test/yosupo_dynamic_tree_vertex_set_path_composite.test.cpp

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• Last update: 2026-03-22 13:47:31+09:00
• Problem: https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite

Depends on

• Link-Cut Tree (tree/link_cut_tree.cpp)
• 高速入出力(Fast IO) (util/fastio.cpp)
• modint(固定MOD) (util/modint.cpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite"
#include <bits/stdc++.h>

static const int MOD = 998244353;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

#include "../util/fastio.cpp"
#include "../util/modint.cpp"
#include "../tree/link_cut_tree.cpp"

struct Monoid {
    using T = array<mint, 2>;
    static T f(T a, T b) { return {a[0] * b[0], a[1] * b[0] + b[1]}; }
    static T e() { return {1, 0}; }
};

int main() {
    Scanner in;
    Printer out;
    int n, q;
    in.read(n, q);
    LinkCutTree<Monoid> lct(n);
    for (int i = 0; i < n; ++i) {
        int a, b;
        in.read(a, b);
        lct.set(i, {a, b});
    }
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        in.read(u, v);
        lct.link(u, v);
    }
    for (int i = 0; i < q; ++i) {
        int t;
        in.read(t);
        if (t == 0) {
            int u, v, w, x;
            in.read(u, v, w, x);
            lct.cut(u, v);
            lct.link(w, x);
        } else if (t == 1) {
            int p, c, d;
            in.read(p, c, d);
            lct.set(p, {c, d});
        } else {
            int u, v, x;
            in.read(u, v, x);
            auto f = lct.fold(u, v);
            out.println((f[0] * x + f[1]).val);
        }
    }
    return 0;
}

#line 1 "test/yosupo_dynamic_tree_vertex_set_path_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite"
#include <bits/stdc++.h>

static const int MOD = 998244353;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

#line 1 "util/fastio.cpp"
using namespace std;

extern "C" int fileno(FILE *);
extern "C" int isatty(int);

template<class T, class = void>
struct is_fastio_range : false_type {};

template<class T>
struct is_fastio_range<T, void_t<decltype(declval<T &>().begin()), decltype(declval<T &>().end())>> : true_type {};

template<class T, class = void>
struct has_fastio_value : false_type {};

template<class T>
struct has_fastio_value<T, void_t<decltype(declval<const T &>().value())>> : true_type {};

struct FastIoDigitTable {
    char num[40000];

    constexpr FastIoDigitTable() : num() {
        for (int i = 0; i < 10000; ++i) {
            int x = i;
            for (int j = 3; j >= 0; --j) {
                num[i * 4 + j] = char('0' + x % 10);
                x /= 10;
            }
        }
    }
};

struct Scanner {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE + 1];
    int idx, size;
    bool interactive;

    Scanner() : idx(0), size(0), interactive(isatty(fileno(stdin))) {}

    inline void load() {
        int len = size - idx;
        memmove(buf, buf + idx, len);
        if (interactive) {
            if (fgets(buf + len, BUFSIZE + 1 - len, stdin)) size = len + (int)strlen(buf + len);
            else size = len;
        } else {
            size = len + (int)fread(buf + len, 1, BUFSIZE - len, stdin);
        }
        idx = 0;
        buf[size] = 0;
    }

    inline void ensure() {
        if (idx + OFFSET > size) load();
    }

    inline void ensure_interactive() {
        if (idx == size) load();
    }

    inline char skip() {
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            return buf[idx++];
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        return buf[idx++];
    }

    template<class T, typename enable_if<is_integral<T>::value, int>::type = 0>
    void read(T &x) {
        if (interactive) {
            char c = skip();
            bool neg = false;
            if constexpr (is_signed<T>::value) {
                if (c == '-') {
                    neg = true;
                    ensure_interactive();
                    c = buf[idx++];
                }
            }
            x = 0;
            while (c >= '0') {
                x = x * 10 + (c & 15);
                ensure_interactive();
                c = buf[idx++];
            }
            if constexpr (is_signed<T>::value) {
                if (neg) x = -x;
            }
            return;
        }
        char c = skip();
        bool neg = false;
        if constexpr (is_signed<T>::value) {
            if (c == '-') {
                neg = true;
                c = buf[idx++];
            }
        }
        x = 0;
        while (c >= '0') {
            x = x * 10 + (c & 15);
            c = buf[idx++];
        }
        if constexpr (is_signed<T>::value) {
            if (neg) x = -x;
        }
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void read(T &x) {
        long long v;
        read(v);
        x = T(v);
    }

    template<class Head, class Next, class... Tail>
    void read(Head &head, Next &next, Tail &...tail) {
        read(head);
        read(next, tail...);
    }

    template<class T, class U>
    void read(pair<T, U> &p) {
        read(p.first, p.second);
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void read(T &a) {
        for (auto &x : a) read(x);
    }

    void read(char &c) {
        c = skip();
    }

    void read(string &s) {
        s.clear();
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            while (true) {
                int start = idx;
                while (idx < size && buf[idx] > ' ') ++idx;
                s.append(buf + start, idx - start);
                if (idx < size) break;
                load();
                if (size == 0) break;
            }
            if (idx < size) ++idx;
            return;
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        while (true) {
            int start = idx;
            while (idx < size && buf[idx] > ' ') ++idx;
            s.append(buf + start, idx - start);
            if (idx < size) break;
            load();
        }
        if (idx < size) ++idx;
    }
};

struct Printer {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE];
    int idx;
    bool interactive;
    inline static constexpr FastIoDigitTable table{};

    Printer() : idx(0), interactive(isatty(fileno(stdout))) {}
    ~Printer() { flush(); }

    inline void flush() {
        if (idx) {
            fwrite(buf, 1, idx, stdout);
            idx = 0;
        }
    }

    inline void pc(char c) {
        if (idx > BUFSIZE - OFFSET) flush();
        buf[idx++] = c;
        if (interactive && c == '\n') flush();
    }

    inline void print_range(const char *s, size_t n) {
        size_t pos = 0;
        while (pos < n) {
            if (idx == BUFSIZE) flush();
            size_t chunk = min(n - pos, (size_t)(BUFSIZE - idx));
            memcpy(buf + idx, s + pos, chunk);
            idx += (int)chunk;
            pos += chunk;
        }
    }

    void print(const char *s) {
        print_range(s, strlen(s));
    }

    void print(const string &s) {
        print_range(s.data(), s.size());
    }

    void print(char c) {
        pc(c);
    }

    void print(bool b) {
        pc(char('0' + (b ? 1 : 0)));
    }

    template<class T, typename enable_if<is_integral<T>::value && !is_same<T, bool>::value, int>::type = 0>
    void print(T x) {
        if (idx > BUFSIZE - 100) flush();
        using U = typename make_unsigned<T>::type;
        U y;
        if constexpr (is_signed<T>::value) {
            if (x < 0) {
                buf[idx++] = '-';
                y = U(0) - static_cast<U>(x);
            } else {
                y = static_cast<U>(x);
            }
        } else {
            y = x;
        }
        if (y == 0) {
            buf[idx++] = '0';
            return;
        }
        static constexpr int TMP_SIZE = sizeof(U) * 10 / 4;
        char tmp[TMP_SIZE];
        int pos = TMP_SIZE;
        while (y >= 10000) {
            pos -= 4;
            memcpy(tmp + pos, table.num + (y % 10000) * 4, 4);
            y /= 10000;
        }
        if (y >= 1000) {
            memcpy(buf + idx, table.num + (y << 2), 4);
            idx += 4;
        } else if (y >= 100) {
            memcpy(buf + idx, table.num + (y << 2) + 1, 3);
            idx += 3;
        } else if (y >= 10) {
            unsigned q = (unsigned(y) * 205) >> 11;
            buf[idx] = char('0' + q);
            buf[idx + 1] = char('0' + (unsigned(y) - q * 10));
            idx += 2;
        } else {
            buf[idx++] = char('0' + y);
        }
        memcpy(buf + idx, tmp + pos, TMP_SIZE - pos);
        idx += TMP_SIZE - pos;
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void print(const T &x) {
        print(x.value());
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void print(const T &a) {
        bool first = true;
        for (auto &&x : a) {
            if (!first) pc(' ');
            first = false;
            print(x);
        }
    }

    template<class T>
    void println(const T &x) {
        print(x);
        pc('\n');
    }

    template<class Head, class... Tail>
    void println(const Head &head, const Tail &...tail) {
        print(head);
        ((pc(' '), print(tail)), ...);
        pc('\n');
    }

    void println() {
        pc('\n');
    }
};

template<class T>
Scanner &operator>>(Scanner &in, T &x) {
    in.read(x);
    return in;
}

template<class T>
Printer &operator<<(Printer &out, const T &x) {
    out.print(x);
    return out;
}

/**
 * @brief 高速入出力(Fast IO)
 */
#line 1 "util/modint.cpp"



template <uint Mod>
struct modint {
    uint val;
public:
    static modint raw(int v) { modint x; x.val = v; return x; }
    static constexpr uint get_mod() { return Mod; }
    static constexpr uint M() { return Mod; }
    modint() : val(0) {}
    template <class T>
    modint(T v) { ll x = (ll)(v % (ll)(Mod)); if (x < 0) x += Mod; val = uint(x); }
    modint(bool v) { val = ((unsigned int)(v) % Mod); }
    uint &value() noexcept { return val; }
    const uint &value() const noexcept { return val; }
    modint& operator++() { val++; if (val == Mod) val = 0; return *this; }
    modint& operator--() { if (val == 0) val = Mod; val--; return *this; }
    modint operator++(int) { modint result = *this; ++*this; return result; }
    modint operator--(int) { modint result = *this; --*this; return result; }
    modint& operator+=(const modint& b) { val += b.val; if (val >= Mod) val -= Mod; return *this; }
    modint& operator-=(const modint& b) { val -= b.val; if (val >= Mod) val += Mod; return *this; }
    modint& operator*=(const modint& b) { ull z = val; z *= b.val; val = (uint)(z % Mod); return *this; }
    modint& operator/=(const modint& b) { return *this = *this * b.inv(); }
    modint operator+() const { return *this; }
    modint operator-() const { return modint() - *this; }
    modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; }
    modint inv() const { return pow(Mod - 2); }
    friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; }
    friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; }
    friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; }
    friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; }
    friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; }
    friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; }
};
using mint = modint<MOD>;
#define FIRIEXP_LIBRARY_MINT_ALIAS_DEFINED

/**
 * @brief modint(固定MOD)
 */


#line 1 "tree/link_cut_tree.cpp"
template <class M>
struct LinkCutTree {
    using T = typename M::T;

    struct Node {
        int l, r, p, sz;
        bool rev;
        T val, sum, rsum;
        Node() : l(-1), r(-1), p(-1), sz(1), rev(false), val(M::e()), sum(M::e()), rsum(M::e()) {}
    };

    int n;
    vector<Node> nodes;
    vector<int> push_stack;

    explicit LinkCutTree(int n) : n(n), nodes(n), push_stack() {
        push_stack.reserve(64);
    }

    bool is_root(int x) const {
        int p = nodes[x].p;
        return p == -1 || (nodes[p].l != x && nodes[p].r != x);
    }

    void reverse(int x) {
        if (x == -1) return;
        Node &nx = nodes[x];
        swap(nx.l, nx.r);
        swap(nx.sum, nx.rsum);
        nx.rev ^= 1;
    }

    void push(int x) {
        if (x == -1 || !nodes[x].rev) return;
        reverse(nodes[x].l);
        reverse(nodes[x].r);
        nodes[x].rev = false;
    }

    void pull(int x) {
        Node &nx = nodes[x];
        nx.sz = 1;
        nx.sum = nx.val;
        nx.rsum = nx.val;
        if (nx.l != -1) {
            int y = nx.l;
            nx.sz += nodes[y].sz;
            nx.sum = M::f(nodes[y].sum, nx.sum);
            nx.rsum = M::f(nx.rsum, nodes[y].rsum);
        }
        if (nx.r != -1) {
            int y = nx.r;
            nx.sz += nodes[y].sz;
            nx.sum = M::f(nx.sum, nodes[y].sum);
            nx.rsum = M::f(nodes[y].rsum, nx.rsum);
        }
    }

    void rotate(int x) {
        Node &nx = nodes[x];
        int p = nx.p;
        Node &np = nodes[p];
        int g = np.p;
        if (np.l == x) {
            int b = nx.r;
            nx.r = p;
            np.l = b;
            if (b != -1) nodes[b].p = p;
        } else {
            int b = nx.l;
            nx.l = p;
            np.r = b;
            if (b != -1) nodes[b].p = p;
        }
        np.p = x;
        nx.p = g;
        if (g != -1) {
            Node &ng = nodes[g];
            if (ng.l == p) {
                ng.l = x;
            } else if (ng.r == p) {
                ng.r = x;
            }
        }
        pull(p);
        pull(x);
    }

    void splay(int x) {
        push_stack.clear();
        push_stack.emplace_back(x);
        for (int y = x; !is_root(y); y = nodes[y].p) push_stack.emplace_back(nodes[y].p);
        for (int i = (int)push_stack.size() - 1; i >= 0; --i) {
            push(push_stack[i]);
        }
        while (!is_root(x)) {
            int p = nodes[x].p;
            int g = nodes[p].p;
            if (!is_root(p)) {
                bool zigzig = (nodes[p].l == x) == (nodes[g].l == p);
                rotate(zigzig ? p : x);
            }
            rotate(x);
        }
    }

    int expose(int x) {
        int rp = -1;
        for (int cur = x; cur != -1; cur = nodes[cur].p) {
            splay(cur);
            nodes[cur].r = rp;
            pull(cur);
            rp = cur;
        }
        splay(x);
        return rp;
    }

    void evert(int x) {
        expose(x);
        reverse(x);
    }

    int get_root(int x) {
        expose(x);
        while (nodes[x].l != -1) {
            push(x);
            x = nodes[x].l;
        }
        splay(x);
        return x;
    }

    bool connected(int u, int v) {
        return get_root(u) == get_root(v);
    }

    bool link(int u, int v) {
        evert(u);
        if (get_root(v) == u) return false;
        expose(v);
        nodes[u].p = v;
        nodes[v].r = u;
        pull(v);
        return true;
    }

    bool cut(int u, int v) {
        evert(u);
        expose(v);
        if (nodes[v].l != u || nodes[u].r != -1) return false;
        nodes[v].l = -1;
        nodes[u].p = -1;
        pull(v);
        return true;
    }

    int lca(int u, int v) {
        if (!connected(u, v)) return -1;
        expose(u);
        return expose(v);
    }

    int parent(int x) {
        expose(x);
        if (nodes[x].l == -1) return -1;
        x = nodes[x].l;
        push(x);
        while (nodes[x].r != -1) {
            x = nodes[x].r;
            push(x);
        }
        splay(x);
        return x;
    }

    void set(int x, const T &val) {
        expose(x);
        nodes[x].val = val;
        pull(x);
    }

    T get(int x) {
        expose(x);
        return nodes[x].val;
    }

    T fold(int u, int v) {
        evert(u);
        expose(v);
        return nodes[v].sum;
    }

    int dist(int u, int v) {
        evert(u);
        expose(v);
        return nodes[v].sz - 1;
    }
};

/**
 * @brief Link-Cut Tree
 */
#line 13 "test/yosupo_dynamic_tree_vertex_set_path_composite.test.cpp"

struct Monoid {
    using T = array<mint, 2>;
    static T f(T a, T b) { return {a[0] * b[0], a[1] * b[0] + b[1]}; }
    static T e() { return {1, 0}; }
};

int main() {
    Scanner in;
    Printer out;
    int n, q;
    in.read(n, q);
    LinkCutTree<Monoid> lct(n);
    for (int i = 0; i < n; ++i) {
        int a, b;
        in.read(a, b);
        lct.set(i, {a, b});
    }
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        in.read(u, v);
        lct.link(u, v);
    }
    for (int i = 0; i < q; ++i) {
        int t;
        in.read(t);
        if (t == 0) {
            int u, v, w, x;
            in.read(u, v, w, x);
            lct.cut(u, v);
            lct.link(w, x);
        } else if (t == 1) {
            int p, c, d;
            in.read(p, c, d);
            lct.set(p, {c, d});
        } else {
            int u, v, x;
            in.read(u, v, x);
            auto f = lct.fold(u, v);
            out.println((f[0] * x + f[1]).val);
        }
    }
    return 0;
}

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