test/point_set_tree_path_composite_sum_fixed_root.test.cpp

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• Last update: 2025-05-18 02:48:12+08:00
• Problem: https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root

Depends on

• default/t.cpp
• dp/dynamicTreeDP.cpp
• ds/staticTopTree.cpp
• modint/MontgomeryModInt.cpp

Code

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

#include "../default/t.cpp"
#define eb emplace_back
#define pb push_back
#include "../modint/MontgomeryModInt.cpp"
#include "../ds/staticTopTree.cpp"
#include "../dp/dynamicTreeDP.cpp"

struct M {
  mint a, b, ans, sz;
};

M rake(const M &a, const M &b) {
  return M{a.a, a.b, a.ans + b.ans, a.sz + b.sz};
}
M compress(const M &a, const M &b) {
  return M{a.a * b.a, a.a * b.b + a.b, a.ans + b.ans * a.a + a.b * b.sz, a.sz + b.sz};
}

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n, q; cin >> n >> q;
  vector<mint> a(n);
  for(mint &x : a) cin >> x;

  vector<array<int, 4>> uvbc(n - 1);
  for(auto &[u, v, b, c] : uvbc)
    cin >> u >> v >> b >> c;

  vector<vector<int>> g(n);
  for(auto [u, v, _, __] : uvbc)
    g[u].eb(v), g[v].eb(u);
  uvbc.pb({-1, 0, 1, 0});

  static_top_tree stt(g);

  vector<int> eid(n);
  for(int i = 0; auto &[u, v, _, __] : uvbc) {
    if (stt.r[v] == u) swap(u, v);
    eid[u] = i++;
  }

  auto get = [&](int v) {
    auto [_, __, b, c] = uvbc[eid[v]];
    return M{b, c, a[v] * b + c, 1};
  };

  vector<M> init(n);
  for(int i = 0; i < n; i++)
    init[i] = get(i);

  dynamic_tree_dp<M, rake, compress> ddp(g, init);

  while(q--) {
    int op; cin >> op;
    if (op == 0) {
      int w, x; cin >> w >> x;
      a[w] = x;
      ddp.set(w, get(w));
    } else {
      int e, y, z; cin >> e >> y >> z;
      auto &[u, _, b, c] = uvbc[e];
      b = y, c = z;
      ddp.set(u, get(u));
    }
    cout << ddp.query().ans << '\n';
  }

  return 0;
}

#line 1 "test/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 1 "default/t.cpp"
#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 <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x;
    if (++i != size(m)) os << ' ';
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &v) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &v, OP op) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = op(p, x);
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
  rng ret = v;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = v[i];
  return ret;
}

template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
  vector<vector<int>> g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) {
  msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 4 "test/point_set_tree_path_composite_sum_fixed_root.test.cpp"
#define eb emplace_back
#define pb push_back
#line 1 "modint/MontgomeryModInt.cpp"
//reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10
//note: mod should be an odd prime less than 2^30.

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

  static constexpr u32 get_r() {
    u32 res = 1, base = mod;
    for(i32 i = 0; i < 31; i++)
      res *= base, base *= base;
    return -res;
  }

  static constexpr u32 get_mod() {
    return mod;
  }

  static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod
  static constexpr u32 r = get_r(); //-P^{-1} % 2^32

  u32 a;

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

  static u32 transform(const u64 &b) {
    return reduce(u64(b) * n2);
  }

  MontgomeryModInt() : a(0) {}
  MontgomeryModInt(const int64_t &b) 
    : a(transform(b % mod + mod)) {}

  mint pow(u64 k) const {
    mint res(1), base(*this);
    while(k) {
      if (k & 1) 
        res *= base;
      base *= base, k >>= 1;
    }
    return res;
  }

  mint inverse() const { return (*this).pow(mod - 2); }

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

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

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

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

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

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

  friend mint operator+(mint c, mint d) { return c += d; }
  friend mint operator-(mint c, mint d) { return c -= d; }
  friend mint operator*(mint c, mint d) { return c *= d; }
  friend mint operator/(mint c, mint d) { return c /= d; }

  friend ostream& operator<<(ostream& os, const mint& b) {
    return os << b.get();
  }
  friend istream& operator>>(istream& is, mint& b) {
    int64_t val;
    is >> val;
    b = mint(val);
    return is;
  }
};

using mint = MontgomeryModInt<998244353>;
#line 1 "ds/staticTopTree.cpp"
//rake keep left child as exposed path
//compress keep left child as higher path
struct static_top_tree {
  vector<vector<int>> g;
  int n;
  vector<int> l, r, lc, rc, pa;
  vector<bool> rake;

  using a2 = array<int, 2>;

  static_top_tree(vector<vector<int>> &_g, int R = 0)
    : g(_g), n(size(g)), l(n, -1), r(l), lc(l), rc(l), pa(l), rake(n) {
    vector<int> sz(n, 1);
    auto dfs = [&](int v, int p, auto &self) -> void {
      l[v] = v, r[v] = p;
      int mx_c = -1;
      for(int x : g[v]) {
        if (x == p) continue;
        self(x, v, self);
        sz[v] += sz[x];
        if (mx_c == -1 or sz[x] > sz[mx_c])
          mx_c = x;
      }
      if (auto ite = ranges::find(g[v], p); ite != g[v].end())
        g[v].erase(ite);
      if (mx_c != -1)
        swap(g[v][0], *ranges::find(g[v], mx_c));
    };

    dfs(R, -1, dfs);
    build(R);
  }

  int new_node(int _lc, int _rc, int _l, int _r, bool _rake) {
    lc.eb(_lc), rc.eb(_rc), l.eb(_l), r.eb(_r), pa.eb(-1), rake.eb(_rake);
    return pa[_lc] = pa[_rc] = ssize(lc) - 1;
  }

  a2 build(int s) {
    vector<int> path = {s};
    while(!g[path.back()].empty())
      path.eb(g[path.back()][0]);
    vector<a2> exposed = {{0, s}};
    for(int i = 0; int v : path | views::drop(1)) {
      priority_queue<a2, vector<a2>, greater<a2>> pq;
      pq.push({0, v});
      for(int x : g[path[i++]] | views::drop(1))
        pq.push(build(x));
      while(ssize(pq) > 1) {
        auto [h1, v1] = pq.top(); pq.pop();
        auto [h2, v2] = pq.top(); pq.pop();
        if (v2 == v) swap(v1, v2);
        int v3 = new_node(v1, v2, l[v1], r[v1], true);
        pq.push({max(h1, h2) + 1, v3});
        if (v1 == v) v = v3;
      }
      exposed.eb(pq.top());
    }
    auto dc = [&](int ql, int qr, auto &self) -> a2 {
      if (ql + 1 == qr) return exposed[ql];
      int mid = (ql + qr) / 2;
      auto [hl, vl] = self(ql, mid, self);
      auto [hr, vr] = self(mid, qr, self);
      int v = new_node(vl, vr, l[vr], r[vl], false);
      return {max(hl, hr) + 1, v};
    };
    return dc(0, ssize(exposed), dc);
  }
};
#line 1 "dp/dynamicTreeDP.cpp"
//#include "ds/staticTopTree.cpp"
template<class M, M(*rake)(const M&, const M&), M(*compress)(const M&, const M&)>
struct dynamic_tree_dp {
  vector<M> dp;
  static_top_tree stt;

  void pull(int v) {
    if (stt.rake[v]) dp[v] = rake(dp[stt.lc[v]], dp[stt.rc[v]]);
    else dp[v] = compress(dp[stt.lc[v]], dp[stt.rc[v]]);
  }

  dynamic_tree_dp(vector<vector<int>> &g, vector<M> &init)
    : dp(2 * ssize(g) - 1), stt(g) {
    for(int i = 0; i < ssize(g); i++)
      dp[i] = init[i];
    for(int i = ssize(g); i < 2 * ssize(g) - 1; i++)
      pull(i);
  }

  void set(int v, M x) {
    dp[v] = x;
    while((v = stt.pa[v]) != -1) pull(v);
  }

  M query() { return dp.back(); }
};
#line 9 "test/point_set_tree_path_composite_sum_fixed_root.test.cpp"

struct M {
  mint a, b, ans, sz;
};

M rake(const M &a, const M &b) {
  return M{a.a, a.b, a.ans + b.ans, a.sz + b.sz};
}
M compress(const M &a, const M &b) {
  return M{a.a * b.a, a.a * b.b + a.b, a.ans + b.ans * a.a + a.b * b.sz, a.sz + b.sz};
}

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n, q; cin >> n >> q;
  vector<mint> a(n);
  for(mint &x : a) cin >> x;

  vector<array<int, 4>> uvbc(n - 1);
  for(auto &[u, v, b, c] : uvbc)
    cin >> u >> v >> b >> c;

  vector<vector<int>> g(n);
  for(auto [u, v, _, __] : uvbc)
    g[u].eb(v), g[v].eb(u);
  uvbc.pb({-1, 0, 1, 0});

  static_top_tree stt(g);

  vector<int> eid(n);
  for(int i = 0; auto &[u, v, _, __] : uvbc) {
    if (stt.r[v] == u) swap(u, v);
    eid[u] = i++;
  }

  auto get = [&](int v) {
    auto [_, __, b, c] = uvbc[eid[v]];
    return M{b, c, a[v] * b + c, 1};
  };

  vector<M> init(n);
  for(int i = 0; i < n; i++)
    init[i] = get(i);

  dynamic_tree_dp<M, rake, compress> ddp(g, init);

  while(q--) {
    int op; cin >> op;
    if (op == 0) {
      int w, x; cin >> w >> x;
      a[w] = x;
      ddp.set(w, get(w));
    } else {
      int e, y, z; cin >> e >> y >> z;
      auto &[u, _, b, c] = uvbc[e];
      b = y, c = z;
      ddp.set(u, get(u));
    }
    cout << ddp.query().ans << '\n';
  }

  return 0;
}

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