &p) const { return x != p.x; }

    modint inverse() const
    {
        int a = x, b = Mod, u = 1, v = 0, t;
        while (b > 0)
        {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return modint(u);
    }

    modint pow(int64_t n) const
    {
        modint ret(1), mul(x);
        while (n > 0)
        {
            if (n & 1)
                ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const modint &p)
    {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, modint &a)
    {
        long long t;
        is >> t;
        a = modint<Mod>(t);
        return (is);
    }

    static int get_mod() { return Mod; }

    constexpr int get() const { return x; }
};
#line 1 "library/structure/segtree/SegmentTree.cpp"
/**
 * @brief Segment Tree
 * @docs docs/segmenttree.md
 */
template <typename Monoid>
struct SegmentTree {
    using F = function<Monoid(Monoid, Monoid)>;

    int sz;
    vector<Monoid> seg;

    const F f;
    const Monoid M1;

    SegmentTree(int n, const F f, const Monoid& M1) : f(f), M1(M1) {
        sz = 1;
        while (sz < n) sz <<= 1;
        seg.assign(2 * sz, M1);
    }

    void set(int k, const Monoid& x) { seg[k + sz] = x; }

    void build() {
        for (int k = sz - 1; k > 0; k--) {
            seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
        }
    }

    void update(int k, const Monoid& x) {
        k += sz;
        seg[k] = x;
        while (k >>= 1) {
            seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
        }
    }

    Monoid query(int a, int b) {
        Monoid L = M1, R = M1;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1) L = f(L, seg[a++]);
            if (b & 1) R = f(seg[--b], R);
        }
        return f(L, R);
    }

    Monoid operator[](const int& k) const { return seg[k + sz]; }

    template <typename C>
    int find_subtree(int a, const C& check, Monoid& M, bool type) {
        while (a < sz) {
            Monoid nxt =
                type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
            if (check(nxt))
                a = 2 * a + type;
            else
                M = nxt, a = 2 * a + 1 - type;
        }
        return a - sz;
    }

    // check(seg.query(b, i))を満たす最小のb<=iを返す.なければ-1
    template <typename C>
    int find_first(int a, const C& check) {
        Monoid L = M1;
        if (a <= 0) {
            if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
            return -1;
        }
        int b = sz;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1) {
                Monoid nxt = f(L, seg[a]);
                if (check(nxt)) return find_subtree(a, check, L, false);
                L = nxt;
                ++a;
            }
        }
        return -1;
    }

    // check(seg.query(i, b))を満たす最小のi<bを返す.なければ-1
    template <typename C>
    int find_last(int b, const C& check) {
        Monoid R = M1;
        if (b >= sz) {
            if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
            return -1;
        }
        int a = sz;
        for (b += sz; a < b; a >>= 1, b >>= 1) {
            if (b & 1) {
                Monoid nxt = f(seg[--b], R);
                if (check(nxt)) return find_subtree(b, check, R, true);
                R = nxt;
            }
        }
        return -1;
    }
};
#line 8 "verify/yuki-650.test.cpp"
using mint = modint<1000000007>;
using mmat = Matrix<mint>;
int main() {
    int n, q;
    cin >> n;
    HLD hld(n);
    vector<Pi> etov(n - 1);
    rep(i, n - 1) {
        int a, b;
        cin >> a >> b;
        hld.add_edge(a, b);
        etov[i] = mp(a, b);
    }
    cin >> q;
    SegmentTree<mmat> seg(
        n, [&](mmat a, mmat b) { return a * b; }, mmat::I(2));
    hld.build();
    rep(_, q) {
        char t;
        cin >> t;
        if (t == 'g') {
            int u, v;
            cin >> u >> v;
            mmat res = hld.query_edge(
                u, v, mmat::I(2),
                [&](int a, int b) { return seg.query(a, b + 1); },
                [&](mmat a, mmat b) { return a * b; });
            cout << res[0][0] << " " << res[0][1] << " " << res[1][0] << " "
                 << res[1][1] << "\n";
        } else {
            int i, a, b, c, d;
            cin >> i >> a >> b >> c >> d;
            int u = etov[i].first, v = etov[i].second;
            hld.update_edge(u, v, [&](int l, int r) {
                return seg.update(l, mmat({{a, b}, {c, d}}));
            });
        }
    }
}

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