test/library-checker/data-structure/segment-add-get-min.test.cpp

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• Last update: 2024-09-08 23:17:50+09:00
• Problem: https://judge.yosupo.jp/problem/segment_add_get_min

Depends on

• Li Chao Tree (data-structure/segtree/li-chao-tree.hpp)
• template/template.cpp

Code

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

int main() {
    int N, Q;
    cin >> N >> Q;
    vector<ll> xs;
    vector<tuple<ll, ll, ll, ll>> segs(N);
    REP(i, N) {
        ll l, r, a, b;
        cin >> l >> r >> a >> b;
        segs[i] = {l, r, a, b};
        xs.push_back(l);
        xs.push_back(r);
    }
    vector<tuple<int, ll, ll, ll, ll>> qs(Q);
    REP(i, Q) {
        int t;
        cin >> t;
        if(t == 0) {
            ll l, r, a, b;
            cin >> l >> r >> a >> b;
            qs[i] = {t, l, r, a, b};
            xs.push_back(l);
            xs.push_back(r);
        } else {
            ll x;
            cin >> x;
            qs[i] = {t, x, -1, -1, -1};
            xs.push_back(x);
        }
    }
    LiChaoTree<ll, LLINF> lc(xs);
    for(const auto& [l, r, a, b] : segs) lc.add_segment(a, b, l, r);
    for(const auto& [t, l, r, a, b] : qs) {
        if(t == 0) {
            lc.add_segment(a, b, l, r);
        } else {
            ll ans = lc.get_min(l);
            if(ans == LLINF) {
                cout << "INFINITY\n";
            } else {
                cout << lc.get_min(l) << '\n';
            }
        }
    }
}

#line 1 "test/library-checker/data-structure/segment-add-get-min.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"
#line 1 "template/template.cpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
// input output utils
namespace siro53_io {
    // https://maspypy.github.io/library/other/io_old.hpp
    struct has_val_impl {
        template <class T>
        static auto check(T &&x) -> decltype(x.val(), std::true_type{});

        template <class T> static auto check(...) -> std::false_type;
    };

    template <class T>
    class has_val : public decltype(has_val_impl::check<T>(std::declval<T>())) {
    };

    // debug
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void dump(const T t) {
        cerr << t;
    }
    template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
    void dump(const T t) {
        cerr << t;
    }
    template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
    void dump(const T &t) {
        cerr << t.val();
    }
    void dump(__int128_t n) {
        if(n == 0) {
            cerr << '0';
            return;
        } else if(n < 0) {
            cerr << '-';
            n = -n;
        }
        string s;
        while(n > 0) {
            s += (char)('0' + n % 10);
            n /= 10;
        }
        reverse(s.begin(), s.end());
        cerr << s;
    }
    void dump(const string &s) { cerr << s; }
    void dump(const char *s) {
        int n = (int)strlen(s);
        for(int i = 0; i < n; i++) cerr << s[i];
    }
    template <class T1, class T2> void dump(const pair<T1, T2> &p) {
        cerr << '(';
        dump(p.first);
        cerr << ',';
        dump(p.second);
        cerr << ')';
    }
    template <class T> void dump(const vector<T> &v) {
        cerr << '{';
        for(int i = 0; i < (int)v.size(); i++) {
            dump(v[i]);
            if(i < (int)v.size() - 1) cerr << ',';
        }
        cerr << '}';
    }
    template <class T> void dump(const set<T> &s) {
        cerr << '{';
        for(auto it = s.begin(); it != s.end(); it++) {
            dump(*it);
            if(next(it) != s.end()) cerr << ',';
        }
        cerr << '}';
    }
    template <class Key, class Value> void dump(const map<Key, Value> &mp) {
        cerr << '{';
        for(auto it = mp.begin(); it != mp.end(); it++) {
            dump(*it);
            if(next(it) != mp.end()) cerr << ',';
        }
        cerr << '}';
    }
    template <class Key, class Value>
    void dump(const unordered_map<Key, Value> &mp) {
        cerr << '{';
        for(auto it = mp.begin(); it != mp.end(); it++) {
            dump(*it);
            if(next(it) != mp.end()) cerr << ',';
        }
        cerr << '}';
    }
    template <class T> void dump(const deque<T> &v) {
        cerr << '{';
        for(int i = 0; i < (int)v.size(); i++) {
            dump(v[i]);
            if(i < (int)v.size() - 1) cerr << ',';
        }
        cerr << '}';
    }
    template <class T> void dump(queue<T> q) {
        cerr << '{';
        while(!q.empty()) {
            dump(q.front());
            if((int)q.size() > 1) cerr << ',';
            q.pop();
        }
        cerr << '}';
    }

    void debug_print() { cerr << endl; }
    template <class Head, class... Tail>
    void debug_print(const Head &h, const Tail &...t) {
        dump(h);
        if(sizeof...(Tail)) dump(' ');
        debug_print(t...);
    }
    // print
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void print_single(const T t) {
        cout << t;
    }
    template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
    void print_single(const T t) {
        cout << t;
    }
    template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
    void print_single(const T t) {
        cout << t.val();
    }
    void print_single(__int128_t n) {
        if(n == 0) {
            cout << '0';
            return;
        } else if(n < 0) {
            cout << '-';
            n = -n;
        }
        string s;
        while(n > 0) {
            s += (char)('0' + n % 10);
            n /= 10;
        }
        reverse(s.begin(), s.end());
        cout << s;
    }
    void print_single(const string &s) { cout << s; }
    void print_single(const char *s) {
        int n = (int)strlen(s);
        for(int i = 0; i < n; i++) cout << s[i];
    }
    template <class T1, class T2> void print_single(const pair<T1, T2> &p) {
        print_single(p.first);
        cout << ' ';
        print_single(p.second);
    }
    template <class T> void print_single(const vector<T> &v) {
        for(int i = 0; i < (int)v.size(); i++) {
            print_single(v[i]);
            if(i < (int)v.size() - 1) cout << ' ';
        }
    }
    template <class T> void print_single(const set<T> &s) {
        for(auto it = s.begin(); it != s.end(); it++) {
            print_single(*it);
            if(next(it) != s.end()) cout << ' ';
        }
    }
    template <class T> void print_single(const deque<T> &v) {
        for(int i = 0; i < (int)v.size(); i++) {
            print_single(v[i]);
            if(i < (int)v.size() - 1) cout << ' ';
        }
    }
    template <class T> void print_single(queue<T> q) {
        while(!q.empty()) {
            print_single(q.front());
            if((int)q.size() > 1) cout << ' ';
            q.pop();
        }
    }

    void print() { cout << '\n'; }
    template <class Head, class... Tail>
    void print(const Head &h, const Tail &...t) {
        print_single(h);
        if(sizeof...(Tail)) print_single(' ');
        print(t...);
    }

    // input
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void input_single(T &t) {
        cin >> t;
    }
    template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
    void input_single(T &t) {
        cin >> t;
    }
    template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
    void input_single(T &t) {
        cin >> t;
    }
    void input_single(__int128_t &n) {
        string s;
        cin >> s;
        if(s == "0") {
            n = 0;
            return;
        }
        bool is_minus = false;
        if(s[0] == '-') {
            s = s.substr(1);
            is_minus = true;
        }
        n = 0;
        for(int i = 0; i < (int)s.size(); i++) n = n * 10 + (int)(s[i] - '0');
        if(is_minus) n = -n;
    }
    void input_single(string &s) { cin >> s; }
    template <class T1, class T2> void input_single(pair<T1, T2> &p) {
        input_single(p.first);
        input_single(p.second);
    }
    template <class T> void input_single(vector<T> &v) {
        for(auto &e : v) input_single(e);
    }
    void input() {}
    template <class Head, class... Tail> void input(Head &h, Tail &...t) {
        input_single(h);
        input(t...);
    }
}; // namespace siro53_io
#ifdef DEBUG
#define debug(...)                                                             \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debug_print(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
// io setup
struct Setup {
    Setup() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
    }
} __Setup;
using namespace siro53_io;
// types
using ll = long long;
using i128 = __int128_t;
// input macros
#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    input(__VA_ARGS__)
#define LL(...)                                                                \
    ll __VA_ARGS__;                                                            \
    input(__VA_ARGS__)
#define STRING(...)                                                            \
    string __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define CHAR(...)                                                              \
    char __VA_ARGS__;                                                          \
    input(__VA_ARGS__)
#define DBL(...)                                                               \
    double __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define LD(...)                                                                \
    long double __VA_ARGS__;                                                   \
    input(__VA_ARGS__)
#define UINT(...)                                                              \
    unsigned int __VA_ARGS__;                                                  \
    input(__VA_ARGS__)
#define ULL(...)                                                               \
    unsigned long long __VA_ARGS__;                                            \
    input(__VA_ARGS__)
#define VEC(name, type, len)                                                   \
    vector<type> name(len);                                                    \
    input(name);
#define VEC2(name, type, len1, len2)                                           \
    vector name(len1, vector<type>(len2));                                     \
    input(name);
// other macros
// https://trap.jp/post/1224/
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define REP1(i, n) for(int i = 0; i < int(n); i++)
#define REP2(i, a, b) for(int i = (a); i < int(b); i++)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define UNIQUE(v)                                                              \
    sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()), v.shrink_to_fit()
#define REV(v) reverse(ALL(v))
#define SZ(v) ((int)(v).size())
#define MIN(v) (*min_element(ALL(v)))
#define MAX(v) (*max_element(ALL(v)))
// util const
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
constexpr int MOD = 1000000007;
constexpr int MOD2 = 998244353;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
// util functions
void Case(int i) { cout << "Case #" << i << ": "; }
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
template <class T> inline bool chmax(T &a, T b) {
    return (a < b ? a = b, true : false);
}
template <class T> inline bool chmin(T &a, T b) {
    return (a > b ? a = b, true : false);
}
template <class T, int dim>
auto make_vector_impl(vector<int>& sizes, const T &e) {
    if constexpr(dim == 1) {
        return vector(sizes[0], e);
    } else {
        int n = sizes[dim - 1];
        sizes.pop_back();
        return vector(n, make_vector_impl<T, dim - 1>(sizes, e));
    }
}
template <class T, int dim>
auto make_vector(const int (&sizes)[dim], const T &e = T()) {
    vector<int> s(dim);
    for(int i = 0; i < dim; i++) s[i] = sizes[dim - i - 1];
    return make_vector_impl<T, dim>(s, e);
}
vector<int> iota_gen(int n, int start = 0) {
    vector<int> ord(n);
    iota(ord.begin(), ord.end(), start);
    return ord;
}
template<typename T>
vector<int> ord_sort(const vector<T>& v, bool greater = false) {
    auto ord = iota_gen((int)v.size());
    sort(ALL(ord), [&](int i, int j) {
        if(greater) return v[i] > v[j];
        return v[i] < v[j];
    });
    return ord;
}
#pragma endregion Macros
#line 2 "data-structure/segtree/li-chao-tree.hpp"

#line 7 "data-structure/segtree/li-chao-tree.hpp"

template <typename T, T inf>
class LiChaoTree {
public:
    LiChaoTree() = default;
    explicit LiChaoTree(const std::vector<T>& x): xs(x) {
        std::sort(xs.begin(), xs.end());
        xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
        n = (int)xs.size();
        sz = 1;
        while(sz < n) sz <<= 1;
        while((int)xs.size() < sz) xs.emplace_back(xs.back() + 1);
        node.resize(sz * 2, Line(T(0), inf));
    }
    // 直線 ax + b を追加
    void add_line(T a, T b) {
        update(a, b, 0, sz, 1);
    }
    // 線分 ax + b (x_l <= x < x_r) を追加
    void add_segment(T a, T b, T x_l, T x_r) {
        int l = std::lower_bound(xs.begin(), xs.end(), x_l) - xs.begin();
        int r = std::lower_bound(xs.begin(), xs.end(), x_r) - xs.begin();
        l += sz;
        r += sz;
        int width = 1, seg_idx_left = sz;
        while(l < r) {
            if(l & 1) {
                int L = (l - seg_idx_left) * width;
                int R = L + width;
                update(a, b, L, R, l);
                l++;
            }
            if(r & 1) {
                r--;
                int L = (r - seg_idx_left) * width;
                int R = L + width;
                update(a, b, L, R, r);
            }
            l >>= 1;
            r >>= 1;
            width <<= 1;
            seg_idx_left >>= 1;
        }
    }
    // min_{i} (a_i * x + b) を求める
    T get_min(T x) {
        int pos = std::lower_bound(xs.begin(), xs.end(), x) - xs.begin();
        assert(0 <= pos and pos < sz);
        pos += sz;
        T ret = node[pos].eval(x);
        while(pos > 1) {
            pos >>= 1;
            ret = std::min(ret, node[pos].eval(x));
        }
        return ret;
    }
private:
    struct Line {
        T a, b;
        Line(T a, T b): a(a), b(b) {}
        inline T eval(T x) const { return (a * x + b); }
    };
    std::vector<T> xs;
    std::vector<Line> node;
    int n, sz;

    void update(T a, T b, int l, int r, int pos) {
        Line new_line(a, b);
        while(1) {
            bool is_over_l = (new_line.eval(xs[l]) >= node[pos].eval(xs[l]));
            bool is_over_r = (new_line.eval(xs[r-1]) >= node[pos].eval(xs[r-1]));
            if(is_over_l == is_over_r) {
                if(!is_over_l) node[pos] = new_line;
                break;
            }
            int mid = (l + r) >> 1;
            bool is_over_mid = (new_line.eval(xs[mid]) >= node[pos].eval(xs[mid]));
            if(!is_over_l and is_over_r) {
                if(is_over_mid) {
                    r = mid;
                    pos = (pos << 1);
                } else {
                    std::swap(new_line, node[pos]);
                    l = mid;
                    pos = (pos << 1) | 1;
                }
            } else {
                if(is_over_mid) {
                    l = mid;
                    pos = (pos << 1) | 1;
                } else {
                    std::swap(new_line, node[pos]);
                    r = mid;
                    pos = (pos << 1);
                }
            }
        }
    }
};
#line 4 "test/library-checker/data-structure/segment-add-get-min.test.cpp"

int main() {
    int N, Q;
    cin >> N >> Q;
    vector<ll> xs;
    vector<tuple<ll, ll, ll, ll>> segs(N);
    REP(i, N) {
        ll l, r, a, b;
        cin >> l >> r >> a >> b;
        segs[i] = {l, r, a, b};
        xs.push_back(l);
        xs.push_back(r);
    }
    vector<tuple<int, ll, ll, ll, ll>> qs(Q);
    REP(i, Q) {
        int t;
        cin >> t;
        if(t == 0) {
            ll l, r, a, b;
            cin >> l >> r >> a >> b;
            qs[i] = {t, l, r, a, b};
            xs.push_back(l);
            xs.push_back(r);
        } else {
            ll x;
            cin >> x;
            qs[i] = {t, x, -1, -1, -1};
            xs.push_back(x);
        }
    }
    LiChaoTree<ll, LLINF> lc(xs);
    for(const auto& [l, r, a, b] : segs) lc.add_segment(a, b, l, r);
    for(const auto& [t, l, r, a, b] : qs) {
        if(t == 0) {
            lc.add_segment(a, b, l, r);
        } else {
            ll ans = lc.get_min(l);
            if(ans == LLINF) {
                cout << "INFINITY\n";
            } else {
                cout << lc.get_min(l) << '\n';
            }
        }
    }
}

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