verify/yosupo/data-structure/convex/li-chao-tree/segment_add_get_min.test.cpp

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• Last update: 2026-10-24 00:10:28+07:00
• Problem: https://judge.yosupo.jp/problem/segment_add_get_min

Depends on

• data-structure/convex/li-chao-tree.hpp
• template.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"
#include "template.hpp"
#include "data-structure/convex/li-chao-tree.hpp"

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,q;
    cin >> n >> q;
    vector<tuple<ll,ll,ll,ll>> lines(n);
    vector<ll> xs;
    for(auto &[a,b,l,r]:lines){
        cin >> l >> r >> a >> b;
        r--;
        xs.emplace_back(l);
        xs.emplace_back(r);
    }
    vector<tuple<int,ll,ll,ll,ll>> qrs(q);
    for(auto &[op,a,b,l,r]:qrs){
        cin >> op;
        if(op){
            cin >> a;
            xs.emplace_back(a);
        }else{
            cin >> l >> r >> a >> b;
            r--;
            xs.emplace_back(l);
            xs.emplace_back(r);
        }
    }
    LiChaoTree<ll> lct(xs);
    for(auto [a,b,l,r]:lines)lct.insert_range(a,b,l,r);
    for(auto [op,a,b,l,r]:qrs){
        if(op){
            ll res=lct.query(a);
            if(res>=lct.INF)cout << "INFINITY\n";
            else cout << res << "\n";
        }else{
            lct.insert_range(a,b,l,r);
        }
    }
}

#line 1 "verify/yosupo/data-structure/convex/li-chao-tree/segment_add_get_min.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"
#line 2 "template.hpp"
#include<bits/stdc++.h>

using namespace std;

using ll = long long;
using db = long double;
using i128 = __int128_t;
using u32 = uint32_t;
using u64 = uint64_t;
template<class T>
using PQ = priority_queue<T,vector<T>,greater<T>>;

const int INF=INT_MAX/2;
const ll LINF=LLONG_MAX/4;
const db DINF=numeric_limits<db>::infinity();
const db EPS=1e-9;
const db PI=acos(db(-1));

#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define SZ(a) (int)(a.size())
#define SORT(a) sort(ALL(a))
#define RSORT(a) sort(RALL(a))
#define REV(a) reverse(ALL(a))
#define UNI(a) a.erase(unique(ALL(a)),a.end())
#define LB(a,x) (int)(lower_bound(ALL(a),x)-a.begin())
#define UB(a,x) (int)(upper_bound(ALL(a),x)-a.begin())
#define FIND(a,x) (int)(find(ALL(a),x)-a.begin())
#define COUNT(a,x) (int)count(ALL(a),x)
#define MIN(a) *min_element(ALL(a))
#define MAX(a) *max_element(ALL(a))

template<class T,class U>
bool chmin(T &a,U b){return b<a?a=b,1:0;}
template<class T,class U>
bool chmax(T &a,U b){return a<b?a=b,1:0;}

template<class T>
T floor(T a,T b){return a/b-((a^b)<0&&a%b);}
template<class T>
T ceil(T a,T b){return a/b+((a^b)>=0&&a%b);}

int popcnt(ll x){return __builtin_popcountll(x);}
int topbit(ll x){return x==0?-1:63-__builtin_clzll(x);}
int lowbit(ll x){return x==0?-1:__builtin_ctzll(x);}

template<class T,class U>
T SUM(const U &a){return accumulate(ALL(a),T{});}
template<class T>
vector<int> argsort(const vector<T> &a){
    vector<int> p(SZ(a));
    iota(ALL(p),0);
    stable_sort(ALL(p),[&](int i,int j){return a[i]<a[j];});
    return p;
}

template<class T,size_t D=0>
struct VecBuilder{
    array<size_t,D> d;
    VecBuilder<T,D+1> operator[](size_t n)const{
        VecBuilder<T,D+1> res{};
        for(size_t i=0;i<D;i++)res.d[i]=d[i];
        res.d[D]=n;
        return res;
    }
    template<size_t I=0>
    auto build(const T &x)const{
        if constexpr(I+1==D)return vector<T>(d[I],x);
        else return vector<decltype(build<I+1>(x))>(d[I],build<I+1>(x));
    }
    auto operator()(const T &x=T())const{
        static_assert(D>0);
        return build(x);
    }
};
template<class T>
inline constexpr VecBuilder<T> VEC{};

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
#line 2 "data-structure/convex/li-chao-tree.hpp"

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

template<class T>
struct LiChaoTree{
    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;}
    };
    vector<T> xs;
    vector<Line> t;
    LiChaoTree(){}
    LiChaoTree(const vector<T> &x):xs(x){init(x);}
    LiChaoTree(int n):xs(n){
        vector<T> x(n);
        iota(x.begin(),x.end(),0);
        init(x);
    }
    void init(const vector<T> &x){
        xs=x;
        sort(xs.begin(),xs.end());
        xs.erase(unique(xs.begin(),xs.end()),xs.end());
        t.assign(4<<(31-__builtin_clz(xs.size())),Line(0,INF));
    }
    void insert(int l,int r,int i,Line v){
        int m=(l+r)/2;
        if(v.eval(xs[m])<t[i].eval(xs[m]))swap(t[i],v);
        if(v.eval(xs[l])<t[i].eval(xs[l]))insert(l,m,i*2,v);
        if(v.eval(xs[r])<t[i].eval(xs[r]))insert(m+1,r,i*2+1,v);
    }
    inline void insert(T m,T c){
        insert(0,(int)xs.size()-1,1,Line(m,c));
    }
    void insert_range(int l,int r,int i,T x,T y,Line v){
        if(y<xs[l]||xs[r]<x)return;
        if(x<=xs[l]&&xs[r]<=y)return insert(l,r,i,v);
        int m=(l+r)/2;
        insert_range(l,m,i*2,x,y,v);
        insert_range(m+1,r,i*2+1,x,y,v);
    }
    inline void insert_range(T m,T c,T x,T y){
        insert_range(0,(int)xs.size()-1,1,x,y,Line(m,c));
    }
    T query(int l,int r,int i,T x){
        if(l==r)return t[i].eval(x);
        int m=(l+r)/2;
        if(x<=xs[m])return min(t[i].eval(x),query(l,m,i*2,x));
        return min(t[i].eval(x),query(m+1,r,i*2+1,x));
    }
    inline T query(T x){
        return query(0,(int)xs.size()-1,1,x);
    }
};

#line 4 "verify/yosupo/data-structure/convex/li-chao-tree/segment_add_get_min.test.cpp"

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,q;
    cin >> n >> q;
    vector<tuple<ll,ll,ll,ll>> lines(n);
    vector<ll> xs;
    for(auto &[a,b,l,r]:lines){
        cin >> l >> r >> a >> b;
        r--;
        xs.emplace_back(l);
        xs.emplace_back(r);
    }
    vector<tuple<int,ll,ll,ll,ll>> qrs(q);
    for(auto &[op,a,b,l,r]:qrs){
        cin >> op;
        if(op){
            cin >> a;
            xs.emplace_back(a);
        }else{
            cin >> l >> r >> a >> b;
            r--;
            xs.emplace_back(l);
            xs.emplace_back(r);
        }
    }
    LiChaoTree<ll> lct(xs);
    for(auto [a,b,l,r]:lines)lct.insert_range(a,b,l,r);
    for(auto [op,a,b,l,r]:qrs){
        if(op){
            ll res=lct.query(a);
            if(res>=lct.INF)cout << "INFINITY\n";
            else cout << res << "\n";
        }else{
            lct.insert_range(a,b,l,r);
        }
    }
}

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