library_for_cpp

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

View the Project on GitHub Kazun1998/library_for_cpp

:heavy_check_mark: verify/yosupo_library_checker/data_structure/Lazy_Segment_Tree.test.cpp

Depends on

Code

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

#include"../../../template/template.hpp"
#include"../../../Algebra/modint.hpp"
#include"../../../Segment_Tree/Lazy_Segment_Tree.hpp"

using L = modint<998244353>;
using M = pair<L, int>;
using F = pair<L, L>;

auto op = [](M x, M y) -> M {
    auto first  = x.first  + y.first;
    auto second = x.second + y.second;
    return { first, second };
};

auto act = [](F a, M x) -> M {
    auto first  = a.first * x.first + a.second * x.second;
    auto second = x.second;
    return { first, second };
};

auto comp = [](F a, F b) -> F {
    auto first  = a.first * b.first;
    auto second = a.first * b.second + a.second;
    return { first, second };
};

M unit = make_pair(0, 0);
F id = make_pair(1, 0);

int main(){
    int N, Q; cin >> N >> Q;

    vector<M> a(N);
    for (int i = 0; i < N; i++){
        int x; scanf("%d", &x);
        a[i] = {x, 1};
    }

    Lazy_Segment_Tree<M, F> S(a, op, unit, act, comp, id);

    for (int q = 0; q < Q; q++){
        int t, l, r;
        scanf("%d", &t);

        if (t == 0){
            int b, c;
            scanf("%d%d%d%d", &l, &r, &b, &c);
            S.action(l, r - 1, {b, c});
        } elif (t == 1) {
            scanf("%d%d", &l, &r);
            cout << S.product(l, r - 1).first << "\n";
        }
    }
}
#line 1 "verify/yosupo_library_checker/data_structure/Lazy_Segment_Tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"

#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 2 "template/utility.hpp"

using ll = long long;

// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
    return (a < b ? a = b, 1: 0);
}

// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
    return (a > b ? a = b, 1: 0);
}
#line 59 "template/template.hpp"

// math
#line 2 "template/math.hpp"

// 除算に関する関数

// floor(x / y) を求める.
template<typename T, typename U>
T div_floor(T x, U y){ return (x > 0 ? x / y: (x - y + 1) / y); }

// ceil(x / y) を求める.
template<typename T, typename U>
T div_ceil(T x, U y){ return (x > 0 ? (x + y - 1) / y: x / y) ;}

// x を y で割った余りを求める.
template<typename T, typename U>
T mod(T x, U y){
    T q = div_floor(x, y);
    return x - q * y ;
}

// x を y で割った商と余りを求める.
template<typename T, typename U>
pair<T, T> divmod(T x, U y){
    T q = div_floor(x, y);
    return {q, x - q * y};
}

// 四捨五入を求める.
template<typename T, typename U>
T round(T x, U y){
    T q, r;
    tie (q, r) = divmod(x, y);
    return (r >= div_ceil(y, 2)) ? q + 1 : q;
}

// 指数に関する関数

// x の y 乗を求める.
ll intpow(ll x, ll y){
    ll a = 1;
    while (y){
        if (y & 1) { a *= x; }
        x *= x;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
ll modpow(ll x, ll y, ll z){
    ll a = 1;
    while (y){
        if (y & 1) { (a *= x) %= z; }
        (x *= x) %= z;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
template<typename T, typename U>
T modpow(T x, U y, T z) {
    T a = 1;
    while (y) {
        if (y & 1) { (a *= x) %= z; }

        (x *= x) %= z;
        y >>= 1;
    }

    return a;
}

// vector の要素の総和を求める.
ll sum(vector<ll> &X){
    ll y = 0;
    for (auto &&x: X) { y+=x; }
    return y;
}

// vector の要素の総和を求める.
template<typename T>
T sum(vector<T> &X){
    T y = T(0);
    for (auto &&x: X) { y += x; }
    return y;
}

// a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める.
tuple<ll, ll, ll> Extended_Euclid(ll a, ll b) {
    ll s = 1, t = 0, u = 0, v = 1;
    while (b) {
        ll q;
        tie(q, a, b) = make_tuple(div_floor(a, b), b, mod(a, b));
        tie(s, t) = make_pair(t, s - q * t);
        tie(u, v) = make_pair(v, u - q * v);
    }

    return make_tuple(s, u, a);
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll isqrt(const ll &N) { 
    if (N <= 0) { return 0; }

    ll x = sqrt(N);
    while ((x + 1) * (x + 1) <= N) { x++; }
    while (x * x > N) { x--; }

    return x;
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll floor_sqrt(const ll &N) { return isqrt(N); }

// ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll ceil_sqrt(const ll &N) {
    ll x = isqrt(N);
    return x * x == N ? x : x + 1;
}
#line 62 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }

void print(){ cout << "\n"; }

template<class T, class... Ts>
void print(const T& a, const Ts&... b){
    cout << a;
    (cout << ... << (cout << " ", b));
    cout << "\n";
}

template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
    is >> P.first >> P.second;
    return is;
}

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

template<typename T>
vector<T> vector_input(int N, int index){
    vector<T> X(N+index);
    for (int i=index; i<index+N; i++) cin >> X[i];
    return X;
}

template<typename T>
istream &operator>>(istream &is, vector<T> &X){
    for (auto &x: X) { is >> x; }
    return is;
}

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

template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
    int i = 0;
    for (T a: S) {os << (i ? " ": "") << a; i++;}
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}
#line 65 "template/template.hpp"

// macro
#line 2 "template/macro.hpp"

// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
#define until(cond) while (!(cond))
#define loop while (true)

// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name

// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 68 "template/template.hpp"

// bitop
#line 2 "template/bitop.hpp"

// 非負整数 x の bit legnth を求める.
ll bit_length(ll x) {
    if (x == 0) { return 0; }
    return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x);
}

// 非負整数 x の popcount を求める.
ll popcount(ll x) { return __builtin_popcountll(x); }

// 正の整数 x に対して, floor(log2(x)) を求める.
ll floor_log2(ll x) { return bit_length(x) - 1; }

// 正の整数 x に対して, ceil(log2(x)) を求める.
ll ceil_log2(ll x) { return bit_length(x - 1); }

// x の第 k ビットを取得する
int get_bit(ll x, int k) { return (x >> k) & 1; }

// x のビット列を取得する.
// k はビット列の長さとする.
vector<int> get_bits(ll x, int k) {
    vector<int> bits(k);
    rep(i, k) {
        bits[i] = x & 1;
        x >>= 1;
    }

    return bits;
}

// x のビット列を取得する.
vector<int> get_bits(ll x) { return get_bits(x, bit_length(x)); }
#line 2 "Algebra/modint.hpp"

#line 4 "Algebra/modint.hpp"

template<int M>
class modint {
    public:
    static constexpr int Mod = M; 
    int64_t x;

    public:
    // 初期化
    constexpr modint(): x(0) {}
    constexpr modint(int64_t a): x((a % Mod + Mod) % Mod) {}

    // マイナス元
    modint operator-() const { return modint(-x); }

    // 加法
    modint& operator+=(const modint &b){
        if ((x += b.x) >= Mod) x -= Mod;
        return *this;
    }

    friend modint operator+(const modint &x, const modint &y) { return modint(x) += y; }

    // 減法
    modint& operator-=(const modint &b){
        if ((x += Mod - b.x) >= Mod) x -= Mod;
        return *this;
    }

    friend modint operator-(const modint &x, const modint &y) { return modint(x) -= y; }

    // 乗法
    modint& operator*=(const modint &b){
        (x *= b.x) %= Mod;
        return *this;
    }

    friend modint operator*(const modint &x, const modint &y) { return modint(x) *= y; }
    friend modint operator*(const int &x, const modint &y) { return modint(x) *= y; }
    friend modint operator*(const ll &x, const modint &y) { return modint(x) *= y; }

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

    friend modint operator/(const modint &x, const modint &y) { return modint(x) /= y; }

    modint inverse() const {
        int64_t s = 1, t = 0;
        int64_t a = x, b = Mod;

        while (b > 0) {
            int64_t q = a / b;

            a -= q * b; swap(a, b);
            s -= q * t; swap(s, t);
        }

        assert (a == 1);

        return modint(s);
    }

    // 比較
    friend bool operator==(const modint &a, const modint &b) { return (a.x == b.x); }
    friend bool operator==(const modint &a, const int &b) { return a.x == mod(b, Mod); }
    friend bool operator!=(const modint &a, const modint &b) { return (a.x != b.x); }

    // 入力
    friend istream &operator>>(istream &is, modint &a) {
        is >> a.x;
        a.x = (a.x % Mod + Mod) % Mod;
        return is;
    }

    // 出力
    friend ostream &operator<<(ostream &os, const modint &a) { return os << a.x; }

    bool is_zero() const { return x == 0; }
    bool is_member(ll a) const { return x == (a % Mod + Mod) % Mod; }
};

template<int Mod>
modint<Mod> pow(modint<Mod> x, long long n) {
    if (n < 0) { return pow(x, -n).inverse(); }

    auto res = modint<Mod>(1);
    for (; n; n >>= 1) {
        if (n & 1) { res *= x; }
        x *= x;
    }

    return res;
}
#line 2 "Segment_Tree/Lazy_Segment_Tree.hpp"

/* 遅延セグメント木
M を Monoid とする. M 上の列に対して, Monid F からの区間作用と, 連続部分列に対する区間積の計算の処理を高速に行う.

* M: Monoid
* F: Monoid
* op: M x M → M: M 上の演算
* unit: M の単位元
* act: F x M → M: F からの M の演算
* comp: F x F → F: F 同士の合成 (左の要素が新しい)
* id: F の単位元

(条件)
M: Monoid, F = {f: F x M → M: 作用素} に対して, 以下が成立する.
* F は写像の合成に閉じている. つまり, 任意の f,g in F に対して, comp(f,g) in F
* F は M に作用する. つまり, 以下が成り立つ.
    * F の単位元 id は恒等的に作用する. つまり, 任意の x in M に対して id(x) = x となる.
    * 任意の f in F, x,y in M に対して, f(xy) = f(x) f(y) である.


(注意)
作用素は左から掛ける. 更新も左から行う.
*/

template<typename M, typename F>
class Lazy_Segment_Tree {
    public:
    int n, depth;
    const function<M(M, M)> op;
    const function<M(F, M)> act;
    const function<F(F, F)> comp;
    vector<M> data; const M unit;
    vector<F> lazy; const F id;

    public:
    Lazy_Segment_Tree(int size, const function<M(M, M)> op, const M unit, const function<M(F, M)> act, const function<F(F, F)> comp, const F id):
        n(), op(op), unit(unit), act(act), comp(comp), id(id), depth(0) {
            int m = 1;
            while (size > m) { depth++, m *= 2; }
            n = m;
            data.assign(2 * m, unit);
            lazy.assign(2 * m, id);
        }

    Lazy_Segment_Tree(const vector<M> &vec, const function<M(M, M)> op, const M unit, const function<M(F, M)> act, const function<F(F, F)> comp, const F id):
        Lazy_Segment_Tree(vec.size(), op, unit, act, comp, id){
            for (int k = 0; k < vec.size(); k++) { data[k+n] = vec[k]; }
            for (int k = n - 1; k > 0; k--) { data[k] = op(data[k << 1], data[k << 1 | 1]); }
        }

    private:
    inline M evaluate_at(int m){ return lazy[m] == id ? data[m] : act(lazy[m], data[m]); }

    void propagate_at(int m){
        data[m] = evaluate_at(m);

        if ((m < n) && (lazy[m] != id)){
            int left = m << 1;
            lazy[left] = (lazy[left] == id) ? lazy[m] : comp(lazy[m], lazy[left]);

            int right = m << 1 | 1;
            lazy[right] = (lazy[right] == id) ? lazy[m] : comp(lazy[m], lazy[right]); 
        }

        lazy[m] = id;
    }

    inline void propagate_above(int m){
        int h = 0, mm = m;
        for (mm; mm; mm >>= 1, h++){}

        for (h--; h >= 0; h--) { propagate_at(m>>h); }
    }

    inline void recalc_above(int m){
        while (m > 1){
            m >>= 1;
            data[m] = op(evaluate_at(m << 1), evaluate_at(m << 1 | 1));
        }
    }

    pair<int, int> range_propagate(int l, int r){
        int X = l + n, Y = r + n - 1, L0 = -1, R0 = -1;
    
        while (X < Y){
            if (X & 1) { L0 = max(L0, X++); }
            if ((Y & 1) ==0 ) { R0 = max(R0, Y--); }

            X >>= 1; Y >>= 1;
        }

        L0 = max(L0, X); R0 = max(R0, Y);
        propagate_above(L0); propagate_above(R0);
        return make_pair(L0, R0);
    }

    public:
    // 第 k 項を取得する.
    inline M operator[](int k){
        int m = k + n;
        propagate_above(m);
        lazy[m] = id;
        return data[m] = evaluate_at(m);
    }

    // i = l, l + 1, ..., r に対して, alpha を作用させる.
    // 作用の範囲が閉区間であることに注意.
    void action(int l, int r, F alpha){
        int L0, R0;
        tie(L0, R0) = range_propagate(l, r + 1);

        int L = l + n, R = r + n + 1;
        while (L < R){
            if (L & 1){
                lazy[L] = (alpha == id) ? id : comp(alpha, lazy[L]); 
                L++;
            }

            if (R & 1){
                R--;
                lazy[R] = (alpha == id) ? id : comp(alpha, lazy[R]);
            }

            L >>= 1; R >>= 1;
        }

        recalc_above(L0); recalc_above(R0);
    }

    // 第 k 項を x に更新する.
    inline void update(int k, M x){
        int m = k + n;
        propagate_above(m);
        data[m] = x; lazy[m] = id;
        recalc_above(m);
    }

    // 積 x[l] * x[l + 1] * ... * x[r] を求める.
    // 積を取る範囲が閉区間であることに注意.
    M product(int l, int r){
        int L0, R0;
        tie(L0, R0) = range_propagate(l, r + 1);

        int L = l + n, R = r + n + 1;
        M vL = unit, vR = unit;
        while (L < R){
            if (L & 1) { vL = op(vL, evaluate_at(L)); L++; }
            if (R & 1) { R--; vR=op(evaluate_at(R), vR); }

            L >>= 1; R >>= 1;
        }

        return op(vL, vR);
    }

    // 全要素の積を求める.
    inline M all_product() {return product(0, n);}

    void refresh() {
        for (int m = 1; m < 2 * n; m++){
            data[m] = evaluate_at(m);
            if ((m < n) && (lazy[m] != id)){
                int left = m << 1;
                lazy[left] = (lazy[left] == id) ? lazy[m] : comp(lazy[m], lazy[left]);

                int right = m << 1 | 1;
                lazy[right] = (lazy[right] == id) ? lazy[m] : comp(lazy[m], lazy[m << 1 | 1]);
            }
            lazy[m] = id;
        }
    }
};
#line 6 "verify/yosupo_library_checker/data_structure/Lazy_Segment_Tree.test.cpp"

using L = modint<998244353>;
using M = pair<L, int>;
using F = pair<L, L>;

auto op = [](M x, M y) -> M {
    auto first  = x.first  + y.first;
    auto second = x.second + y.second;
    return { first, second };
};

auto act = [](F a, M x) -> M {
    auto first  = a.first * x.first + a.second * x.second;
    auto second = x.second;
    return { first, second };
};

auto comp = [](F a, F b) -> F {
    auto first  = a.first * b.first;
    auto second = a.first * b.second + a.second;
    return { first, second };
};

M unit = make_pair(0, 0);
F id = make_pair(1, 0);

int main(){
    int N, Q; cin >> N >> Q;

    vector<M> a(N);
    for (int i = 0; i < N; i++){
        int x; scanf("%d", &x);
        a[i] = {x, 1};
    }

    Lazy_Segment_Tree<M, F> S(a, op, unit, act, comp, id);

    for (int q = 0; q < Q; q++){
        int t, l, r;
        scanf("%d", &t);

        if (t == 0){
            int b, c;
            scanf("%d%d%d%d", &l, &r, &b, &c);
            S.action(l, r - 1, {b, c});
        } elif (t == 1) {
            scanf("%d%d", &l, &r);
            cout << S.product(l, r - 1).first << "\n";
        }
    }
}
Back to top page