penguin8331's Library

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:heavy_check_mark: 区間をsetで管理するテク
(others/range-set.hpp)

使い方

宣言

RangeSet<T> hoge;

クエリ

convered(T l, T r) : 区間 [l,r] がカバーされているか
convered_by(T l, T r) : 区間 [l,r] が完全にカバーされている区間が存在する場合その区間を返す
insert(T l, T r) : 区間 [l,r] を挿入
erase(T l, T r) : 区間 [l,r] を削除
mex(T x) : x 以上ではじめにカバーされていない場所を返す

参考

区間をsetで管理するやつでもうバグらせたくない-むげんのぶろぐ
要素の追加・削除と mex を対数時間で処理するよ-えびちゃんの日記

Depends on

Verified with

Code

#pragma once
#include "../template/template.hpp"

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) {
            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) {
            ret += r - ite->first + 1;
            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 2 "template/template.hpp"
#include <bits/stdc++.h>
#line 3 "template/macro.hpp"

#define overload3(_1, _2, _3, name, ...) name
#define all1(v) std::begin(v), std::end(v)
#define all2(v, a) std::begin(v), std::begin(v) + a
#define all3(v, a, b) std::begin(v) + a, std::begin(v) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define rall1(v) std::rbegin(v), std::rend(v)
#define rall2(v, a) std::rbegin(v), std::rbegin(v) + a
#define rall3(v, a, b) std::rbegin(v) + a, std::rbegin(v) + b
#define rall(...) overload3(__VA_ARGS__, rall3, rall2, rall1)(__VA_ARGS__)
#define elif else if
#define updiv(N, X) (((N) + (X) - 1) / (X))
#define sigma(a, b) (((a) + (b)) * ((b) - (a) + 1) / 2)
#define INT(...)     \
    int __VA_ARGS__; \
    scan(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    scan(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    scan(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    scan(__VA_ARGS__)
#define DOU(...)        \
    double __VA_ARGS__; \
    scan(__VA_ARGS__)
#define LD(...)     \
    ld __VA_ARGS__; \
    scan(__VA_ARGS__)
#define pb push_back
#define eb emplace_back
#line 3 "template/alias.hpp"

using ll = long long;
using ld = long double;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;
constexpr int inf = 1 << 30;
constexpr ll INF = 1LL << 60;
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, 1, -1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
constexpr int mod = 998244353;
constexpr int MOD = 1e9 + 7;
#line 3 "template/func.hpp"

template <typename T>
inline bool chmax(T& a, T b) { return ((a < b) ? (a = b, true) : (false)); }
template <typename T>
inline bool chmin(T& a, T b) { return ((a > b) ? (a = b, true) : (false)); }
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (auto it = std::begin(v); it != std::end(v);) {
        os << *it << ((++it) != std::end(v) ? " " : "");
    }
    return os;
}
template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &in : v) {
        is >> in;
    }
    return is;
}
inline void scan() {}
template <class Head, class... Tail>
inline void scan(Head &head, Tail &...tail) {
    std::cin >> head;
    scan(tail...);
}
template <class T>
inline void print(const T &t) { std::cout << t << '\n'; }
template <class Head, class... Tail>
inline void print(const Head &head, const Tail &...tail) {
    std::cout << head << ' ';
    print(tail...);
}
template <class... T>
inline void fin(const T &...a) {
    print(a...);
    exit(0);
}
#line 3 "template/util.hpp"

struct IOSetup {
    IOSetup() {
        std::cin.tie(nullptr);
        std::ios::sync_with_stdio(false);
        std::cout.tie(0);
        std::cout << std::fixed << std::setprecision(12);
        std::cerr << std::fixed << std::setprecision(12);
    }
} IOSetup;
#line 3 "template/debug.hpp"

#ifdef LOCAL
#include <dump.hpp>
#else
#define debug(...)
#endif
#line 8 "template/template.hpp"
using namespace std;
#line 3 "others/range-set.hpp"

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) {
            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) {
            ret += r - ite->first + 1;
            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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