verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum-fixed-root.test.cpp

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Last update: 2024-05-03 23:21:26+09:00
Problem: https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
//
#include "../../template/template.hpp"
//
#include "../../modint/montgomery-modint.hpp"
//
#include "../../tree/static-top-tree-vertex-based.hpp"
//
using mint = LazyMontgomeryModInt<998244353>;

struct Path {
  mint a, b, s, x;
};
struct Point {
  mint s, x;
};
vector<mint> calc(int N, int Q, vector<int> A, vector<int> U, vector<int> V,
                  vector<int> B, vector<int> C, vector<int> cmd, vector<int> I,
                  vector<int> X, vector<int> Y) {
  vector<vector<int>> g(2 * N - 1);
  rep(e, N - 1) {
    g[N + e].push_back(U[e]), g[U[e]].push_back(N + e);
    g[N + e].push_back(V[e]), g[V[e]].push_back(N + e);
  }
  auto vertex = [&](int i) -> Path {
    if (i < N) return {1, 0, A[i], 1};
    int e = i - N;
    return {B[e], C[e], 0, 0};
  };
  auto compress = [&](const Path& p, const Path& c) -> Path {
    return {p.a * c.a, p.a * c.b + p.b, p.s + p.a * c.s + p.b * c.x, p.x + c.x};
  };
  auto rake = [&](const Point& a, const Point& b) -> Point {
    return {a.s + b.s, a.x + b.x};
  };
  auto add_edge = [&](const Path& a) -> Point { return {a.s, a.x}; };
  auto add_vertex = [&](const Point& a, int i) -> Path {
    if (i < N) return {1, 0, a.s + A[i], a.x + 1};
    int e = i - N;
    return {B[e], C[e], a.s * B[e] + a.x * C[e], a.x};
  };

  HeavyLightDecomposition hld{g};
  DPonStaticTopTreeVertexBased<
      vector<vector<int>>, Path, Point, decltype(vertex), decltype(compress),
      decltype(rake), decltype(add_edge), decltype(add_vertex)>
      dp(hld, vertex, compress, rake, add_edge, add_vertex);

  vector<mint> ans(Q);
  rep(q, Q) {
    if (cmd[q] == 0) {
      A[I[q]] = X[q];
      dp.update(I[q]);
    } else {
      B[I[q]] = X[q], C[I[q]] = Y[q];
      dp.update(N + I[q]);
    }
    ans[q] = dp.get().s;
  }
  return ans;
}

void Nyaan::solve() {
  int N, Q;
  in(N, Q);
  vector<int> A(N);
  for (auto& x : A) in(x);
  vector<int> U(N - 1), V(N - 1), B(N - 1), C(N - 1);
  rep(i, N - 1) in(U[i], V[i], B[i], C[i]);
  vector<int> cmd(Q), I(Q), X(Q), Y(Q, -1);
  rep(i, Q) {
    in(cmd[i], I[i], X[i]);
    if (cmd[i] == 1) in(Y[i]);
  }
  auto ac = calc(N, Q, A, U, V, B, C, cmd, I, X, Y);
  for (auto& x : ac) out(x.get());
}

#line 1 "verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum-fixed-root.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
//
#line 2 "template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
#line 61 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan
#line 64 "template/template.hpp"

// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(std::forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...)                           \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
#line 70 "template/template.hpp"

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum-fixed-root.test.cpp"
//
#line 2 "modint/montgomery-modint.hpp"

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  static_assert(r * mod == 1, "this code has bugs.");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint operator+() const { return mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  constexpr mint inverse() const {
    int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
    while (y > 0) {
      t = x / y;
      x -= t * y, u -= t * v;
      tmp = x, x = y, y = tmp;
      tmp = u, u = v, v = tmp;
    }
    return mint{u};
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
#line 6 "verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum-fixed-root.test.cpp"
//
#line 2 "tree/static-top-tree-vertex-based.hpp"

#line 6 "tree/static-top-tree-vertex-based.hpp"
using namespace std;

#line 2 "tree/convert-tree.hpp"

#line 2 "graph/graph-template.hpp"

template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true,
                 bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}

/**
 * @brief グラフテンプレート
 * @docs docs/graph/graph-template.md
 */
#line 4 "tree/convert-tree.hpp"

template <typename T>
struct has_cost {
 private:
  template <typename U>
  static auto confirm(U u) -> decltype(u.cost, std::true_type());
  static auto confirm(...) -> std::false_type;

 public:
  enum : bool { value = decltype(confirm(std::declval<T>()))::value };
};

template <typename T>
vector<vector<T>> inverse_tree(const vector<vector<T>>& g) {
  int N = (int)g.size();
  vector<vector<T>> rg(N);
  for (int i = 0; i < N; i++) {
    for (auto& e : g[i]) {
      if constexpr (is_same<T, int>::value) {
        rg[e].push_back(i);
      } else if constexpr (has_cost<T>::value) {
        rg[e].emplace_back(e.to, i, e.cost);
      } else {
        assert(0);
      }
    }
  }
  return rg;
}

template <typename T>
vector<vector<T>> rooted_tree(const vector<vector<T>>& g, int root = 0) {
  int N = (int)g.size();
  vector<vector<T>> rg(N);
  vector<char> v(N, false);
  v[root] = true;
  queue<int> que;
  que.emplace(root);
  while (!que.empty()) {
    auto p = que.front();
    que.pop();
    for (auto& e : g[p]) {
      if (v[e] == false) {
        v[e] = true;
        que.push(e);
        rg[p].push_back(e);
      }
    }
  }
  return rg;
}

/**
 * @brief 根付き木・逆辺からなる木への変換
 */
#line 2 "tree/heavy-light-decomposition.hpp"

#line 4 "tree/heavy-light-decomposition.hpp"

template <typename G>
struct HeavyLightDecomposition {
 private:
  void dfs_sz(int cur) {
    size[cur] = 1;
    for (auto& dst : g[cur]) {
      if (dst == par[cur]) {
        if (g[cur].size() >= 2 && int(dst) == int(g[cur][0]))
          swap(g[cur][0], g[cur][1]);
        else
          continue;
      }
      depth[dst] = depth[cur] + 1;
      par[dst] = cur;
      dfs_sz(dst);
      size[cur] += size[dst];
      if (size[dst] > size[g[cur][0]]) {
        swap(dst, g[cur][0]);
      }
    }
  }

  void dfs_hld(int cur) {
    down[cur] = id++;
    for (auto dst : g[cur]) {
      if (dst == par[cur]) continue;
      nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst));
      dfs_hld(dst);
    }
    up[cur] = id;
  }

  // [u, v)
  vector<pair<int, int>> ascend(int u, int v) const {
    vector<pair<int, int>> res;
    while (nxt[u] != nxt[v]) {
      res.emplace_back(down[u], down[nxt[u]]);
      u = par[nxt[u]];
    }
    if (u != v) res.emplace_back(down[u], down[v] + 1);
    return res;
  }

  // (u, v]
  vector<pair<int, int>> descend(int u, int v) const {
    if (u == v) return {};
    if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}};
    auto res = descend(u, par[nxt[v]]);
    res.emplace_back(down[nxt[v]], down[v]);
    return res;
  }

 public:
  G& g;
  int root, id;
  vector<int> size, depth, down, up, nxt, par;
  HeavyLightDecomposition(G& _g, int _root = 0)
      : g(_g),
        root(_root),
        id(0),
        size(g.size(), 0),
        depth(g.size(), 0),
        down(g.size(), -1),
        up(g.size(), -1),
        nxt(g.size(), root),
        par(g.size(), root) {
    dfs_sz(root);
    dfs_hld(root);
  }

  pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); }

  template <typename F>
  void path_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) {
      int s = a + 1, t = b;
      s > t ? f(t, s) : f(s, t);
    }
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) {
      int s = a, t = b + 1;
      s > t ? f(t, s) : f(s, t);
    }
  }

  template <typename F>
  void path_noncommutative_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) f(a + 1, b);
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) f(a, b + 1);
  }

  template <typename F>
  void subtree_query(int u, bool vertex, const F& f) {
    f(down[u] + int(!vertex), up[u]);
  }

  int lca(int a, int b) {
    while (nxt[a] != nxt[b]) {
      if (down[a] < down[b]) swap(a, b);
      a = par[nxt[a]];
    }
    return depth[a] < depth[b] ? a : b;
  }

  int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; }
};

/**
 * @brief Heavy Light Decomposition(重軽分解)
 * @docs docs/tree/heavy-light-decomposition.md
 */
#line 10 "tree/static-top-tree-vertex-based.hpp"

namespace StaticTopTreeVertexBasedImpl {

enum Type { Vertex, Compress, Rake, Add_Edge, Add_Vertex };

template <typename G>
struct StaticTopTreeVertexBased {
  const HeavyLightDecomposition<G>& hld;
  vector<vector<int>> g;
  int root;     // 元の木の root
  int tt_root;  // top tree の root
  vector<int> P, L, R;
  vector<Type> T;

  StaticTopTreeVertexBased(const HeavyLightDecomposition<G>& _hld) : hld(_hld) {
    root = hld.root;
    g = rooted_tree(hld.g, root);
    int n = g.size();
    P.resize(n, -1), L.resize(n, -1), R.resize(n, -1);
    T.resize(n, Type::Vertex);
    build();
  }

 private:
  int add(int l, int r, Type t) {
    if (t == Type::Compress or t == Type::Rake) {
      assert(l != -1 and r != -1);
    }
    if (t == Type::Add_Edge) {
      assert(l != -1 and r == -1);
    }
    assert(t != Type::Vertex and t != Type::Add_Vertex);
    int k = P.size();
    P.push_back(-1), L.push_back(l), R.push_back(r), T.push_back(t);
    if (l != -1) P[l] = k;
    if (r != -1) P[r] = k;
    return k;
  }
  int add2(int k, int l, int r, Type t) {
    assert(k < (int)g.size());
    assert(t == Type::Vertex or t == Type::Add_Vertex);
    if (t == Type::Vertex) {
      assert(l == -1 and r == -1);
    } else {
      assert(l != -1 and r == -1);
    }
    P[k] = -1, L[k] = l, R[k] = r, T[k] = t;
    if (l != -1) P[l] = k;
    if (r != -1) P[r] = k;
    return k;
  }
  pair<int, int> merge(const vector<pair<int, int>>& a, Type t) {
    assert(!a.empty());
    if (a.size() == 1) return a[0];
    int sum_s = 0;
    for (auto& [_, s] : a) sum_s += s;
    vector<pair<int, int>> b, c;
    for (auto& [i, s] : a) {
      (sum_s > s ? b : c).emplace_back(i, s);
      sum_s -= s * 2;
    }
    auto [i, si] = merge(b, t);
    auto [j, sj] = merge(c, t);
    return {add(i, j, t), si + sj};
  }
  pair<int, int> compress(int i) {
    vector<pair<int, int>> chs;
    while (true) {
      chs.push_back(add_vertex(i));
      if (g[i].empty()) break;
      i = g[i][0];
    }
    return merge(chs, Type::Compress);
  }
  pair<int, int> rake(int i) {
    vector<pair<int, int>> chs;
    for (int j = 1; j < (int)g[i].size(); j++) chs.push_back(add_edge(g[i][j]));
    if (chs.empty()) return {-1, 0};
    return merge(chs, Type::Rake);
  }
  pair<int, int> add_edge(int i) {
    auto [j, sj] = compress(i);
    return {add(j, -1, Type::Add_Edge), sj};
  }
  pair<int, int> add_vertex(int i) {
    auto [j, sj] = rake(i);
    return {add2(i, j, -1, j == -1 ? Type::Vertex : Type::Add_Vertex), sj + 1};
  }
  void build() {
    auto [i, n] = compress(root);
    assert((int)g.size() == n);
    tt_root = i;
  }
};

template <typename G, typename Path, typename Point, typename Vertex,
          typename Compress, typename Rake, typename Add_edge,
          typename Add_vertex>
struct DPonStaticTopTreeVertexBased {
  const StaticTopTreeVertexBased<G> tt;
  vector<Path> path;
  vector<Point> point;
  const Vertex vertex;
  const Compress compress;
  const Rake rake;
  const Add_edge add_edge;
  const Add_vertex add_vertex;

  DPonStaticTopTreeVertexBased(const HeavyLightDecomposition<G>& hld,
                               const Vertex& _vertex, const Compress& _compress,
                               const Rake& _rake, const Add_edge& _add_edge,
                               const Add_vertex& _add_vertex)
      : tt(hld),
        vertex(_vertex),
        compress(_compress),
        rake(_rake),
        add_edge(_add_edge),
        add_vertex(_add_vertex) {
    int n = tt.P.size();
    path.resize(n), point.resize(n);
    dfs(tt.tt_root);
  }

  Path get() { return path[tt.tt_root]; }
  void update(int k) {
    while (k != -1) _update(k), k = tt.P[k];
  }

 private:
  void _update(int k) {
    if (tt.T[k] == Type::Vertex) {
      path[k] = vertex(k);
    } else if (tt.T[k] == Type::Compress) {
      path[k] = compress(path[tt.L[k]], path[tt.R[k]]);
    } else if (tt.T[k] == Type::Rake) {
      point[k] = rake(point[tt.L[k]], point[tt.R[k]]);
    } else if (tt.T[k] == Type::Add_Edge) {
      point[k] = add_edge(path[tt.L[k]]);
    } else {
      path[k] = add_vertex(point[tt.L[k]], k);
    }
  }

  void dfs(int k) {
    if (tt.L[k] != -1) dfs(tt.L[k]);
    if (tt.R[k] != -1) dfs(tt.R[k]);
    _update(k);
  }
};

}  // namespace StaticTopTreeVertexBasedImpl

using StaticTopTreeVertexBasedImpl::DPonStaticTopTreeVertexBased;
using StaticTopTreeVertexBasedImpl::StaticTopTreeVertexBased;

/*

  // template
  using Path = ;
  using Point = ;
  auto vertex = [&](int i) -> Path {

  };
  auto compress = [&](const Path& p, const Path& c) -> Path {

  };
  auto rake = [&](const Point& a, const Point& b) -> Point {

  };
  auto add_edge = [&](const Path& a) -> Point {

  };
  auto add_vertex = [&](const Point& a, int i) -> Path {

  };
  HeavyLightDecomposition hld{g};
  DPonStaticTopTreeVertexBased<vector<vector<int>>, Path, Point,
  decltype(vertex), decltype(compress), decltype(rake), decltype(add_edge),
                    decltype(add_vertex)>
      dp(hld, vertex, compress, rake, add_edge, add_vertex);
*/

/**
 * @brief Static Top Tree
 */
#line 8 "verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum-fixed-root.test.cpp"
//
using mint = LazyMontgomeryModInt<998244353>;

struct Path {
  mint a, b, s, x;
};
struct Point {
  mint s, x;
};
vector<mint> calc(int N, int Q, vector<int> A, vector<int> U, vector<int> V,
                  vector<int> B, vector<int> C, vector<int> cmd, vector<int> I,
                  vector<int> X, vector<int> Y) {
  vector<vector<int>> g(2 * N - 1);
  rep(e, N - 1) {
    g[N + e].push_back(U[e]), g[U[e]].push_back(N + e);
    g[N + e].push_back(V[e]), g[V[e]].push_back(N + e);
  }
  auto vertex = [&](int i) -> Path {
    if (i < N) return {1, 0, A[i], 1};
    int e = i - N;
    return {B[e], C[e], 0, 0};
  };
  auto compress = [&](const Path& p, const Path& c) -> Path {
    return {p.a * c.a, p.a * c.b + p.b, p.s + p.a * c.s + p.b * c.x, p.x + c.x};
  };
  auto rake = [&](const Point& a, const Point& b) -> Point {
    return {a.s + b.s, a.x + b.x};
  };
  auto add_edge = [&](const Path& a) -> Point { return {a.s, a.x}; };
  auto add_vertex = [&](const Point& a, int i) -> Path {
    if (i < N) return {1, 0, a.s + A[i], a.x + 1};
    int e = i - N;
    return {B[e], C[e], a.s * B[e] + a.x * C[e], a.x};
  };

  HeavyLightDecomposition hld{g};
  DPonStaticTopTreeVertexBased<
      vector<vector<int>>, Path, Point, decltype(vertex), decltype(compress),
      decltype(rake), decltype(add_edge), decltype(add_vertex)>
      dp(hld, vertex, compress, rake, add_edge, add_vertex);

  vector<mint> ans(Q);
  rep(q, Q) {
    if (cmd[q] == 0) {
      A[I[q]] = X[q];
      dp.update(I[q]);
    } else {
      B[I[q]] = X[q], C[I[q]] = Y[q];
      dp.update(N + I[q]);
    }
    ans[q] = dp.get().s;
  }
  return ans;
}

void Nyaan::solve() {
  int N, Q;
  in(N, Q);
  vector<int> A(N);
  for (auto& x : A) in(x);
  vector<int> U(N - 1), V(N - 1), B(N - 1), C(N - 1);
  rep(i, N - 1) in(U[i], V[i], B[i], C[i]);
  vector<int> cmd(Q), I(Q), X(Q), Y(Q, -1);
  rep(i, Q) {
    in(cmd[i], I[i], X[i]);
    if (cmd[i] == 1) in(Y[i]);
  }
  auto ac = calc(N, Q, A, U, V, B, C, cmd, I, X, Y);
  for (auto& x : ac) out(x.get());
}

Nyaan's Library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum-fixed-root.test.cpp

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