cp-library

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

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Code

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

using mint = mint998;
using Action = AddCountAffineAction<mint>;
using Info = Action::Info;
using Tag = Action::Tag;

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,q;
    cin >> n >> q;
    vector<Info> a(n);
    for(auto &[x,y]:a)cin >> x,y=1;
    using Tree = LazyReversibleSplayTree<Action>;
    using Node = Tree::Node;
    using Ptr = Node*;
    Tree s;
    Ptr root=s.build(a);
    while(q--){
        int op;
        cin >> op;
        if(op==0){
            int i;
            mint x;
            cin >> i >> x;
            s.insert(root,i,new Node(Info(x,1)));
        }else if(op==1){
            int i;
            cin >> i;
            s.erase(root,i);
        }else if(op==2){
            int l,r;
            cin >> l >> r;
            s.reverse(root,l,r-1);
        }else if(op==3){
            int l,r;
            mint b,c;
            cin >> l >> r >> b >> c;
            s.apply(root,l,r-1,Tag(b,c));
        }else{
            int l,r;
            cin >> l >> r;
            cout << s.query(root,l,r-1).first << "\n";
        }
    }
}
#line 1 "verify/yosupo/data-structure/dynamic_sequence_range_affine_range_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_sequence_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/link-cut-tree/splay-tree-base.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-04-13
 * Description: Splay Tree. splay(u) will make node u be the root of the tree in amortized O(log n) time.
 */

template<class Node>
struct SplayTreeBase{
    using Ptr = Node*;
    bool is_root(Ptr t){
        return !(t->p)||(t->p->l!=t&&t->p->r!=t);
    } // The parent of the root stores the path parant in link cut tree.
    int size(Ptr t){
        return t?t->size:0;
    }
    virtual void push(Ptr t){};
    virtual void pull(Ptr t){};
    int pos(Ptr t){
        if(t->p){
            if(t->p->l==t)return -1;
            if(t->p->r==t)return 1;
        }
        return 0;
    }
    void rotate(Ptr t){
        Ptr x=t->p,y=x->p;
        if(pos(t)==-1){
            if((x->l=t->r))t->r->p=x;
            t->r=x,x->p=t;
        }else{
            if((x->r=t->l))t->l->p=x;
            t->l=x,x->p=t;
        }
        pull(x),pull(t);
        if((t->p=y)){
            if(y->l==x)y->l=t;
            if(y->r==x)y->r=t;
        }
    }
    void splay(Ptr t){
        if(!t)return;
        push(t);
        while(!is_root(t)){
            Ptr x=t->p;
            if(is_root(x)){
                push(x),push(t);
                rotate(t);
            }else{
                Ptr y=x->p;
                push(y),push(x),push(t);
                if(pos(x)==pos(t))rotate(x),rotate(t);
                else rotate(t),rotate(t);
            }
        }
    }
    Ptr get_first(Ptr t){
        while(t->l)push(t),t=t->l;
        splay(t);
        return t;
    }
    Ptr get_last(Ptr t){
        while(t->r)push(t),t=t->r;
        splay(t);
        return t;
    }
    Ptr merge(Ptr l,Ptr r){
        splay(l),splay(r);
        if(!l)return r;
        if(!r)return l;
        l=get_last(l);
        l->r=r;
        r->p=l;
        pull(l);
        return l;
    }
    pair<Ptr,Ptr> split(Ptr t,int k){
        if(!t)return {nullptr,nullptr};
        if(k==0)return {nullptr,t};
        if(k==size(t))return {t,nullptr};
        push(t);
        if(k<=size(t->l)){
            auto x=split(t->l,k);
            t->l=x.second;
            t->p=nullptr;
            if(x.second)x.second->p=t;
            pull(t);
            return {x.first,t};
        }else{
            auto x=split(t->r,k-size(t->l)-1);
            t->r=x.first;
            t->p=nullptr;
            if(x.first)x.first->p=t;
            pull(t);
            return {t,x.second};
        }
    }
    void insert(Ptr &t,int k,Ptr v){
        splay(t);
        auto x=split(t,k);
        t=merge(merge(x.first,v),x.second);
    }
    void erase(Ptr &t,int k){
        splay(t);
        auto x=split(t,k);
        auto y=split(x.second,1);
        // delete y.first;
        t=merge(x.first,y.second);
    }
    template<class T>
    Ptr build(const vector<T> &v){
        if(v.empty())return nullptr;
        function<Ptr(int,int)> build=[&](int l,int r){
            if(l==r)return new Node(v[l]);
            int m=(l+r)/2;
            return merge(build(l,m),build(m+1,r));
        };
        return build(0,v.size()-1);
    }
};

#line 2 "data-structure/link-cut-tree/lazy-reversible-bbst.hpp"

/**
 * Author: Teetat Info.
 * Date: 2024-04-13
 * Description: Lazy Reversible BBST Base.
 */

template<class Tree,class Node,class MonoidAction>
struct LazyReversibleBBST:Tree{
    using Tree::merge;
    using Tree::split;
    using typename Tree::Ptr;
    using InfoMonoid = typename MonoidAction::InfoMonoid;
    using TagMonoid = typename MonoidAction::TagMonoid;
    using Info = typename MonoidAction::Info;
    using Tag = typename MonoidAction::Tag;

    LazyReversibleBBST()=default;

    Info sum(Ptr t){
        return t?t->sum:InfoMonoid::unit();
    }
    void pull(Ptr t){
        if(!t)return;
        push(t);
        t->size=1;
        t->sum=t->val;
        t->revsum=t->val;
        if(t->l){
            t->size+=t->l->size;
            t->sum=InfoMonoid::op(t->l->sum,t->sum);
            t->revsum=InfoMonoid::op(t->revsum,t->l->revsum);
        }
        if(t->r){
            t->size+=t->r->size;
            t->sum=InfoMonoid::op(t->sum,t->r->sum);
            t->revsum=InfoMonoid::op(t->r->revsum,t->revsum);
        }
    }
    void push(Ptr t){
        if(!t)return;
        if(t->rev){
            toggle(t->l);
            toggle(t->r);
            t->rev=false;
        }
        if(t->lz!=TagMonoid::unit()){
            propagate(t->l,t->lz);
            propagate(t->r,t->lz);
            t->lz=TagMonoid::unit();
        }
    }
    void toggle(Ptr t){
        if(!t)return;
        swap(t->l,t->r);
        swap(t->sum,t->revsum);
        t->rev^=true;
    }
    void propagate(Ptr t,const Tag &v){
        if(!t)return;
        t->val=MonoidAction::op(t->val,v);
        t->sum=MonoidAction::op(t->sum,v);
        t->revsum=MonoidAction::op(t->revsum,v);
        t->lz=TagMonoid::op(t->lz,v);
    }
    void apply(Ptr &t,int l,int r,const Tag &v){
        if(l>r)return;
        auto x=split(t,l);
        auto y=split(x.second,r-l+1);
        propagate(y.first,v);
        t=merge(x.first,merge(y.first,y.second));
    }
    Info query(Ptr &t,int l,int r){
        if(l>r)return InfoMonoid::unit();
        auto x=split(t,l);
        auto y=split(x.second,r-l+1);
        Info res=sum(y.first);
        t=merge(x.first,merge(y.first,y.second));
        return res;
    }
    void reverse(Ptr &t,int l,int r){
        if(l>r)return;
        auto x=split(t,l);
        auto y=split(x.second,r-l+1);
        toggle(y.first);
        t=merge(x.first,merge(y.first,y.second));
    }
};

#line 4 "data-structure/link-cut-tree/lazy-reversible-splay-tree.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-04-13
 * Description: Lazy Reversible Splay Tree.
 */

template<class MonoidAction>
struct LazyReversibleSplayTreeNode{
    using Ptr = LazyReversibleSplayTreeNode*;
    using InfoMonoid = typename MonoidAction::InfoMonoid;
    using TagMonoid = typename MonoidAction::TagMonoid;
    using Info = typename MonoidAction::Info;
    using Tag = typename MonoidAction::Tag;
    using value_type = Info;
    Ptr l,r,p;
    Info val,sum,revsum;
    Tag lz;
    int size;
    bool rev;
    LazyReversibleSplayTreeNode(const Info &_val=InfoMonoid::unit(),const Tag &_lz=TagMonoid::unit())
        :l(),r(),p(),val(_val),sum(_val),revsum(_val),lz(_lz),size(1),rev(false){}
};

template<class MonoidAction>
struct LazyReversibleSplayTree
    : LazyReversibleBBST<SplayTreeBase<LazyReversibleSplayTreeNode<MonoidAction>>,
      LazyReversibleSplayTreeNode<MonoidAction>,MonoidAction>{
    using Node = LazyReversibleSplayTreeNode<MonoidAction>;
};

#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/dynamic_sequence_range_affine_range_sum.test.cpp"

using mint = mint998;
using Action = AddCountAffineAction<mint>;
using Info = Action::Info;
using Tag = Action::Tag;

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,q;
    cin >> n >> q;
    vector<Info> a(n);
    for(auto &[x,y]:a)cin >> x,y=1;
    using Tree = LazyReversibleSplayTree<Action>;
    using Node = Tree::Node;
    using Ptr = Node*;
    Tree s;
    Ptr root=s.build(a);
    while(q--){
        int op;
        cin >> op;
        if(op==0){
            int i;
            mint x;
            cin >> i >> x;
            s.insert(root,i,new Node(Info(x,1)));
        }else if(op==1){
            int i;
            cin >> i;
            s.erase(root,i);
        }else if(op==2){
            int l,r;
            cin >> l >> r;
            s.reverse(root,l,r-1);
        }else if(op==3){
            int l,r;
            mint b,c;
            cin >> l >> r >> b >> c;
            s.apply(root,l,r-1,Tag(b,c));
        }else{
            int l,r;
            cin >> l >> r;
            cout << s.query(root,l,r-1).first << "\n";
        }
    }
}
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