procon

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:heavy_check_mark: 区間をセットで管理するやつ
(DataStructure/RangeSet.cpp)

概要

https://mugen1337.hatenablog.com/entry/2020/10/14/134022

なんか

int, ll以外の使用を想定していない.

できること

全ての操作が存在している区間数をnとしてO(logn).(一部ならしでO(logn))

Verified with

Code

// 閉区間の範囲を管理
template<typename T>
struct RangeSet{
    set<pair<T,T>> st;
    T TINF;
 
    RangeSet(){
        TINF=numeric_limits<T>::max()/2;
        st.emplace(TINF,TINF);
        st.emplace(-TINF,-TINF);
    }
    // [l,r] covered?
    bool covered(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        return ite->first<=l and r<=ite->second;
    }
    bool covered(T x){
        return covered(x,x);
    }
    // [l, r]がカバーされているなら,その区間を返す. されていないなら[-TINF,-TINF]を返す
    pair<T,T> covered_by(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        if(ite->first<=l and r<=ite->second) return *ite;
        return make_pair(-TINF,-TINF);
    }
    pair<T,T> covered_by(T x){
        return covered_by(x,x);
    }
    // insert[l,r], 増加量を返す
    T insert(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        if(ite->first<=l and r<=ite->second) return T(0);
        T sum_erased=T(0);
        if(ite->first<=l and l<=ite->second+1){
            l=ite->first;
            sum_erased+=ite->second-ite->first+1;
            ite=st.erase(ite);
        }else ite=next(ite);
        while(r>ite->second){
            sum_erased+=ite->second-ite->first+1;
            ite=st.erase(ite);
        }
        if(ite->first-1<=r and r<=ite->second){
            sum_erased+=ite->second-ite->first+1;
            r=ite->second;
            st.erase(ite);
        }
        st.emplace(l,r);
        return r-l+1-sum_erased;
    }
    T insert(T x){
        return insert(x,x);
    }
    // erase [l,r], 減少量を返す
    T erase(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        if(ite->first<=l and r<=ite->second){
            // 完全に1つの区間に包含されている
            if(ite->first<l)  st.emplace(ite->first,l-1);
            if(r<ite->second) st.emplace(r+1,ite->second);
            st.erase(ite);
            return r-l+1;
        }
 
        T ret=T(0);
        if(ite->first<=l and l<=ite->second){
            ret+=ite->second-l+1;// 消えた
            if(ite->first<l) st.emplace(ite->first,l-1);
            ite=st.erase(ite);// 次へ
        }else ite=next(ite);
        while(ite->second<=r){
            ret+=ite->second-ite->first+1;
            ite=st.erase(ite);
        }
        // 右端が区間の間にあるか
        if(ite->first<=r and r<=ite->second){
            ret+=r-ite->first+1;
            if(r<ite->second) st.emplace(r+1,ite->second);
            st.erase(ite);
        }
        return ret;
    }
    T erase(T x){
        return erase(x,x);
    }
    // number of range
    int size(){
        return (int)st.size()-2;
    }
    // mex [x,~)
    T mex(T x=0){
        auto ite=prev(st.lower_bound({x+1,x+1}));
        if(ite->first<=x and x<=ite->second) return ite->second+1;
        else return x;
    }
    void output(){
        cout<<"RangeSet : ";
        for(auto &p:st){
            if(p.first==-TINF or p.second==TINF) continue;
            cout<<"["<<p.first<<", "<<p.second<<"] ";
        }
        cout<<"\n";
    }
};
#line 1 "DataStructure/RangeSet.cpp"
// 閉区間の範囲を管理
template<typename T>
struct RangeSet{
    set<pair<T,T>> st;
    T TINF;
 
    RangeSet(){
        TINF=numeric_limits<T>::max()/2;
        st.emplace(TINF,TINF);
        st.emplace(-TINF,-TINF);
    }
    // [l,r] covered?
    bool covered(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        return ite->first<=l and r<=ite->second;
    }
    bool covered(T x){
        return covered(x,x);
    }
    // [l, r]がカバーされているなら,その区間を返す. されていないなら[-TINF,-TINF]を返す
    pair<T,T> covered_by(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        if(ite->first<=l and r<=ite->second) return *ite;
        return make_pair(-TINF,-TINF);
    }
    pair<T,T> covered_by(T x){
        return covered_by(x,x);
    }
    // insert[l,r], 増加量を返す
    T insert(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        if(ite->first<=l and r<=ite->second) return T(0);
        T sum_erased=T(0);
        if(ite->first<=l and l<=ite->second+1){
            l=ite->first;
            sum_erased+=ite->second-ite->first+1;
            ite=st.erase(ite);
        }else ite=next(ite);
        while(r>ite->second){
            sum_erased+=ite->second-ite->first+1;
            ite=st.erase(ite);
        }
        if(ite->first-1<=r and r<=ite->second){
            sum_erased+=ite->second-ite->first+1;
            r=ite->second;
            st.erase(ite);
        }
        st.emplace(l,r);
        return r-l+1-sum_erased;
    }
    T insert(T x){
        return insert(x,x);
    }
    // erase [l,r], 減少量を返す
    T erase(T l,T r){
        assert(l<=r);
        auto ite=prev(st.lower_bound({l+1,l+1}));
        if(ite->first<=l and r<=ite->second){
            // 完全に1つの区間に包含されている
            if(ite->first<l)  st.emplace(ite->first,l-1);
            if(r<ite->second) st.emplace(r+1,ite->second);
            st.erase(ite);
            return r-l+1;
        }
 
        T ret=T(0);
        if(ite->first<=l and l<=ite->second){
            ret+=ite->second-l+1;// 消えた
            if(ite->first<l) st.emplace(ite->first,l-1);
            ite=st.erase(ite);// 次へ
        }else ite=next(ite);
        while(ite->second<=r){
            ret+=ite->second-ite->first+1;
            ite=st.erase(ite);
        }
        // 右端が区間の間にあるか
        if(ite->first<=r and r<=ite->second){
            ret+=r-ite->first+1;
            if(r<ite->second) st.emplace(r+1,ite->second);
            st.erase(ite);
        }
        return ret;
    }
    T erase(T x){
        return erase(x,x);
    }
    // number of range
    int size(){
        return (int)st.size()-2;
    }
    // mex [x,~)
    T mex(T x=0){
        auto ite=prev(st.lower_bound({x+1,x+1}));
        if(ite->first<=x and x<=ite->second) return ite->second+1;
        else return x;
    }
    void output(){
        cout<<"RangeSet : ";
        for(auto &p:st){
            if(p.first==-TINF or p.second==TINF) continue;
            cout<<"["<<p.first<<", "<<p.second<<"] ";
        }
        cout<<"\n";
    }
};
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