CP-templates

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:heavy_check_mark: test/dynamic_sequence_range_affine_range_sum.test.cpp

Depends on

Code

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

#include "../default/t.cpp"
#include "../modint/MontgomeryModInt.cpp"
#include "../ds/treap.cpp"
#include "../actedmonoid/actedMonoid_affineSum.cpp"

using am = actedMonoid_affineSum<mint>;
using Treap = treap<am::M, am::Mid, am::Mop, am::T, am::Tid, am::Top, am::act>;

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

  int n, q; cin >> n >> q;
  vector<array<mint, 2>> a(n, {0, 1});
  for(auto &[x, _] : a)
    cin >> x;

  Treap::node* tr = Treap::build(a);

  while(q--) {
    int t; cin >> t;
    if (t == 0) {
      int i, x; cin >> i >> x;
      Treap::insert(tr, i, {x, 1});
    } else if (t == 1) {
      int i; cin >> i;
      Treap::erase(tr, i);
    } else if (t == 2) {
      int l, r; cin >> l >> r;
      Treap::modify(tr, l, r, am::Tid(), true);
    } else if (t == 3) {
      int l, r, b, c; cin >> l >> r >> b >> c;
      Treap::modify(tr, l, r, {b, c});
    } else if (t == 4) {
      int l, r; cin >> l >> r;
      cout << Treap::query(tr, l, r)[0] << '\n';
    }
  }

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

#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 "ds/treap.cpp"
mt19937 rng(clock);

template<class M, M(*Mid)(), M(*Mop)(const M&, const M&), class T, T(*Tid)(), T(*Top)(const T&, const T&), M(*act)(const M&, const T&)>
struct treap {
  struct node {
    int pri, size = 1;
    bool rev = false;
    node *l = nullptr, *r = nullptr;
    M data, prod;
    T tag;
    node(M init = M()) : pri(rng()), data(init), prod(init), tag(Tid()) {}
  };

  static int size(node *v) { return v ? v -> size : 0; }
  static M get(node *v) { return v ? v -> prod : Mid(); }

  static node* build(vector<M> init) {
    node* r = nullptr;
    for(M &x : init) r = merge(r, new node(x));
    return r;
  }

  static void apply(node *v, T x, bool rev) {
    if (!v) return;
    if (x != Tid()) {
      v -> data = act(v -> data, x);
      v -> prod = act(v -> prod, x);
      v -> tag = Top(v -> tag, x);
    }
    if (rev) {
      v -> rev ^= 1;
      swap(v -> l, v -> r);
    }
  }

  static void push(node *v) {
    if (!v) return;
    for(node* c : {v -> l, v -> r})
      apply(c, v -> tag, v -> rev);
    v -> tag = Tid(), v -> rev = false;
  }

  static void pull(node *v) {
    if (!v) return;
    v -> size = 1, v -> prod = v -> data;
    if (node* lc = v -> l; lc) {
      v -> size += lc -> size;
      v -> prod = Mop(lc -> prod, v -> prod);
    }
    if (node* rc = v -> r; rc) {
      v -> size += rc -> size;
      v -> prod = Mop(v -> prod, rc -> prod);
    }
  }

  static void split(node *v, int x, node *&l, node *&r, int add = 0) {
    if (!v) {
      l = r = nullptr;
      return;
    }
    push(v);
    if (int key = add + size(v -> l); key < x)
      split(v -> r, x, v -> r, r, add + size(v -> l) + 1), l = v;
    else
      split(v -> l, x, l, v -> l, add), r = v;
    pull(v);
  }

  static node* merge(node *l, node *r) {
    if (!l or !r) return l ? l : r;
    push(l), push(r);
    if (l -> pri < r -> pri) {
      l -> r = merge(l -> r, r);
      pull(l);
      return l;
    } else {
      r -> l = merge(l, r -> l);
      pull(r);
      return r;
    }
  }

  static array<node*, 3> cut(node *root, int l, int r) {
    array<node*, 3> tmp = {};
    split(root, l, tmp[0], tmp[1]);
    split(tmp[1], r - l, tmp[1], tmp[2]);
    return tmp;
  }

  static node* uncut(array<node*, 3> roots) {
    return merge(roots[0], merge(roots[1], roots[2]));
  }

  static void modify(node *root, int l, int r, T x, bool rev = false) {
    auto tmp = cut(root, l, r);
    apply(tmp[1], x, rev);
    uncut(tmp);
  }

  static M query(node *root, int l, int r) {
    auto tmp = cut(root, l, r);
    M res = get(tmp[1]);
    uncut(tmp);
    return res;
  }

  static void insert(node *&root, int i, M x) {
    array<node*, 3> tmp = {};
    tmp[1] = new node(x);
    split(root, i, tmp[0], tmp[2]);
    root = uncut(tmp);
  }

  static void erase(node *&root, int i) {
    auto tmp = cut(root, i, i + 1);
    delete tmp[1];
    tmp[1] = nullptr;
    root = uncut(tmp);
  }
};
#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 7 "test/dynamic_sequence_range_affine_range_sum.test.cpp"

using am = actedMonoid_affineSum<mint>;
using Treap = treap<am::M, am::Mid, am::Mop, am::T, am::Tid, am::Top, am::act>;

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

  int n, q; cin >> n >> q;
  vector<array<mint, 2>> a(n, {0, 1});
  for(auto &[x, _] : a)
    cin >> x;

  Treap::node* tr = Treap::build(a);

  while(q--) {
    int t; cin >> t;
    if (t == 0) {
      int i, x; cin >> i >> x;
      Treap::insert(tr, i, {x, 1});
    } else if (t == 1) {
      int i; cin >> i;
      Treap::erase(tr, i);
    } else if (t == 2) {
      int l, r; cin >> l >> r;
      Treap::modify(tr, l, r, am::Tid(), true);
    } else if (t == 3) {
      int l, r, b, c; cin >> l >> r >> b >> c;
      Treap::modify(tr, l, r, {b, c});
    } else if (t == 4) {
      int l, r; cin >> l >> r;
      cout << Treap::query(tr, l, r)[0] << '\n';
    }
  }

  return 0;
}
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