cp-library

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:heavy_check_mark: verify/yosupo/data-structure/range_affine_range_sum.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#include "template.hpp"
#include "modular-arithmetic/montgomery-modint.hpp"
#include "data-structure/segment-tree/lazy-segment-tree.hpp"
#include "group/monoid-action/add-count-affine.hpp"

using mint = mint998;
using Monoid = AddCountMonoid<mint>;
using Action = AddCountAffineAction<mint>;
using T = Monoid::value_type;

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,q;
    cin >> n >> q;
    vector<mint> a(n);
    for(auto &x:a)cin >> x;
    LazySegmentTree<Action> s(n,[&](int i){return Monoid::make(a[i]);});
    while(q--){
        int op;
        cin >> op;
        if(op){
            int l,r;
            cin >> l >> r;
            cout << s.query(l,r-1).first << "\n";
        }else{
            int l,r,b,c;
            cin >> l >> r >> b >> c;
            s.update(l,r-1,T(b,c));
        }
    }
}
#line 1 "verify/yosupo/data-structure/range_affine_range_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#line 1 "template.hpp"
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

using ll = long long;
using db = long double;
using vi = vector<int>;
using vl = vector<ll>;
using vd = vector<db>;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pdd = pair<db,db>;
const int INF=INT_MAX/2;
const int MOD=998244353;
const int MOD2=1000000007;
const ll LINF=LLONG_MAX/2;
const db DINF=numeric_limits<db>::infinity();
const db EPS=1e-9;
const db PI=acos(db(-1));

template<class T>
using ordered_set = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
template<class T>
using ordered_multiset = tree<T,null_type,less_equal<T>,rb_tree_tag,tree_order_statistics_node_update>;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
#line 2 "modular-arithmetic/montgomery-modint.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-03-17
 * Description: modular arithmetic operators using Montgomery space
 */

template<uint32_t mod,uint32_t root=0>
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;
        for(i32 i=0;i<5;i++)res*=2-mod*res;
        return res;
    }

    static const u32 r=get_r();
    static const u32 n2=-u64(mod)%mod;
    static_assert(mod<(1<<30));
    static_assert((mod&1)==1);
    static_assert(r*mod==1);

    u32 x;

    constexpr MontgomeryModInt():x(0){}
    constexpr MontgomeryModInt(const int64_t &v):x(reduce(u64(v%mod+mod)*n2)){}

    static constexpr u32 get_mod(){return mod;}
    static constexpr mint get_root(){return mint(root);}
    explicit constexpr operator int64_t()const{return val();}

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

    constexpr u32 val()const{
        u32 res=reduce(x);
        return res>=mod?res-mod:res;
    }

    constexpr mint inv()const{
        int a=val(),b=mod,u=1,v=0,q=0;
        while(b>0){
            q=a/b;
            a-=q*b;
            u-=q*v;
            swap(a,b);
            swap(u,v);
        }
        return mint(u);
    }

    constexpr mint &operator+=(const mint &rhs){
        if(i32(x+=rhs.x-2*mod)<0)x+=2*mod;
        return *this;
    }
    constexpr mint &operator-=(const mint &rhs){
        if(i32(x-=rhs.x)<0)x+=2*mod;
        return *this;
    }
    constexpr mint &operator*=(const mint &rhs){
        x=reduce(u64(x)*rhs.x);
        return *this;
    }
    constexpr mint &operator/=(const mint &rhs){
        return *this*=rhs.inv();
    }

    constexpr mint &operator++(){return *this+=mint(1);}
    constexpr mint &operator--(){return *this-=mint(1);}
    constexpr mint operator++(int){
        mint res=*this;
        return *this+=mint(1),res;
    }
    constexpr mint operator--(int){
        mint res=*this;
        return *this-=mint(1),res;
    }

    constexpr mint operator-()const{return mint()-mint(*this);};
    constexpr mint operator+()const{return mint(*this);};

    friend constexpr mint operator+(const mint &lhs,const mint &rhs){return mint(lhs)+=rhs;}
    friend constexpr mint operator-(const mint &lhs,const mint &rhs){return mint(lhs)-=rhs;}
    friend constexpr mint operator*(const mint &lhs,const mint &rhs){return mint(lhs)*=rhs;}
    friend constexpr mint operator/(const mint &lhs,const mint &rhs){return mint(lhs)/=rhs;}
    friend constexpr bool operator==(const mint &lhs,const mint &rhs){
        return (lhs.x>=mod?lhs.x-mod:lhs.x)==(rhs.x>=mod?rhs.x-mod:rhs.x);
    }
    friend constexpr bool operator!=(const mint &lhs,const mint &rhs){
        return (lhs.x>=mod?lhs.x-mod:lhs.x)!=(rhs.x>=mod?rhs.x-mod:rhs.x);
    }
    friend constexpr bool operator<(const mint &lhs,const mint &rhs){
        return (lhs.x>=mod?lhs.x-mod:lhs.x)<(rhs.x>=mod?rhs.x-mod:rhs.x); // for std::map
    }

    friend istream &operator>>(istream &is,mint &o){
        int64_t v;
        is >> v;
        o=mint(v);
        return is;
    }
    friend ostream &operator<<(ostream &os,const mint &o){
        return os << o.val();
    }
};
using mint998 = MontgomeryModInt<998244353,3>;
using mint107 = MontgomeryModInt<1000000007>;

#line 2 "data-structure/segment-tree/lazy-segment-tree.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-01-15
 * Description: Segment Tree with Lazy Propagation
 */

template<class MonoidAction>
struct LazySegmentTree{
    using InfoMonoid = typename MonoidAction::InfoMonoid;
    using TagMonoid = typename MonoidAction::TagMonoid;
    using Info = typename MonoidAction::Info;
    using Tag = typename MonoidAction::Tag;
    int n;
    vector<Info> t;
    vector<Tag> lz;
    LazySegmentTree(){}
    LazySegmentTree(int n,function<Info(int)> create){init(n,create);}
    LazySegmentTree(int n,Info v=InfoMonoid::unit()){init(n,[&](int){return v;});}
    template<class T>
    LazySegmentTree(const vector<T> &a){init((int)a.size(),[&](int i){return Info(a[i]);});}
    void init(int _n,function<Info(int)> create){
        n=_n;
        int m=4<<(31-__builtin_clz(n));
        t.assign(m,InfoMonoid::unit());
        lz.assign(m,TagMonoid::unit());
        function<void(int,int,int)> build=[&](int l,int r,int i){
            if(l==r)return void(t[i]=create(l));
            int m=(l+r)/2;
            build(l,m,i*2);
            build(m+1,r,i*2+1);
            pull(i);
        };
        build(0,n-1,1);
    }
    void pull(int i){
        t[i]=InfoMonoid::op(t[i*2],t[i*2+1]);
    }
    void apply(int i,const Tag &v){
        t[i]=MonoidAction::op(t[i],v);
        lz[i]=TagMonoid::op(lz[i],v);
    }
    void push(int i){
        apply(i*2,lz[i]);
        apply(i*2+1,lz[i]);
        lz[i]=TagMonoid::unit();
    }
    void modify(int l,int r,int i,int x,const Info &v){
        if(x<l||r<x)return;
        if(l==r)return void(t[i]=v);
        int m=(l+r)/2;
        push(i);
        modify(l,m,i*2,x,v);
        modify(m+1,r,i*2+1,x,v);
        pull(i);
    }
    void modify(int x,const Info &v){
        modify(0,n-1,1,x,v);
    }
    void update(int l,int r,int i,int x,int y,const Tag &v){
        if(y<l||r<x)return;
        if(x<=l&&r<=y)return apply(i,v);
        int m=(l+r)/2;
        push(i);
        update(l,m,i*2,x,y,v);
        update(m+1,r,i*2+1,x,y,v);
        pull(i);
    }
    void update(int x,int y,const Tag &v){
        update(0,n-1,1,x,y,v);
    }
    Info query(int l,int r,int i,int x,int y){
        if(y<l||r<x)return InfoMonoid::unit();
        if(x<=l&&r<=y)return t[i];
        int m=(l+r)/2;
        push(i);
        return InfoMonoid::op(query(l,m,i*2,x,y),query(m+1,r,i*2+1,x,y));
    }
    Info query(int x,int y){
        return query(0,n-1,1,x,y);
    }
    template<class F>
    int findfirst(int l,int r,int i,int x,int y,const F &f){
        if(y<l||r<x||!f(t[i]))return n;
        if(l==r)return l;
        int m=(l+r)/2;
        push(i);
        int res=findfirst(l,m,i*2,x,y,f);
        if(res==n)res=findfirst(m+1,r,i*2+1,x,y,f);
        return res;
    }
    template<class F>
    int findfirst(int x,int y,const F &f){
        return findfirst(0,n-1,1,x,y,f);
    }
    template<class F>
    int findlast(int l,int r,int i,int x,int y,const F &f){
        if(y<l||r<x||!f(t[i]))return -1;
        if(l==r)return l;
        int m=(l+r)/2;
        push(i);
        int res=findlast(m+1,r,i*2+1,x,y,f);
        if(res==-1)res=findlast(l,m,i*2,x,y,f);
        return res;
    }
    template<class F>
    int findlast(int x,int y,const F &f){
        return findlast(0,n-1,1,x,y,f);
    }
};

#line 2 "group/monoid/affine.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-04-14
 * Description: Affine Transfomation Monoid class.
 */

template<class T>
struct AffineMonoid{
    using P = pair<T,T>;
    using value_type = P;
    static constexpr P op(const P &x,const P &y){
        return P(x.first*y.first,x.second*y.first+y.second);
    }
    static constexpr P unit(){return P(T(1),T(0));}
    static constexpr T eval(const P &f,const T &x){
        return f.first*x+f.second;
    }
};

#line 2 "group/monoid/add-count.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-04-14
 * Description: Add & Count Monoid class.
 */

template<class T>
struct AddCountMonoid{
    using P = pair<T,int>;
    using value_type = P;
    static constexpr P op(const P &x,const P &y){
        return P(x.first+y.first,x.second+y.second);
    }
    static constexpr P inverse(const P &x){return P(-x.first,-x.second);}
    static constexpr P unit(){return P(T(0),0);}
    static constexpr P make(const T &x){return P(x,1);}
};

#line 4 "group/monoid-action/add-count-affine.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-04-14
 * Description: Affine to Add & Count Action class.
 */

template<class T>
struct AddCountAffineAction{
    using InfoMonoid = AddCountMonoid<T>;
    using TagMonoid = AffineMonoid<T>;
    using Info = typename InfoMonoid::value_type;
    using Tag = typename TagMonoid::value_type;
    static constexpr Info op(const Info &a,const Tag &b){
        return Info(a.first*b.first+a.second*b.second,a.second);
    }
};

#line 6 "verify/yosupo/data-structure/range_affine_range_sum.test.cpp"

using mint = mint998;
using Monoid = AddCountMonoid<mint>;
using Action = AddCountAffineAction<mint>;
using T = Monoid::value_type;

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,q;
    cin >> n >> q;
    vector<mint> a(n);
    for(auto &x:a)cin >> x;
    LazySegmentTree<Action> s(n,[&](int i){return Monoid::make(a[i]);});
    while(q--){
        int op;
        cin >> op;
        if(op){
            int l,r;
            cin >> l >> r;
            cout << s.query(l,r-1).first << "\n";
        }else{
            int l,r,b,c;
            cin >> l >> r >> b >> c;
            s.update(l,r-1,T(b,c));
        }
    }
}
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