data-structure/convex/dynamic-li-chao-tree.hpp

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• Last update: 2024-06-12 17:31:48+07:00
• Include: #include "data-structure/convex/dynamic-li-chao-tree.hpp"

Verified with

• verify/yosupo/data-structure/segment_add_get_min_online.test.cpp

Code

#pragma once

/**
 * Author: Teetat T.
 * Date: 2024-06-12
 * Description: Dynamic Li-Chao Tree (minimize).
 */

template<class T>
struct DynamicLiChaoTree{
    static const T INF=numeric_limits<T>::max()/2;
    struct Line{
        T m,c;
        Line(T _m,T _c):m(_m),c(_c){}
        inline T eval(T x)const{return m*x+c;}
    };
    struct Node;
    using Ptr = Node*;
    struct Node{
        Line v;
        Ptr l,r;
        Node():v(0,INF),l(nullptr),r(nullptr){}
        Node(Line _v):v(_v),l(nullptr),r(nullptr){}
    };
    ll lb,ub;
    Ptr root;
    DynamicLiChaoTree(ll _lb,ll _ub):lb(_lb),ub(_ub),root(nullptr){}
    void insert(T l,T r,Ptr &t,Line v){
        if(!t)return void(t=new Node(v));
        T m=l+(r-l)/2;
        if(v.eval(m)<t->v.eval(m))swap(t->v,v);
        if(v.eval(l)<t->v.eval(l))insert(l,m,t->l,v);
        if(v.eval(r)<t->v.eval(r))insert(m+1,r,t->r,v);
    }
    inline void insert(T m,T c){
        insert(lb,ub,root,Line(m,c));
    }
    void insert_range(T l,T r,Ptr &t,T x,T y,Line v){
        if(y<l||r<x)return;
        if(!t)t=new Node();
        if(x<=l&&r<=y)return insert(l,r,t,v);
        T m=l+(r-l)/2;
        insert_range(l,m,t->l,x,y,v);
        insert_range(m+1,r,t->r,x,y,v);
    }
    inline void insert_range(T m,T c,T x,T y){
        insert_range(lb,ub,root,x,y,Line(m,c));
    }
    T query(T l,T r,Ptr t,T x){
        if(!t)return INF;
        T m=l+(r-l)/2;
        if(x<=m)return min(t->v.eval(x),query(l,m,t->l,x));
        return min(t->v.eval(x),query(m+1,r,t->r,x));
    }
    inline T query(T x){
        return query(lb,ub,root,x);
    }
};

#line 2 "data-structure/convex/dynamic-li-chao-tree.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-06-12
 * Description: Dynamic Li-Chao Tree (minimize).
 */

template<class T>
struct DynamicLiChaoTree{
    static const T INF=numeric_limits<T>::max()/2;
    struct Line{
        T m,c;
        Line(T _m,T _c):m(_m),c(_c){}
        inline T eval(T x)const{return m*x+c;}
    };
    struct Node;
    using Ptr = Node*;
    struct Node{
        Line v;
        Ptr l,r;
        Node():v(0,INF),l(nullptr),r(nullptr){}
        Node(Line _v):v(_v),l(nullptr),r(nullptr){}
    };
    ll lb,ub;
    Ptr root;
    DynamicLiChaoTree(ll _lb,ll _ub):lb(_lb),ub(_ub),root(nullptr){}
    void insert(T l,T r,Ptr &t,Line v){
        if(!t)return void(t=new Node(v));
        T m=l+(r-l)/2;
        if(v.eval(m)<t->v.eval(m))swap(t->v,v);
        if(v.eval(l)<t->v.eval(l))insert(l,m,t->l,v);
        if(v.eval(r)<t->v.eval(r))insert(m+1,r,t->r,v);
    }
    inline void insert(T m,T c){
        insert(lb,ub,root,Line(m,c));
    }
    void insert_range(T l,T r,Ptr &t,T x,T y,Line v){
        if(y<l||r<x)return;
        if(!t)t=new Node();
        if(x<=l&&r<=y)return insert(l,r,t,v);
        T m=l+(r-l)/2;
        insert_range(l,m,t->l,x,y,v);
        insert_range(m+1,r,t->r,x,y,v);
    }
    inline void insert_range(T m,T c,T x,T y){
        insert_range(lb,ub,root,x,y,Line(m,c));
    }
    T query(T l,T r,Ptr t,T x){
        if(!t)return INF;
        T m=l+(r-l)/2;
        if(x<=m)return min(t->v.eval(x),query(l,m,t->l,x));
        return min(t->v.eval(x),query(m+1,r,t->r,x));
    }
    inline T query(T x){
        return query(lb,ub,root,x);
    }
};

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