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:heavy_check_mark: Verify/LC_vertex_set_path_composite.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"

#include "Template/template.hpp"

#include "Utility/fastio.hpp"

#include "Math/modint.hpp"

#include "Graph/hld.hpp"

#include "DataStructure/segtree.hpp"


using Fp=fp<998244353>;
using P=array<Fp,2>;
P f(P a,P b){return P{a[0]*b[0],a[1]*b[0]+b[1]};}
struct X{
    P base,rev;
    X(Fp a=1,Fp b=0):base({a,b}),rev({a,b}){}
};
X f(X a,X b){
    X ret;
    ret.base=f(a.base,b.base);
    ret.rev=f(b.rev,a.rev);
    return ret; 
}
X g(X a,X b){return b;}
X e(){return X();}

int main(){
    int N,Q;
    cin>>N>>Q;
    vector<X> A(N);
    rep(i,0,N){
        int a,b;
        cin>>a>>b;
        A[i]=X(a,b);
    }
    HLD hld(N);
    rep(_,0,N-1){
        int x,y;
        cin>>x>>y;
        hld.add_edge(x,y);
    }
    hld.run();

    SegmentTree<X,X,f,g,e> seg(N);
    rep(i,0,N)seg.update(hld.in[i],A[i]);
    while(Q--){
        int t;
        cin>>t;
        if(t==0){
            int p,c,d;
            cin>>p>>c>>d;
            seg.update(hld.in[p],X{c,d});
        }
        else{
            int u,v,x;
            cin>>u>>v>>x;
            int lca=hld.lca(u,v);
            auto ps=hld.get(u,lca);
            P ret=P{1,0},add=P{1,0};
            for(auto& [L,R]:ps)ret=f(ret,seg.query(L,R).rev);
            ps=hld.get(v,lca,1);
            for(auto& [L,R]:ps)add=f(seg.query(L,R).base,add);
            ret=f(ret,add);
            cout<<ret[0]*x+ret[1]<<'\n';
        }
    }
    return 0;
}
#line 1 "Verify/LC_vertex_set_path_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"

#line 1 "Template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T, template <class> class C>
ostream &operator<<(ostream &os, const C<T> &v) {
    os << "[";
    for (auto d : v)
        os << d << ", ";
    os << "]";
    return os;
}
#line 2 "Utility/fastio.hpp"
#include <unistd.h>

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf


uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memmove(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if (pir < SZ)
        ibuf[pir++] = '\n';
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

void rd(char &c) {
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
}

void rd(string &x) {
    x.clear();
    char c;
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
    do {
        x += c;
        if (pil == pir)
            load();
        c = ibuf[pil++];
    } while (!isspace(c));
}

template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}

template <typename T> void rd_integer(T &x) {
    if (pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while (c < '-');
    bool minus = 0;
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while ('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (minus)
            x = -x;
    }
}

void rd(int &x) {
    rd_integer(x);
}
void rd(ll &x) {
    rd_integer(x);
}
void rd(i128 &x) {
    rd_integer(x);
}
void rd(uint &x) {
    rd_integer(x);
}
void rd(ull &x) {
    rd_integer(x);
}
void rd(u128 &x) {
    rd_integer(x);
}
void rd(double &x) {
    rd_real(x);
}
void rd(long double &x) {
    rd_real(x);
}

template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) {
    rd_tuple(tpl);
}

template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for (auto &d : x)
        rd(d);
}
template <class T> void rd(vector<T> &x) {
    for (auto &d : x)
        rd(d);
}

void read() {}
template <class H, class... T> void read(H &h, T &...t) {
    rd(h), read(t...);
}

void wt(const char c) {
    if (por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for (char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++)
        wt(s[i]);
}

template <typename T> void wt_integer(T x) {
    if (por > SZ - 100)
        flush();
    if (x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for (outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if (x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if (x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if (x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}

template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}

void wt(int x) {
    wt_integer(x);
}
void wt(ll x) {
    wt_integer(x);
}
void wt(i128 x) {
    wt_integer(x);
}
void wt(uint x) {
    wt_integer(x);
}
void wt(ull x) {
    wt_integer(x);
}
void wt(u128 x) {
    wt_integer(x);
}
void wt(double x) {
    wt_real(x);
}
void wt(long double x) {
    wt_real(x);
}

template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) {
    wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}

void print() {
    wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if (sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
    flush();
}
} // namespace fastio


using fastio::flush;
using fastio::print;
using fastio::read;

inline void first(bool i = true) {
    print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
    print(i ? "Alice" : "Bob");
}
inline void yes(bool i = true) {
    print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
    print(i ? "Yes" : "No");
}
inline void No() {
    print("No");
}
inline void YES(bool i = true) {
    print(i ? "YES" : "NO");
}
inline void NO() {
    print("NO");
}
inline void Yay(bool i = true) {
    print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
    print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
    print(i ? "POSSIBLE" : "IMPOSSIBLE");
}

/**
 * @brief Fast IO
 */
#line 2 "Math/modint.hpp"

template <unsigned mod = 1000000007> struct fp {
    unsigned v;
    static constexpr int get_mod() {
        return mod;
    }
    constexpr unsigned inv() const {
        assert(v != 0);
        int x = v, y = mod, p = 1, q = 0, t = 0, tmp = 0;
        while (y > 0) {
            t = x / y;
            x -= t * y, p -= t * q;
            tmp = x, x = y, y = tmp;
            tmp = p, p = q, q = tmp;
        }
        if (p < 0)
            p += mod;
        return p;
    }
    constexpr fp(ll x = 0) : v(x >= 0 ? x % mod : (mod - (-x) % mod) % mod) {}
    fp operator-() const {
        return fp() - *this;
    }
    fp pow(ull t) {
        fp res = 1, b = *this;
        while (t) {
            if (t & 1)
                res *= b;
            b *= b;
            t >>= 1;
        }
        return res;
    }
    fp &operator+=(const fp &x) {
        if ((v += x.v) >= mod)
            v -= mod;
        return *this;
    }
    fp &operator-=(const fp &x) {
        if ((v += mod - x.v) >= mod)
            v -= mod;
        return *this;
    }
    fp &operator*=(const fp &x) {
        v = ull(v) * x.v % mod;
        return *this;
    }
    fp &operator/=(const fp &x) {
        v = ull(v) * x.inv() % mod;
        return *this;
    }
    fp operator+(const fp &x) const {
        return fp(*this) += x;
    }
    fp operator-(const fp &x) const {
        return fp(*this) -= x;
    }
    fp operator*(const fp &x) const {
        return fp(*this) *= x;
    }
    fp operator/(const fp &x) const {
        return fp(*this) /= x;
    }
    bool operator==(const fp &x) const {
        return v == x.v;
    }
    bool operator!=(const fp &x) const {
        return v != x.v;
    }
    friend istream &operator>>(istream &is, fp &x) {
        return is >> x.v;
    }
    friend ostream &operator<<(ostream &os, const fp &x) {
        return os << x.v;
    }
};

template <unsigned mod> void rd(fp<mod> &x) {
    fastio::rd(x.v);
}
template <unsigned mod> void wt(fp<mod> x) {
    fastio::wt(x.v);
}

template <typename T> T Inv(ll n) {
    static const int md = T::get_mod();
    static vector<T> buf({0, 1});
    assert(n > 0);
    n %= md;
    while (SZ(buf) <= n) {
        int k = SZ(buf), q = (md + k - 1) / k;
        buf.push_back(buf[k * q - md] * q);
    }
    return buf[n];
}

template <typename T> T Fact(ll n, bool inv = 0) {
    static const int md = T::get_mod();
    static vector<T> buf({1, 1}), ibuf({1, 1});
    assert(n >= 0 and n < md);
    while (SZ(buf) <= n) {
        buf.push_back(buf.back() * SZ(buf));
        ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
    }
    return inv ? ibuf[n] : buf[n];
}

template <typename T> T nPr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nHr(int n, int r, bool inv = 0) {
    return nCr<T>(n + r - 1, r, inv);
}

/**
 * @brief Modint
 */
#line 2 "Graph/hld.hpp"

struct HLD{
    using P=pair<int,int>;
    vector<vector<int>> g; vector<int> sz,in,out,rev,hs,par,dist;
    void dfs(int v,int p){
        par[v]=p; sz[v]=1;
        if(p!=-1)dist[v]=dist[p]+1;
        if(!g[v].empty() and g[v][0]==p)swap(g[v][0],g[v].back());
        for(auto& to:g[v])if(to!=p){
           dfs(to,v); sz[v]+=sz[to];
           if(sz[g[v][0]]<sz[to])swap(g[v][0],to);
        }
    }
    void dfs2(int v,int p,int& k){
        in[v]=k++; rev[in[v]]=v;
        for(auto& to:g[v])if(to!=p){
            hs[to]=(g[v][0]==to?hs[v]:to);
            dfs2(to,v,k);
        }
        out[v]=k;
    }
    HLD(int _n):g(_n),sz(_n),in(_n),out(_n),rev(_n),hs(_n),par(_n),dist(_n){}
    void add_edge(int u,int v){
        g[u].emplace_back(v); g[v].emplace_back(u);
    }
    void run(int rt=0){dfs(rt,-1); hs[rt]=rt; int k=0; dfs2(rt,-1,k);}
    int lca(int u,int v){
        for(;;v=par[hs[v]]){
            if(in[u]>in[v])swap(u,v);
            if(hs[u]==hs[v])return u;
        }
    }
    vector<P> get(int u,int p,bool es=0){
        assert(in[p]<=in[u] and out[u]<=out[p]);
        vector<P> res;
        while(hs[u]!=hs[p]){
            res.push_back({in[hs[u]],in[u]+1});
            u=par[hs[u]];
        }
        res.push_back({in[p]+es,in[u]+1});
        return res;
    }
    int jump(int u,int v,int k){
        if(k<0)return -1;
        int g=lca(u,v);
        int d0=dist[u]+dist[v]-dist[g]*2;
        if(d0<k)return -1;
        int st=u;
        if(dist[u]-dist[g]<k)st=v,k=d0-k;
        for(;;){
            int to=hs[st];
            if(in[st]-k>=in[to])return rev[in[st]-k];
            k-=in[st]-in[to]+1; st=par[to];
        }
    }
};

/**
 * @brief Heavy Light Decomposition
 */
#line 2 "DataStructure/segtree.hpp"

template<typename M,typename N,M (*f)(M,M),M (*g)(M,N),M (*m1)()>struct SegmentTree{
    int n; vector<M> data;
    SegmentTree(int _n=0){
        n=1; while(n<_n)n<<=1; data.assign(2*n,m1());
    }
    void run(vector<M>& v){
        for(int i=0;i<(int)v.size();i++)data[i+n]=v[i];
        for(int k=n-1;k>0;k--)data[k]=f(data[2*k],data[2*k+1]);
    }
    void set(int k,const M &x){
        k+=n; data[k]=x;
        while(k>>=1)data[k]=f(data[2*k],data[2*k+1]);
    }
    void update(int k,const N &x){
        k+=n; data[k]=g(data[k],x);
        while(k>>=1)data[k]=f(data[2*k],data[2*k+1]);
    }
    M query(int a,int b){
        M L=m1(),R=m1();
        for(a+=n,b+=n;a<b;a>>=1,b>>=1){
            if(a&1)L=f(L,data[a++]);
            if(b&1)R=f(data[--b],R);
        }
        return f(L,R);
    }
    M operator[](const int &k)const{return data[k+n];}
};

/**
 * @brief Segment Tree
 */
#line 8 "Verify/LC_vertex_set_path_composite.test.cpp"

using Fp=fp<998244353>;
using P=array<Fp,2>;
P f(P a,P b){return P{a[0]*b[0],a[1]*b[0]+b[1]};}
struct X{
    P base,rev;
    X(Fp a=1,Fp b=0):base({a,b}),rev({a,b}){}
};
X f(X a,X b){
    X ret;
    ret.base=f(a.base,b.base);
    ret.rev=f(b.rev,a.rev);
    return ret; 
}
X g(X a,X b){return b;}
X e(){return X();}

int main(){
    int N,Q;
    cin>>N>>Q;
    vector<X> A(N);
    rep(i,0,N){
        int a,b;
        cin>>a>>b;
        A[i]=X(a,b);
    }
    HLD hld(N);
    rep(_,0,N-1){
        int x,y;
        cin>>x>>y;
        hld.add_edge(x,y);
    }
    hld.run();

    SegmentTree<X,X,f,g,e> seg(N);
    rep(i,0,N)seg.update(hld.in[i],A[i]);
    while(Q--){
        int t;
        cin>>t;
        if(t==0){
            int p,c,d;
            cin>>p>>c>>d;
            seg.update(hld.in[p],X{c,d});
        }
        else{
            int u,v,x;
            cin>>u>>v>>x;
            int lca=hld.lca(u,v);
            auto ps=hld.get(u,lca);
            P ret=P{1,0},add=P{1,0};
            for(auto& [L,R]:ps)ret=f(ret,seg.query(L,R).rev);
            ps=hld.get(v,lca,1);
            for(auto& [L,R]:ps)add=f(seg.query(L,R).base,add);
            ret=f(ret,add);
            cout<<ret[0]*x+ret[1]<<'\n';
        }
    }
    return 0;
}
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