test/library_checker/data_structure/range_set_range_composite.test.cpp

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• Last update: 2024-11-03 21:58:22+09:00
• Problem: https://judge.yosupo.jp/problem/range_set_range_composite

Depends on

• lib/data_structure/lazy_segment_tree.hpp
• ModInt (lib/math/modint.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/range_set_range_composite"
#include <bits/stdc++.h>
using namespace std;

#include "../../../lib/math/modint.hpp"
#include "../../../lib/data_structure/lazy_segment_tree.hpp"

using mint = ModInt<998244353>;

struct S{
    mint a, b;
    long long size;
};

struct F{
    mint a, b;
    bool id = false;
};

F ID = {1, 0, true};

S op(S l, S r){
    return{l.a * r.a, r.a * l.b + r.b, l.size + r.size};
}

S e(){
    return S{1, 0};
}

S mapping(F f, S x){
    if(f.id){
        return x;
    }
    auto spow = [](S a, long long n){
        S ret = {1, 0, 0};
        while(n > 0){
            if(n & 1) ret = op(ret, a);
            a = op(a, a);
            n >>= 1;
        }
        return ret;
    };
    S pr = spow(S{f.a, f.b, 0}, x.size);
    return S{pr.a, pr.b, x.size};
}

F composition(F f, F g){
    if(f.id){
        return g;
    }
    return f;
}

F id(){
    return ID;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, q;
    cin >> n >> q;
    vector<S> p(n);
    for(int i = 0; i < n; i++){
        int a, b;
        cin >> a >> b;
        p[i] = S{a, b, 1};
    }
    LazySegTree<S, op, e, F, mapping, composition, id> seg(p);
    while(q--){
        int t;
        cin >> t;
        if(t == 0){
            int l, r, c, d;
            cin >> l >> r >> c >> d;
            seg.apply(l, r, F{c, d, false});
        } else{
            int l, r;
            mint x;
            cin >> l >> r >> x;
            S pr = seg.query(l, r);
            cout << pr.a * x + pr.b << "\n";
        }
    }
}

#line 1 "test/library_checker/data_structure/range_set_range_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_set_range_composite"
#include <bits/stdc++.h>
using namespace std;

#line 2 "lib/math/modint.hpp"

#line 5 "lib/math/modint.hpp"

/**
 * @brief ModInt
 * @docs docs/math/modint.md
 */

template <long long Modulus>
struct ModInt{
    long long val;
    static constexpr int mod() { return Modulus; }
    constexpr ModInt(const long long _val = 0) noexcept : val(_val) {
        normalize();
    }
    void normalize(){
        val = (val % Modulus + Modulus) % Modulus;
    }
    inline ModInt &operator+=(const ModInt &rhs) noexcept {
        if(val += rhs.val, val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt &operator-=(const ModInt &rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus;
        return *this;
    }
    inline ModInt &operator*=(const ModInt &rhs) noexcept {
        val = val * rhs.val % Modulus;
        return *this;
    }
    inline ModInt &operator/=(const ModInt &rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus;
        return *this;
    }
    inline ModInt &operator++() noexcept {
        if(++val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus) val -= Modulus;
        return t;
    }
    inline ModInt &operator--() noexcept {
        if(--val < 0) val += Modulus;
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus;
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
    inline ModInt inv(void) const { return inv(val); }
    ModInt pow(long long n) const {
        assert(0 <= n);
        ModInt x = *this, r = 1;
        while(n){
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    ModInt inv(const long long n) const {
        long long a = n, b = Modulus, u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; std::swap(a, b);
            u -= t * v; std::swap(u, v);
        }
        u %= Modulus;
        if(u < 0) u += Modulus;
        return u;
    }
    friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline std::istream &operator>>(std::istream &is, ModInt &x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline std::ostream &operator<<(std::ostream &os, const ModInt &x) noexcept { return os << x.val; }
};
#line 2 "lib/data_structure/lazy_segment_tree.hpp"

template <class S,
    S(*op)(S, S),
    S(*e)(),
    class F,
    S(*mapping)(F, S),
    F(*composition)(F, F),
    F(*id)()>
struct LazySegTree{
private:
    int _n, size, log;
    vector<S> d;
    vector<F> lz;

    void pull(int k){ d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f){
        d[k] = mapping(f, d[k]);
        if(k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k){
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }

public:
    LazySegTree() : LazySegTree(0){}
    LazySegTree(int n) : LazySegTree(vector<S>(n, e())){}
    LazySegTree(const vector<S> &v) : _n(int(v.size())){
        log = 0;
        size = 1;
        while(size < _n) size <<= 1, log++;
        d = vector<S>(2 * size, e());
        lz = vector<F>(size, id());
        for(int i = 0; i < _n; i++) d[size + i] = v[i];
        for(int i = size - 1; i >= 1; i--){
            pull(i);
        }
    }

    void update(int p, S x){
        assert(0 <= p && p < _n);
        p += size;
        for(int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for(int i = 1; i <= log; i++) pull(p >> i);
    }

    S get(int p){
        assert(0 <= p && p < _n);
        p += size;
        for(int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S query(int l, int r){
        assert(0 <= l && l <= r && r <= _n);
        if(l == r) return e();

        l += size;
        r += size;

        for(int i = log; i >= 1; i--){
            if(((l >> i) << i) != l) push(l >> i);
            if(((r >> i) << i) != r) push(r >> i);
        }

        S sml = e(), smr = e();
        while(l < r){
            if(l & 1) sml = op(sml, d[l++]);
            if(r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_query(){ return d[1]; }

    void apply(int p, F f){
        assert(0 <= p && p < _n);
        p += size;
        for(int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for(int i = 1; i <= log; i++) pull(p >> i);
    }
    void apply(int l, int r, F f){
        assert(0 <= l && l <= r && r <= _n);
        if(l == r) return;

        l += size;
        r += size;

        for(int i = log; i >= 1; i--){
            if(((l >> i) << i) != l) push(l >> i);
            if(((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while(l < r){
                if(l & 1) all_apply(l++, f);
                if(r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for(int i = 1; i <= log; i++){
            if(((l >> i) << i) != l) pull(l >> i);
            if(((r >> i) << i) != r) pull((r - 1) >> i);
        }
    }

    template <bool (*g)(S)>
    int max_right(int l){
        return max_right(l, [](S x){ return g(x); });
    }
    template <class G>
    int max_right(int l, G g){
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if(l == _n) return _n;
        l += size;
        for(int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do{
            while(l % 2 == 0) l >>= 1;
            if(!g(op(sm, d[l]))){
                while(l < size){
                    push(l);
                    l = (2 * l);
                    if(g(op(sm, d[l]))){
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)>
    int min_left(int r){
        return min_left(r, [](S x){ return g(x); });
    }
    template <class G>
    int min_left(int r, G g){
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if(r == 0) return 0;
        r += size;
        for(int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do{
            r--;
            while(r > 1 && (r % 2)) r >>= 1;
            if(!g(op(d[r], sm))){
                while(r < size){
                    push(r);
                    r = (2 * r + 1);
                    if(g(op(d[r], sm))){
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while((r & -r) != r);
        return 0;
    }
};
#line 7 "test/library_checker/data_structure/range_set_range_composite.test.cpp"

using mint = ModInt<998244353>;

struct S{
    mint a, b;
    long long size;
};

struct F{
    mint a, b;
    bool id = false;
};

F ID = {1, 0, true};

S op(S l, S r){
    return{l.a * r.a, r.a * l.b + r.b, l.size + r.size};
}

S e(){
    return S{1, 0};
}

S mapping(F f, S x){
    if(f.id){
        return x;
    }
    auto spow = [](S a, long long n){
        S ret = {1, 0, 0};
        while(n > 0){
            if(n & 1) ret = op(ret, a);
            a = op(a, a);
            n >>= 1;
        }
        return ret;
    };
    S pr = spow(S{f.a, f.b, 0}, x.size);
    return S{pr.a, pr.b, x.size};
}

F composition(F f, F g){
    if(f.id){
        return g;
    }
    return f;
}

F id(){
    return ID;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, q;
    cin >> n >> q;
    vector<S> p(n);
    for(int i = 0; i < n; i++){
        int a, b;
        cin >> a >> b;
        p[i] = S{a, b, 1};
    }
    LazySegTree<S, op, e, F, mapping, composition, id> seg(p);
    while(q--){
        int t;
        cin >> t;
        if(t == 0){
            int l, r, c, d;
            cin >> l >> r >> c >> d;
            seg.apply(l, r, F{c, d, false});
        } else{
            int l, r;
            mint x;
            cin >> l >> r >> x;
            S pr = seg.query(l, r);
            cout << pr.a * x + pr.b << "\n";
        }
    }
}

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