CP-templates

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View the Project on GitHub Misuki743/CP-templates

:heavy_check_mark: test/vertex_set_path_composite.test.cpp

Depends on

Code

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

#include "../default/t.cpp"
#include "../modint/MontgomeryModInt.cpp"
#include "../segtree/segmentTree.cpp"
#include "../actedmonoid/actedMonoid_affineSum.cpp"
#include "../ds/heavyLightDecomposition.cpp"

using am = actedMonoid_affineSum<mint>;

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

  int n, q; cin >> n >> q;
  vector<am::T> ab(n);
  for(auto &[a, b] : ab)
    cin >> a >> b;
  vector<vector<int>> g(n);
  for(int i = 1; i < n; i++) {
    int u, v; cin >> u >> v;
    g[u].emplace_back(v);
    g[v].emplace_back(u);
  }

  HLD hld(g);
  vector<am::T> init(n);
  for(int i = 0; i < n; i++)
    init[hld.id[i]] = ab[i];
  segmentTree<am::T, am::Tid, am::Top> st(init);
  ranges::reverse(init);
  segmentTree<am::T, am::Tid, am::Top> str(init);

  while(q--) {
    int t, a, b, c; cin >> t >> a >> b >> c;
    if (t == 0) {
      st.set(hld.id[a], am::T{b, c});
      str.set((n - 1) - hld.id[a], am::T{b, c});
    } else {
      auto res = am::T{0, c};
      for(auto [l, r, rev] : hld.query(a, b)) {
        if (rev)
          res = am::Top(res, str.query(n - r, n - l));
        else
          res = am::Top(res, st.query(l, r));
      }
      cout << res[1] << '\n';
    }
  }

  return 0;
}
#line 1 "test/vertex_set_path_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"

#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 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 "segtree/segmentTree.cpp"
template<class M, M(*id)(), M(*op)(const M&, const M&)>
struct segmentTree {
  int size;
  vector<M> data;

  segmentTree(int _size) : size(_size), data(2 * size, id()) {}
  segmentTree(vector<M> init) : size(ssize(init)), data(2 * size, id()) {
    ranges::copy(init, data.begin() + size);
    for(int i = size - 1; i > 0; i--)
      data[i] = op(data[i << 1], data[i << 1 | 1]);
  }

  void set(int i, M x) {
    data[i += size] = x;
    while(i >>= 1)
      data[i] = op(data[i << 1], data[i << 1 | 1]);
  }

  M get(int i) { return data[i + size]; }

  M query(int l, int r) {
    M L = id(), R = id();
    for(l += size, r += size; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = op(L, data[l++]);
      if (r & 1) R = op(data[--r], R);
    }
    return op(L, R);
  }

  //return first j in [i, size) s.t. f(op([l, j])) is true,
  //assume f(id()) is false.
  int firstTrue(int i, function<bool(const M&)> f) {
    vector<int> idL, idR;
    for(int l = i + size, r = size << 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) idL.emplace_back(l++);
      if (r & 1) idR.emplace_back(--r);
    }
    idL.insert(idL.end(), idR.rbegin(), idR.rend());
    M pre = id();
    int v = -1;
    for(int j : idL) {
      if (f(op(pre, data[j]))) {
        v = j;
        break;
      } else {
        pre = op(pre, data[j]);
      }
    }
    if (v == -1) return size;
    while(v < size) {
      if (f(op(pre, data[v << 1])))
        v = v << 1;
      else
        pre = op(pre, data[v << 1]), v = v << 1 | 1;
    }
    return v - size;
  }

  int lastTrue(int i, function<bool(const M&)> f) {
    vector<int> idL, idR;
    for(int l = size, r = (i + 1) + size; l < r; l >>= 1, r >>= 1) {
      if (l & 1) idL.emplace_back(l++);
      if (r & 1) idR.emplace_back(--r);
    }
    idR.insert(idR.end(), idL.rbegin(), idL.rend());
    M suf = id();
    int v = -1;
    for(int j : idR) {
      if (f(op(data[j], suf))) {
        v = j;
        break;
      } else {
        suf = op(data[j], suf);
      }
    }
    if (v == -1) return -1;
    while(v < size) {
      if (f(op(data[v << 1 | 1], suf)))
        v = v << 1 | 1;
      else
        suf = op(data[v << 1 | 1], suf), v = v << 1;
    }
    return v - size;
  }
};
#line 1 "actedmonoid/actedMonoid_affineSum.cpp"
template<class U>
struct actedMonoid_affineSum {
  using M = array<U, 2>;
  static M Mid() { return M{0, 0}; }
  static M Mop(const M &a, const M &b) { return {a[0] + b[0], a[1] + b[1]}; }
  using T = array<U, 2>;
  static T Tid() { return T{1, 0}; }
  static T Top(const T &a, const T &b) { return T{a[0] * b[0], a[1] * b[0] + b[1]}; }
  static M act(const M &a, const T &b) { return {a[0] * b[0] + a[1] * b[1], a[1]}; }
};
#line 1 "ds/heavyLightDecomposition.cpp"
struct HLD {
  int n;
  vector<int> dep, p, head, id;

  HLD(vector<vector<int>> &g, vector<int> root = vector<int>(1, 0))
  : n(ssize(g)), dep(n), p(n, -1), head(n), id(n) {
    vector<int> sz(n, 1);

    auto dfs = [&](int v, auto self) -> void {
      int mx = -1;
      for(int i = -1; int x : g[v]) {
        i++;
        if (x == p[v]) continue;
        p[x] = v, dep[x] = dep[v] + 1;
        self(x, self);
        sz[v] += sz[x];
        if (mx == -1 or sz[x] > sz[g[v][mx]]) mx = i;
      }
      if (mx != -1) swap(g[v][0], g[v][mx]);
    };

    int nxt = 0;
    auto cut = [&](int v, int h, auto self) -> void {
      id[v] = nxt++, head[v] = h;
      if (!g[v].empty() and g[v][0] != p[v])
        self(g[v][0], h, self);
      for(int x : g[v] | views::drop(1)) if (x != p[v])
          self(x, x, self);
    };

    for(int x : root) {
      dfs(x, dfs);
      cut(x, x, cut);
    }
  }

  //(l, r, rev)
  vector<tuple<int, int, bool>> query(int u, int v, bool edge = false) {
    vector<array<int, 2>> resL, resR;
    while(head[u] != head[v]) {
      if (dep[head[u]] >= dep[head[v]]) {
        resL.push_back({id[head[u]], id[u] + 1});
        u = p[head[u]];
      } else {
        resR.push_back({id[head[v]], id[v] + 1});
        v = p[head[v]];
      }
    }
    if (id[v] + edge <= id[u])
      resL.push_back({id[v] + edge, id[u] + 1});
    else if (id[u] + edge <= id[v])
      resR.push_back({id[u] + edge, id[v] + 1});
    vector<tuple<int, int, bool>> res;
    for(auto [l, r] : resL)
      res.push_back({l, r, true});
    for(auto [l, r] : resR | views::reverse)
      res.push_back({l, r, false});
    return res;
  }
};
#line 8 "test/vertex_set_path_composite.test.cpp"

using am = actedMonoid_affineSum<mint>;

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

  int n, q; cin >> n >> q;
  vector<am::T> ab(n);
  for(auto &[a, b] : ab)
    cin >> a >> b;
  vector<vector<int>> g(n);
  for(int i = 1; i < n; i++) {
    int u, v; cin >> u >> v;
    g[u].emplace_back(v);
    g[v].emplace_back(u);
  }

  HLD hld(g);
  vector<am::T> init(n);
  for(int i = 0; i < n; i++)
    init[hld.id[i]] = ab[i];
  segmentTree<am::T, am::Tid, am::Top> st(init);
  ranges::reverse(init);
  segmentTree<am::T, am::Tid, am::Top> str(init);

  while(q--) {
    int t, a, b, c; cin >> t >> a >> b >> c;
    if (t == 0) {
      st.set(hld.id[a], am::T{b, c});
      str.set((n - 1) - hld.id[a], am::T{b, c});
    } else {
      auto res = am::T{0, c};
      for(auto [l, r, rev] : hld.query(a, b)) {
        if (rev)
          res = am::Top(res, str.query(n - r, n - l));
        else
          res = am::Top(res, st.query(l, r));
      }
      cout << res[1] << '\n';
    }
  }

  return 0;
}
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