#235113 (Text) No.650 行列木クエリ

• 問題: No.650 行列木クエリ
• ユーザー: mai
• 提出日時: 2018-02-09 23:49:25
• 言語: Text (cat 8.3)
• 結果: WA
• 実行時間: -
• コード長: 15,549 bytes
• コンパイル時間: 51 ms
• コンパイル使用メモリ: 6,824 KB
• 実行使用メモリ: 6,820 KB
• 最終ジャッジ日時: 2024-10-09 04:35:40
• 合計ジャッジ時間: 728 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
sample	WA * 1
other	WA * 10

ソースコード

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define debug(v) {printf("L%d %s > ",__LINE__,#v);cout<<(v)<<endl;}
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:(v)){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=0ll;(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
template<typename T1, typename T2> ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }
template<typename T> T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> T& minset(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
inline ll rand_range(ll l, ll h) {
    return uniform_int_distribution<ll>(l, h)(randdev);
}

#if defined(_WIN32) || defined(_WIN64)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#elif defined(__GNUC__)
#else
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0; T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc && cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var * sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) { input_integer<int>(var); return *this; }
        inline MaiScanner& operator>>(long long& var) { input_integer<long long>(var); return *this; }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
            return *this;
        }
        template<typename IT> void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
    };
    class MaiPrinter {
    public:
        template<typename T>
        void output_integer(T var) {
            if (var == 0) { putchar_unlocked('0'); return; }
            if (var < 0)
                putchar_unlocked('-'),
                var = -var;
            char stack[32]; int stack_p = 0;
            while (var)
                stack[stack_p++] = '0' + (var % 10),
                var /= 10;
            while (stack_p)
                putchar_unlocked(stack[--stack_p]);
        }
        inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; }
        inline MaiPrinter& operator<<(int var) { output_integer<int>(var); return *this; }
        inline MaiPrinter& operator<<(long long var) { output_integer<long long>(var); return *this; }
        inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }
        inline MaiPrinter& operator<<(const string& str) {
            const char* p = str.c_str();
            const char* l = p + str.size();
            while (p < l) putchar_unlocked(*p++);
            return *this;
        }
        template<typename IT> void join(IT begin, IT end, char sep = '\n') { for (auto it = begin; it != end; ++it) *this << *it << sep; }
    };
}
MaiScanner scanner;
MaiPrinter printer;




class Graph {
public:
    size_t n;
    vector<vector<int>> vertex_to;

    Graph(size_t n = 1) :n(n), vertex_to(n) {}

    void connect(int from, int to) {
        vertex_to[(size_t)from].emplace_back(to);
        vertex_to[(size_t)to].emplace_back(from);
    }
    void resize(size_t _n) {
        n = _n;
        vertex_to.resize(_n);
    }
};



class llmod {
private:
    ll val_;
    inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; }
public:
    static const ll MOD = MD; // <= 

    llmod() : val_(0) {}
    llmod(ll num) :val_(cut(num)) {}
    llmod(const llmod& lm) : val_(lm.val_) {}

    inline operator ll() const { return val_; }
    inline ll operator *() const { return val_; }
    inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; }
    inline llmod& operator=(ll v) { val_ = cut(v); return *this; }

    inline llmod& operator+=(ll v) { val_ = cut(val_ + v); return *this; }
    inline llmod& operator+=(const llmod& l) { val_ = cut(val_ + l.val_); return *this; }
    inline llmod& operator-=(ll v) { val_ = cut(val_ - v); return *this; }
    inline llmod& operator-=(const llmod& l) { val_ = cut(val_ - l.val_); return *this; }
    inline llmod& operator*=(ll v) { val_ = cut(val_ * v); return *this; }
    inline llmod& operator*=(const llmod& l) { val_ = cut(val_ * l.val_); return *this; }
    inline llmod& operator++() { val_ = (val_ + 1) % MOD; return *this; }
    inline llmod operator++(int) { llmod t = *this; val_ = (val_ + 1) % MOD; return t; }
};
inline ostream& operator<<(ostream& os, const llmod& l) { os << *l; return os; }

inline llmod operator+(llmod t, const llmod& r) { return t += r; }
inline llmod operator-(llmod t, const llmod& r) { return t -= r; }
inline llmod operator*(llmod t, const llmod& r) { return t *= r; }



// MEMO : 逆元...powm(n,MD-2)
llmod pow(llmod x, ll p) {
    llmod y = 1;
    while (0 < p) {
        if (p % 2)
            y *= x;
        x *= x;
        p /= 2;
    }
    return y;
}

inline llmod& operator/=(llmod& l, const llmod& r) { return l *= pow(r, llmod::MOD - 2); }


template<typename T>
//typedef int T;
class SegmentTreeQ {
    int size_;
    vector<T> data_;
    const function<T(T, T)> func_;
    const T zero_;

public:

    SegmentTreeQ(int n, function<T(T, T)> f, T z) : func_(f), zero_(z) {
        size_ = 8;
        while (size_ < n) size_ <<= 1;
        data_.resize(size_ * 2, zero_);
    }

    void fill(T val) {
        std::fill(data_.begin(), data_.end(), val);
    }

    inline T get_val(int index) const {
        return data_[index + size_];
    }

    void set_val(int index, const T e) {
        index += size_;
        data_[index] = e;
        while (1 < index) {
            data_[index >> 1] = func_(data_[index], data_[index ^ 1]); // TODO : この部分の計算順序は正確か？
            index >>= 1;
        }
    }

    inline int get_range(int begin, int end) const {
        T rl = zero_, rr = zero_;
        begin += size_;
        end += size_;
        for (; begin < end; begin >>= 1, end >>= 1) {
            if (begin & 1) rl = func_(data_[begin++], rl);
            if (end & 1) rr = func_(rr, data_[--end]);
        }
        return func_(rl, rr);
    }
};


template<typename T>
// typedef double T;
class Matrix {
public:
    size_t height_, width_;
    valarray<T> data_;
    Matrix(size_t height, size_t width) :height_(height), width_(width), data_(height*width) {}
    Matrix(size_t height, size_t width, const valarray<T>& data) :height_(height), width_(width), data_(data) {}

    inline T& operator()(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T operator() (size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline T& at(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T at(size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h*w); }
    inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h*w, val); }
    inline void fill(T val) { data_ = val; }
    Matrix<T>& setDiag(T val) { for (size_t i = 0, en = min(width_, height_); i < en; ++i)at(i, i) = val; return *this; }

    void print(ostream& os) {
        os << "- - -" << endl; //  << setprecision(3)
        for (size_t y = 0; y < height_; ++y) {
            for (size_t x = 0; x < width_; ++x) {
                os << setw(7) << at(y, x) << ' ';
            }os << endl;
        }
    }
    valarray<valarray<T>> to_valarray() const {
        valarray<valarray<T>> work(height_);
        for (size_t i = 0; i < height_; ++i) {
            auto &v = work[i]; v.resize(height_);
            for (size_t j = 0; j < width_; ++j)
                v[j] = at(i, j);
        } return work;
    }
    // mathematics
    Matrix<T> pow(long long);
    double det() const; T tr();
    Matrix<T>& transpose_self(); Matrix<T> transpose() const;
    struct LU {
        size_t size;
        vector<int> pivot;
        vector<T> elem;
    };
};

// IO
template<typename T> inline ostream& operator << (ostream& os, Matrix<T> mat) { mat.print(os); return os; }

// 掛け算
template<typename T> Matrix<T> multiply(const Matrix<T>& mat1, const Matrix<T>& mat2) {
    assert(mat1.width_ == mat2.height_);
    Matrix<T> result(mat1.height_, mat2.width_);
    for (size_t i = 0; i < mat1.height_; i++) {
        for (size_t j = 0; j < mat2.width_; j++) {
            for (size_t k = 0; k < mat1.width_; k++) {
                result(i, j) += mat1(i, k) * mat2(k, j);
            }
        }
    }
    return result;
}
template<typename T> valarray<T> multiply(const Matrix<T>& mat1, const valarray<T>& vec2) {
    assert(mat1.width_ == vec2.size());
    valarray<T> result(mat1.height_);
    for (size_t i = 0, j; i < mat1.height_; i++) {
        for (j = 0; j < mat1.width_; j++) {
            result[i] += mat1(i, j) * vec2[j];
        }
    }
    return result;
}
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1 = multiply(mat1, mat2); return mat1; }
template<typename T> inline Matrix<T> operator*(Matrix<T>& mat1, Matrix<T>& mat2) { return multiply(mat1, mat2); }


// スカラー
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat, T val) { mat.data_ += val; return mat; }
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat, T val) { mat.data_ *= val; return mat; }
template<typename T> inline Matrix<T>& operator/=(Matrix<T>& mat, T val) { mat.data_ /= val; return mat; }
template<typename T> inline Matrix<T>& operator^=(Matrix<T>& mat, T val) { mat.data_ ^= val; return mat; }

// 行列
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1.data_ += mat2.data_; return mat1; }
template<typename T> inline Matrix<T> operator+(Matrix<T>& mat1, Matrix<T>& mat2) { return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); }


template<typename T> Matrix<T> Matrix<T>::pow(long long p) {
    assert(height_ == width_);
    Matrix<T> a = *this;
    Matrix<T> b(height_, height_); b.setDiag(1);

    while (0 < p) {
        if (p % 2) {
            b *= a;
        }
        a *= a; p /= 2;
    }
    return b;
}


template <typename T>
class SparseTable {
public:
    int size;
    vector<int> log2;
    vector<T> data;
    vector<T> dp;

    SparseTable(int size) :size(size), log2(size + 1), data(size) {
        // for fast calculate log2
        for (int i = 2; i <= size; ++i) {
            log2[i] = log2[i >> 1] + 1;
        }

        dp.resize(size*(log2[size] + 1));
    }

    inline T& operator[](size_t i) { return data[i]; }
    inline T operator[](size_t i)const { return data[i]; }

    void build() {
        int l, i, f, b;
        for (i = 0; i < size; i++) {
            dp[i] = i;
        }
        for (l = 1; (1 << l) <= size; l++) {
            for (i = 0; i + (1 << l) <= size; i++) {
                f = dp[i + size * (l - 1)];
                b = dp[(i + (1 << (l - 1))) + size * (l - 1)];

                dp[i + size * l] = (data[f] <= data[b]) ? f : b; // minimum
            }
        }
    }

    // range [l,r)
    int getminrangeIdx(int l, int r) const {
        int lg = log2[r - l];
        int i1 = dp[l + size * lg];
        int i2 = dp[r - (1 << lg) + size * lg];
        return (data[i1] <= data[i2]) ? i1 : i2; // minimum
    }
};



class LCATable {
    const Graph& graph_; // 構築時に参照するだけ
    vector<int> visited_;
    vector<int> visited_inv_;
    SparseTable<int> depth_;

public:
    LCATable(const Graph& g, int root = 0) :graph_(g), visited_(g.n * 2), visited_inv_(g.n), depth_(g.n * 2) { build(root); }

    int _tour_dfs(int idx, int from = -1, int step = 0, int dep = 0) {
        depth_[step] = dep;
        visited_inv_[idx] = step;
        visited_[step] = idx;

        for (int to : graph_.vertex_to[idx]) {
            if (to == from) continue;
            step = _tour_dfs(to, idx, ++step, dep + 1);
            depth_[step] = dep;
            visited_[step] = idx;
        }
        return ++step;
    }

    void build(int root = 0) {
        _tour_dfs(root);
        depth_.build();
    }

    inline int operator()(int u, int v) {
        return visited_inv_[u] <= visited_inv_[v] ? visited_[depth_.getminrangeIdx(visited_inv_[u], visited_inv_[v])] : operator()(v, u);
    }
};

ll m, n, kei, qu;


Graph graph;

int hl[100010], hlid[100010], hlsize;
int hl_dec(int index = 0, int from = -1) {
    int cnt = 1;
    vector<int> partial_size(graph.vertex_to[index].size());
    int i = 0;
    for (auto to : graph.vertex_to[index]) {
        if (from == to) { ++i; continue; }
        int sz = hl_dec(to, index);
        cnt += sz;
        partial_size[i] = sz;
        ++i;
    }

    if (cnt > 1) {
        auto it = max_element(ALL(partial_size));
        int j = distance(it, partial_size.begin());
        hl[index] = hl[graph.vertex_to[index][j]];
        hlid[index] = hlid[graph.vertex_to[index][j]] + 1;
    }else{
        hl[index] = hlsize++;
    }

    return cnt;
}




int main() {
    scanner >> n;
    m = n - 1;
    graph.resize(n);

    repeat(i, n) {
        int a, b;
        scanner >> a >> b;
        graph.connect(a, b);
    }

    hl_dec();

    vector<SegmentTreeQ<Matrix<llmod>>> hl_segs;

    const Matrix<llmod> one(2, 2, {1,0,0,1});

    repeat(i, hlsize) {
        hl_segs.emplace_back(hl[i], [](Matrix<llmod> x, Matrix<llmod> y) {return x * y; }, one);
    }

    LCATable lca(graph);

    // ==============================

    int qu;
    scanner >> qu;
    repeat(lop, qu) {
        string type;
        scanner >> type;
        if (type[0] == 'x') {
            int i;
            ll a, b, c, d;
            scanner >> i >> a >> b >> c >> d;
            auto mat = Matrix<llmod>(2, 2, { a,b,c,d });
            hl_segs[hl[i]].set_val(hlid[i], mat);
        }
        else {
            int i, j, k;
            scanner >> i >> j;
            k = lca(i, j);

            // 積順序を考慮しないのであれば，
            // [i..root]の積 × [j..root]の積 ÷ [k..root] ÷ [k..root]
            // 行列なので考える必要がある．
            
            // - 逆方向に演算するセグ木メソッドの実装
            // - 逆行列用のセグ木を用意
            // [i..root]の積の計算に用いるHL分解パスを跨いでいく処理が未実装


        }
    }

    return 0;
}