test/yosupo_vertex_set_path_composite_hld_helper.test.cpp

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• Last update: 2026-03-23 22:54:37+09:00
• Problem: https://judge.yosupo.jp/problem/vertex_set_path_composite

Depends on

• Segment Tree (datastructure/segmenttree/segtree.cpp)
• HL分解(HL Decomposition) (tree/hld.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/vertex_set_path_composite"

#include <array>
#include <limits>
#include <vector>
using namespace std;

static const int MOD = 998244353;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#include "../util/fastio.cpp"
#include "../util/modint.cpp"
#include "../tree/hld.cpp"
#include "../datastructure/segmenttree/segtree.cpp"

struct Ml {
    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}; }
};

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

int main() {
    Scanner sc;
    Printer pr;

    int n, q;
    sc.read(n, q);
    HeavyLightDecomposition hld(n);
    SegmentTree<Ml> segl(n);
    SegmentTree<Mr> segr(n);

    vector<int> a(n), b(n);
    for (int i = 0; i < n; ++i) sc.read(a[i], b[i]);
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        sc.read(u, v);
        hld.add_edge(u, v);
    }
    hld.build();
    for (int i = 0; i < n; ++i) {
        int p = hld.id[i];
        segl.set(p, {a[i], b[i]});
        segr.set(p, {a[i], b[i]});
    }
    segl.build();
    segr.build();

    auto ql = [&](int l, int r) { return segl.query(l, r); };
    auto qr = [&](int l, int r) { return segr.query(l, r); };
    auto merge = [&](Ml::T x, Ml::T y) -> Ml::T { return {x[0] * y[0], x[1] * y[0] + y[1]}; };

    for (int i = 0; i < q; ++i) {
        int t, p, c, d;
        sc.read(t, p, c, d);
        if (t == 0) {
            int v = hld.id[p];
            segl.update(v, {c, d});
            segr.update(v, {c, d});
        } else {
            auto val = hld.path_query_ordered(p, c, Ml::e(), ql, qr, merge, false);
            pr.println((val[0] * d + val[1]).val);
        }
    }
    return 0;
}

#line 1 "test/yosupo_vertex_set_path_composite_hld_helper.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"

#include <array>
#include <limits>
#include <vector>
using namespace std;

static const int MOD = 998244353;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#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/hld.cpp"

class HeavyLightDecomposition {
    void dfs_sz(int v){
        int heavy = -1;
        for (auto &&u : G[v]) {
            if(u == par[v]) continue;
            par[u] = v; dep[u] = dep[v] + 1;
            dfs_sz(u);
            sub_size[v] += sub_size[u];
            if(heavy == -1 || sub_size[u] > sub_size[heavy]) heavy = u;
        }
        if (heavy != -1 && G[v][0] != heavy) {
            for (auto &&u : G[v]) {
                if (u == heavy) {
                    swap(u, G[v][0]);
                    break;
                }
            }
        }
    }
    void dfs_hld(int v, int c, int &pos){
        id[v] = pos++;
        id_inv[id[v]]= v;
        tree_id[v] = c;
        for (auto &&u : G[v]) {
            if(u == par[v]) continue;
            head[u] = (u == G[v][0] ? head[v] : u);
            dfs_hld(u, c, pos);
        }
    }
public:
    int n;
    vector<vector<int>> G;
    vector<int> par, dep, sub_size, id, id_inv, tree_id, head;
    explicit HeavyLightDecomposition(int n) : n(n), G(n), par(n), dep(n), sub_size(n, 1), id(n), id_inv(n), tree_id(n), head(n){}
    explicit HeavyLightDecomposition(vector<vector<int>> &G) : n(G.size()), G(G), par(n), dep(n), sub_size(n, 1), id(n), id_inv(n), tree_id(n), head(n) {}

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

    void build(vector<int> roots = {0}){
        fill(par.begin(), par.end(), -1);
        fill(dep.begin(), dep.end(), 0);
        fill(sub_size.begin(), sub_size.end(), 1);
        int c = 0, pos = 0;
        for (auto &&i : roots) {
            dfs_sz(i);
            head[i] = i;
            dfs_hld(i, c++, pos);
        }
    }

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

    int parent(int v) const {
        return par[v];
    }

    int ancestor(int v, int k) {
        if(dep[v] < k) return -1;
        while(true) {
            int u = head[v];
            if(id[v] - k >= id[u]) return id_inv[id[v] - k];
            k -= id[v]-id[u]+1;
            v = par[u];
        }
    }

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

    pair<int, int> subtree(int v, bool edge = false) const {
        return {id[v] + edge, id[v] + sub_size[v]};
    }

    template<typename F>
    void add(int u, int v, const F &f, bool edge){
        while (head[u] != head[v]){
            if(id[u] > id[v]) swap(u, v);
            f(id[head[v]], id[v]+1);
            v = par[head[v]];
        }
        if(id[u] > id[v]) swap(u, v);
        f(id[u]+edge, id[v]+1);
    }

    template<typename F>
    void path(int u, int v, const F &f, bool edge = false){
        add(u, v, f, edge);
    }

    template<typename F>
    void apply_subtree(int v, const F &f, bool edge = false){
        auto [l, r] = subtree(v, edge);
        f(l, r);
    }

    template<typename T, typename Q, typename F>
    T query(int u, int v, const T &e, const Q &q, const F &f, bool edge){
        T l = e, r = e;
        while(head[u] != head[v]){
            if(id[u] > id[v]) swap(u, v), swap(l, r);
            l = f(l, q(id[head[v]], id[v]+1));
            v = par[head[v]];
        }
        if(id[u] > id[v]) swap(u, v), swap(l, r);
        return f(q(id[u]+edge, id[v]+1), f(l, r));
    }

    template<typename T, typename Q, typename F>
    T path_query(int u, int v, const T &e, const Q &q, const F &f, bool edge = false){
        return query(u, v, e, q, f, edge);
    }

    template<typename T, typename QL, typename QR, typename F>
    T query_order(int u, int v, const T &e, const QL &ql, const QR &qr, const F &f, bool edge){
        T l = e, r = e;
        while(head[u] != head[v]){
            if(id[u] > id[v]) {
                l = f(l, qr(id[head[u]], id[u]+1));
                u = par[head[u]];
            }else {
                r = f(ql(id[head[v]], id[v]+1), r);
                v = par[head[v]];
            }
        }
        T mid = (id[u] > id[v] ? qr(id[v]+edge, id[u]+1) : ql(id[u]+edge, id[v]+1));
        return f(f(l, mid), r);
    }

    template<typename T, typename QL, typename QR, typename F>
    T path_query_ordered(int u, int v, const T &e, const QL &ql, const QR &qr, const F &f, bool edge = false){
        return query_order(u, v, e, ql, qr, f, edge);
    }

    template<typename T, typename Q>
    T subtree_query(int v, const Q &q, bool edge = false){
        auto [l, r] = subtree(v, edge);
        return q(l, r);
    }
};

/**
 * @brief HL分解(HL Decomposition)
 */
#line 1 "datastructure/segmenttree/segtree.cpp"
template <class M>
struct SegmentTree{
    using T = typename M::T;
    int sz, n, height{};
    vector<T> seg;
    explicit SegmentTree(int n) : n(n) {
        sz = 1; while(sz < n) sz <<= 1, height++;
        seg.assign(2*sz, M::e());
    }

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

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

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

    T query(int a, int b){
        T l = M::e(), r = M::e();
        for(a += sz, b += sz; a < b; a >>=1, b>>=1){
            if(a & 1) l = M::f(l, seg[a++]);
            if(b & 1) r = M::f(seg[--b], r);
        }
        return M::f(l, r);
    }

    template<class F>
    int search_right(int l, F cond){
        if(l == n) return n;
        T val = M::e();
        l += sz;
        do {
            while(!(l&1)) l >>= 1;
            if(!cond(M::f(val, seg[l]))){
                while(l < sz) {
                    l <<= 1;
                    if (cond(M::f(val, seg[l]))){
                        val = M::f(val, seg[l]);
                        l++;
                    }
                }
                return l - sz;
            }
            val = M::f(val, seg[l]);
            l++;
        } while((l & -l) != l);
        return n;
    }

    template<class F>
    int search_left(int r, F cond){
        if(r == 0) return 0;
        T val = M::e();
        r += sz;
        do {
            r--;
            while(r&1) r >>= 1;
            if(!cond(M::f(seg[r], val))){
                while(r < sz) {
                    r = ((r << 1)|1);
                    if (cond(M::f(seg[r], val))){
                        val = M::f(seg[r], val);
                        r--;
                    }
                }
                return r + 1 - sz;
            }
            val = M::f(seg[r], val);
        } while((r & -r) != r);
        return 0;
    }
    T operator[](const int &k) const { return seg[k + sz]; }
};


/*
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}; }
};
*/

/**
 * @brief Segment Tree
 */
#line 23 "test/yosupo_vertex_set_path_composite_hld_helper.test.cpp"

struct Ml {
    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}; }
};

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

int main() {
    Scanner sc;
    Printer pr;

    int n, q;
    sc.read(n, q);
    HeavyLightDecomposition hld(n);
    SegmentTree<Ml> segl(n);
    SegmentTree<Mr> segr(n);

    vector<int> a(n), b(n);
    for (int i = 0; i < n; ++i) sc.read(a[i], b[i]);
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        sc.read(u, v);
        hld.add_edge(u, v);
    }
    hld.build();
    for (int i = 0; i < n; ++i) {
        int p = hld.id[i];
        segl.set(p, {a[i], b[i]});
        segr.set(p, {a[i], b[i]});
    }
    segl.build();
    segr.build();

    auto ql = [&](int l, int r) { return segl.query(l, r); };
    auto qr = [&](int l, int r) { return segr.query(l, r); };
    auto merge = [&](Ml::T x, Ml::T y) -> Ml::T { return {x[0] * y[0], x[1] * y[0] + y[1]}; };

    for (int i = 0; i < q; ++i) {
        int t, p, c, d;
        sc.read(t, p, c, d);
        if (t == 0) {
            int v = hld.id[p];
            segl.update(v, {c, d});
            segr.update(v, {c, d});
        } else {
            auto val = hld.path_query_ordered(p, c, Ml::e(), ql, qr, merge, false);
            pr.println((val[0] * d + val[1]).val);
        }
    }
    return 0;
}

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