test/verify/yosupo-line-add-get-min-2.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://judge.yosupo.jp/problem/line_add_get_min

Depends on

• Convex Hull Trick Add Monotone (structure/convex-hull-trick/convex-hull-trick-add-monotone.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/line_add_get_min

#include "../../template/template.hpp"

#include "../../structure/convex-hull-trick/convex-hull-trick-add-monotone.hpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  using CHT = ConvexHullTrickAddMonotone< int64, true >;
  vector< CHT > cht;
  auto add = [&](int64 a, int64 b) {
    cht.emplace_back();
    cht.back().add(a, b);
    while(cht.size() >= 2 and cht.back().H.size() >= cht[cht.size() - 2].H.size()) {
      auto X = cht.back().H;
      cht.pop_back();
      auto Y = cht.back().H;
      cht.pop_back();
      reverse(begin(X), end(X));
      reverse(begin(Y), end(Y));
      CHT c;
      int k = 0;
      for(auto &p: X) {
        while(k < (int) Y.size() and Y[k] < p) {
          c.add(Y[k].first, Y[k].second);
          ++k;
        }
        c.add(p.first, p.second);
      }
      while(k < (int) Y.size()) {
        c.add(Y[k].first, Y[k].second);
        ++k;
      }
      cht.emplace_back(c);
    }
  };
  for(int i = 0; i < N; i++) {
    int64 a, b;
    cin >> a >> b;
    add(a, b);
  }
  while(Q--) {
    int t;
    cin >> t;
    if(t == 0) {
      int64 a, b;
      cin >> a >> b;
      add(a, b);
    } else {
      int64 x;
      cin >> x;
      int64 ret = infll;
      for(auto &c: cht) {
        chmin(ret, c.query(x));
      }
      cout << ret << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-line-add-get-min-2.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/line_add_get_min

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-line-add-get-min-2.test.cpp"

#line 1 "structure/convex-hull-trick/convex-hull-trick-add-monotone.hpp"
/**
 * @brief Convex Hull Trick Add Monotone
 *
 */
template <typename T, bool isMin>
struct ConvexHullTrickAddMonotone {
#define F first
#define S second
  using P = pair<T, T>;
  deque<P> H;

  ConvexHullTrickAddMonotone() = default;

  bool empty() const { return H.empty(); }

  void clear() { H.clear(); }

  inline int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); }

  inline bool check(const P &a, const P &b, const P &c) {
    if (b.S == a.S || c.S == b.S)
      return sgn(b.F - a.F) * sgn(c.S - b.S) >= sgn(c.F - b.F) * sgn(b.S - a.S);
    // return (b.F-a.F)*(c.S-b.S) >= (b.S-a.S)*(c.F-b.F);
    if (is_integral<T>::value) {
      return (b.S - a.S) / (a.F - b.F) >= (c.S - b.S) / (b.F - c.F);
    } else {
      return (b.F - a.F) * sgn(c.S - b.S) / abs(b.S - a.S) >=
             (c.F - b.F) * sgn(b.S - a.S) / abs(c.S - b.S);
    }
  }

  void add(T a, T b) {
    if (!isMin) a *= -1, b *= -1;
    P line(a, b);
    if (empty()) {
      H.emplace_front(line);
      return;
    }
    if (H.front().F <= a) {
      if (H.front().F == a) {
        if (H.front().S <= b) return;
        H.pop_front();
      }
      while (H.size() >= 2 && check(line, H.front(), H[1])) H.pop_front();
      H.emplace_front(line);
    } else {
      assert(a <= H.back().F);
      if (H.back().F == a) {
        if (H.back().S <= b) return;
        H.pop_back();
      }
      while (H.size() >= 2 && check(H[H.size() - 2], H.back(), line))
        H.pop_back();
      H.emplace_back(line);
    }
  }

  inline T get_y(const P &a, const T &x) { return a.F * x + a.S; }

  T query(T x) {
    assert(!empty());
    int l = -1, r = H.size() - 1;
    while (l + 1 < r) {
      int m = (l + r) >> 1;
      if (get_y(H[m], x) >= get_y(H[m + 1], x))
        l = m;
      else
        r = m;
    }
    if (isMin) return get_y(H[r], x);
    return -get_y(H[r], x);
  }

  T query_monotone_inc(T x) {
    assert(!empty());
    while (H.size() >= 2 && get_y(H.front(), x) >= get_y(H[1], x))
      H.pop_front();
    if (isMin) return get_y(H.front(), x);
    return -get_y(H.front(), x);
  }

  T query_monotone_dec(T x) {
    assert(!empty());
    while (H.size() >= 2 && get_y(H.back(), x) >= get_y(H[H.size() - 2], x))
      H.pop_back();
    if (isMin) return get_y(H.back(), x);
    return -get_y(H.back(), x);
  }

#undef F
#undef S
};
#line 6 "test/verify/yosupo-line-add-get-min-2.test.cpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  using CHT = ConvexHullTrickAddMonotone< int64, true >;
  vector< CHT > cht;
  auto add = [&](int64 a, int64 b) {
    cht.emplace_back();
    cht.back().add(a, b);
    while(cht.size() >= 2 and cht.back().H.size() >= cht[cht.size() - 2].H.size()) {
      auto X = cht.back().H;
      cht.pop_back();
      auto Y = cht.back().H;
      cht.pop_back();
      reverse(begin(X), end(X));
      reverse(begin(Y), end(Y));
      CHT c;
      int k = 0;
      for(auto &p: X) {
        while(k < (int) Y.size() and Y[k] < p) {
          c.add(Y[k].first, Y[k].second);
          ++k;
        }
        c.add(p.first, p.second);
      }
      while(k < (int) Y.size()) {
        c.add(Y[k].first, Y[k].second);
        ++k;
      }
      cht.emplace_back(c);
    }
  };
  for(int i = 0; i < N; i++) {
    int64 a, b;
    cin >> a >> b;
    add(a, b);
  }
  while(Q--) {
    int t;
    cin >> t;
    if(t == 0) {
      int64 a, b;
      cin >> a >> b;
      add(a, b);
    } else {
      int64 x;
      cin >> x;
      int64 ret = infll;
      for(auto &c: cht) {
        chmin(ret, c.query(x));
      }
      cout << ret << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	6 ms	4 MB
g++	half_00	AC	94 ms	4 MB
g++	hand_max_00	AC	322 ms	10 MB
g++	max_random_00	AC	184 ms	4 MB
g++	max_random_01	AC	179 ms	4 MB
g++	max_random_02	AC	178 ms	4 MB
g++	parabola_random_00	AC	382 ms	10 MB
g++	parabola_random_01	AC	379 ms	11 MB
g++	parabola_random_02	AC	364 ms	11 MB
g++	random_00	AC	129 ms	4 MB
g++	random_01	AC	134 ms	4 MB
g++	random_02	AC	83 ms	4 MB
g++	small_00	AC	7 ms	4 MB
g++	small_01	AC	6 ms	4 MB
clang++	example_00	AC	6 ms	4 MB
clang++	half_00	AC	97 ms	4 MB
clang++	hand_max_00	AC	329 ms	10 MB
clang++	max_random_00	AC	183 ms	4 MB
clang++	max_random_01	AC	181 ms	4 MB
clang++	max_random_02	AC	180 ms	4 MB
clang++	parabola_random_00	AC	387 ms	10 MB
clang++	parabola_random_01	AC	386 ms	11 MB
clang++	parabola_random_02	AC	373 ms	11 MB
clang++	random_00	AC	131 ms	4 MB
clang++	random_01	AC	139 ms	4 MB
clang++	random_02	AC	82 ms	4 MB
clang++	small_00	AC	7 ms	4 MB
clang++	small_01	AC	6 ms	4 MB

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