test/verify/aoj-2725.test.cpp

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• Last update: 2024-07-28 19:56:12+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2725

Depends on

• Dynamic-Li-Chao-Tree (structure/convex-hull-trick/dynamic-li-chao-tree.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2725

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

#include "../../structure/convex-hull-trick/dynamic-li-chao-tree.hpp"

int main() {
  int N, T;
  cin >> N >> T;
  vector< tuple< int, int, int > > dd;
  dd.reserve(N);
  for(int i = 0; i < N; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    if(a <= T) dd.emplace_back(c, a, b);
  }
  sort(begin(dd), end(dd));
  N = (int) dd.size();
  vector< int64 > t(N), p(N), f(N);
  for(int i = 0; i < N; i++) {
    tie(f[i], t[i], p[i]) = dd[i];
  }
  auto dp = make_v< int64 >(N, T + 1);
  fill_v(dp, -infll);
  vector< DynamicLiChaoTree< int64, 0, 10000, infll > > cht(T + 1, DynamicLiChaoTree< int64, 0, 10000, infll >());
  for(int i = 0; i < N; i++) {
    dp[i][t[i]] = p[i];
    for(int j = T; j >= t[i]; j--) {
      dp[i][j] = max(dp[i][j], -cht[j - t[i]].query(f[i]) + p[i] - f[i] * f[i]);
    }
    for(int j = T; j >= 0; j--) {
      if(dp[i][j] == -infll) continue;
      cht[j].add_line(-2 * f[i], -(dp[i][j] - f[i] * f[i]));
    }
  }
  int64 ret = 0;
  for(int i = 0; i < N; i++) {
    for(int j = 0; j <= T; j++) {
      ret = max(ret, dp[i][j]);
    }
  }
  cout << ret << "\n";
}

#line 1 "test/verify/aoj-2725.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2725

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

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(std::forward<F>(f)) {}

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

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/aoj-2725.test.cpp"

#line 1 "structure/convex-hull-trick/dynamic-li-chao-tree.hpp"
/**
 * @brief Dynamic-Li-Chao-Tree
 *
 */
template <typename T, T x_low, T x_high, T id>
struct DynamicLiChaoTree {
  struct Line {
    T a, b;

    Line(T a, T b) : a(a), b(b) {}

    inline T get(T x) const { return a * x + b; }
  };

  struct Node {
    Line x;
    Node *l, *r;

    Node(const Line &x) : x{x}, l{nullptr}, r{nullptr} {}
  };

  Node *root;

  DynamicLiChaoTree() : root{nullptr} {}

  Node *add_line(Node *t, Line &x, const T &l, const T &r, const T &x_l,
                 const T &x_r) {
    if (!t) return new Node(x);

    T t_l = t->x.get(l), t_r = t->x.get(r);

    if (t_l <= x_l && t_r <= x_r) {
      return t;
    } else if (t_l >= x_l && t_r >= x_r) {
      t->x = x;
      return t;
    } else {
      T m = (l + r) / 2;
      if (m == r) --m;
      T t_m = t->x.get(m), x_m = x.get(m);
      if (t_m > x_m) {
        swap(t->x, x);
        if (x_l >= t_l)
          t->l = add_line(t->l, x, l, m, t_l, t_m);
        else
          t->r = add_line(t->r, x, m + 1, r, t_m + x.a, t_r);
      } else {
        if (t_l >= x_l)
          t->l = add_line(t->l, x, l, m, x_l, x_m);
        else
          t->r = add_line(t->r, x, m + 1, r, x_m + x.a, x_r);
      }
      return t;
    }
  }

  void add_line(const T &a, const T &b) {
    Line x(a, b);
    root = add_line(root, x, x_low, x_high, x.get(x_low), x.get(x_high));
  }

  Node *add_segment(Node *t, Line &x, const T &a, const T &b, const T &l,
                    const T &r, const T &x_l, const T &x_r) {
    if (r < a || b < l) return t;
    if (a <= l && r <= b) {
      Line y{x};
      return add_line(t, y, l, r, x_l, x_r);
    }
    if (t) {
      T t_l = t->x.get(l), t_r = t->x.get(r);
      if (t_l <= x_l && t_r <= x_r) return t;
    } else {
      t = new Node(Line(0, id));
    }
    T m = (l + r) / 2;
    if (m == r) --m;
    T x_m = x.get(m);
    t->l = add_segment(t->l, x, a, b, l, m, x_l, x_m);
    t->r = add_segment(t->r, x, a, b, m + 1, r, x_m + x.a, x_r);
    return t;
  }

  void add_segment(const T &l, const T &r, const T &a, const T &b) {
    Line x(a, b);
    root = add_segment(root, x, l, r - 1, x_low, x_high, x.get(x_low),
                       x.get(x_high));
  }

  T query(const Node *t, const T &l, const T &r, const T &x) const {
    if (!t) return id;
    if (l == r) return t->x.get(x);
    T m = (l + r) / 2;
    if (m == r) --m;
    if (x <= m)
      return min(t->x.get(x), query(t->l, l, m, x));
    else
      return min(t->x.get(x), query(t->r, m + 1, r, x));
  }

  T query(const T &x) const { return query(root, x_low, x_high, x); }
};
#line 6 "test/verify/aoj-2725.test.cpp"

int main() {
  int N, T;
  cin >> N >> T;
  vector< tuple< int, int, int > > dd;
  dd.reserve(N);
  for(int i = 0; i < N; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    if(a <= T) dd.emplace_back(c, a, b);
  }
  sort(begin(dd), end(dd));
  N = (int) dd.size();
  vector< int64 > t(N), p(N), f(N);
  for(int i = 0; i < N; i++) {
    tie(f[i], t[i], p[i]) = dd[i];
  }
  auto dp = make_v< int64 >(N, T + 1);
  fill_v(dp, -infll);
  vector< DynamicLiChaoTree< int64, 0, 10000, infll > > cht(T + 1, DynamicLiChaoTree< int64, 0, 10000, infll >());
  for(int i = 0; i < N; i++) {
    dp[i][t[i]] = p[i];
    for(int j = T; j >= t[i]; j--) {
      dp[i][j] = max(dp[i][j], -cht[j - t[i]].query(f[i]) + p[i] - f[i] * f[i]);
    }
    for(int j = T; j >= 0; j--) {
      if(dp[i][j] == -infll) continue;
      cht[j].add_line(-2 * f[i], -(dp[i][j] - f[i] * f[i]));
    }
  }
  int64 ret = 0;
  for(int i = 0; i < N; i++) {
    for(int j = 0; j <= T; j++) {
      ret = max(ret, dp[i][j]);
    }
  }
  cout << ret << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_00	AC	5 ms	3 MB
g++	00_sample_01	AC	4 ms	3 MB
g++	00_sample_02	AC	4 ms	3 MB
g++	00_sample_03	AC	4 ms	3 MB
g++	00_sample_04	AC	4 ms	3 MB
g++	01_rando_medium_031	AC	4 ms	3 MB
g++	01_rando_medium_035	AC	4 ms	3 MB
g++	01_rando_medium_160	AC	4 ms	3 MB
g++	01_rando_medium_278	AC	4 ms	4 MB
g++	01_rando_medium_337	AC	4 ms	3 MB
g++	01_rando_medium_342	AC	4 ms	4 MB
g++	01_rando_medium_355	AC	4 ms	3 MB
g++	01_rando_medium_452	AC	4 ms	3 MB
g++	01_rando_medium_467	AC	4 ms	3 MB
g++	01_rando_medium_665	AC	4 ms	3 MB
g++	02_rando_large_000	AC	6 ms	5 MB
g++	02_rando_large_013	AC	4 ms	4 MB
g++	02_rando_large_048	AC	5 ms	4 MB
g++	02_rando_large_054	AC	8 ms	6 MB
g++	02_rando_large_083	AC	6 ms	4 MB
g++	02_rando_large_147	AC	4 ms	4 MB
g++	02_rando_large_164	AC	7 ms	6 MB
g++	02_rando_large_227	AC	7 ms	6 MB
g++	02_rando_large_283	AC	8 ms	6 MB
g++	02_rando_large_336	AC	7 ms	6 MB
g++	02_rando_large_368	AC	6 ms	5 MB
g++	05_attack_00	AC	4 ms	4 MB
g++	05_attack_01	AC	4 ms	4 MB
g++	05_attack_mi0803_00	AC	4 ms	3 MB
g++	10_random_small_000	AC	4 ms	3 MB
g++	10_random_small_001	AC	4 ms	3 MB
g++	10_random_small_002	AC	4 ms	3 MB
g++	10_random_small_003	AC	4 ms	3 MB
g++	10_random_small_004	AC	4 ms	3 MB
g++	10_random_small_005	AC	4 ms	3 MB
g++	10_random_small_006	AC	4 ms	3 MB
g++	10_random_small_007	AC	4 ms	3 MB
g++	10_random_small_008	AC	4 ms	3 MB
g++	10_random_small_009	AC	4 ms	3 MB
g++	11_rando_medium_000	AC	4 ms	4 MB
g++	11_rando_medium_001	AC	4 ms	4 MB
g++	11_rando_medium_002	AC	4 ms	4 MB
g++	11_rando_medium_003	AC	4 ms	4 MB
g++	11_rando_medium_004	AC	4 ms	4 MB
g++	11_rando_medium_005	AC	4 ms	4 MB
g++	11_rando_medium_006	AC	4 ms	4 MB
g++	11_rando_medium_007	AC	4 ms	3 MB
g++	11_rando_medium_008	AC	4 ms	4 MB
g++	11_rando_medium_009	AC	4 ms	4 MB
g++	12_random_large_000	AC	64 ms	49 MB
g++	12_random_large_001	AC	63 ms	47 MB
g++	12_random_large_002	AC	150 ms	117 MB
g++	12_random_large_003	AC	17 ms	12 MB
g++	12_random_large_004	AC	96 ms	74 MB
g++	12_random_large_005	AC	29 ms	22 MB
g++	12_random_large_006	AC	112 ms	87 MB
g++	12_random_large_007	AC	13 ms	10 MB
g++	12_random_large_008	AC	52 ms	39 MB
g++	12_random_large_009	AC	53 ms	41 MB
g++	22_shortMusics_Large_000	AC	125 ms	65 MB
g++	22_shortMusics_Large_001	AC	104 ms	56 MB
g++	22_shortMusics_Large_002	AC	189 ms	100 MB
g++	22_shortMusics_Large_003	AC	216 ms	112 MB
g++	22_shortMusics_Large_004	AC	151 ms	79 MB
g++	22_shortMusics_Large_005	AC	200 ms	103 MB
g++	22_shortMusics_Large_006	AC	148 ms	75 MB
g++	22_shortMusics_Large_007	AC	177 ms	90 MB
g++	22_shortMusics_Large_008	AC	87 ms	46 MB
g++	22_shortMusics_Large_009	AC	124 ms	63 MB
g++	41_separate_medium_000	AC	5 ms	4 MB
g++	41_separate_medium_001	AC	5 ms	4 MB
g++	41_separate_medium_002	AC	4 ms	4 MB
g++	41_separate_medium_003	AC	4 ms	4 MB
g++	41_separate_medium_004	AC	4 ms	4 MB
g++	42_separate_large_000	AC	58 ms	50 MB
g++	42_separate_large_001	AC	83 ms	71 MB
g++	42_separate_large_002	AC	61 ms	52 MB
g++	42_separate_large_003	AC	105 ms	90 MB
g++	42_separate_large_004	AC	77 ms	66 MB
clang++	00_sample_00	AC	5 ms	3 MB
clang++	00_sample_01	AC	4 ms	3 MB
clang++	00_sample_02	AC	4 ms	3 MB
clang++	00_sample_03	AC	4 ms	3 MB
clang++	00_sample_04	AC	4 ms	3 MB
clang++	01_rando_medium_031	AC	4 ms	3 MB
clang++	01_rando_medium_035	AC	4 ms	3 MB
clang++	01_rando_medium_160	AC	4 ms	3 MB
clang++	01_rando_medium_278	AC	4 ms	3 MB
clang++	01_rando_medium_337	AC	4 ms	3 MB
clang++	01_rando_medium_342	AC	4 ms	4 MB
clang++	01_rando_medium_355	AC	4 ms	3 MB
clang++	01_rando_medium_452	AC	4 ms	3 MB
clang++	01_rando_medium_467	AC	4 ms	3 MB
clang++	01_rando_medium_665	AC	4 ms	3 MB
clang++	02_rando_large_000	AC	6 ms	5 MB
clang++	02_rando_large_013	AC	4 ms	4 MB
clang++	02_rando_large_048	AC	5 ms	4 MB
clang++	02_rando_large_054	AC	8 ms	6 MB
clang++	02_rando_large_083	AC	6 ms	4 MB
clang++	02_rando_large_147	AC	4 ms	4 MB
clang++	02_rando_large_164	AC	8 ms	6 MB
clang++	02_rando_large_227	AC	7 ms	5 MB
clang++	02_rando_large_283	AC	9 ms	6 MB
clang++	02_rando_large_336	AC	8 ms	6 MB
clang++	02_rando_large_368	AC	6 ms	5 MB
clang++	05_attack_00	AC	4 ms	4 MB
clang++	05_attack_01	AC	4 ms	4 MB
clang++	05_attack_mi0803_00	AC	4 ms	3 MB
clang++	10_random_small_000	AC	4 ms	3 MB
clang++	10_random_small_001	AC	4 ms	3 MB
clang++	10_random_small_002	AC	4 ms	3 MB
clang++	10_random_small_003	AC	4 ms	3 MB
clang++	10_random_small_004	AC	4 ms	3 MB
clang++	10_random_small_005	AC	4 ms	3 MB
clang++	10_random_small_006	AC	4 ms	3 MB
clang++	10_random_small_007	AC	4 ms	3 MB
clang++	10_random_small_008	AC	4 ms	3 MB
clang++	10_random_small_009	AC	4 ms	3 MB
clang++	11_rando_medium_000	AC	4 ms	4 MB
clang++	11_rando_medium_001	AC	4 ms	4 MB
clang++	11_rando_medium_002	AC	4 ms	3 MB
clang++	11_rando_medium_003	AC	4 ms	4 MB
clang++	11_rando_medium_004	AC	4 ms	4 MB
clang++	11_rando_medium_005	AC	4 ms	3 MB
clang++	11_rando_medium_006	AC	4 ms	3 MB
clang++	11_rando_medium_007	AC	4 ms	3 MB
clang++	11_rando_medium_008	AC	4 ms	4 MB
clang++	11_rando_medium_009	AC	4 ms	3 MB
clang++	12_random_large_000	AC	77 ms	49 MB
clang++	12_random_large_001	AC	73 ms	47 MB
clang++	12_random_large_002	AC	183 ms	116 MB
clang++	12_random_large_003	AC	18 ms	12 MB
clang++	12_random_large_004	AC	115 ms	74 MB
clang++	12_random_large_005	AC	33 ms	22 MB
clang++	12_random_large_006	AC	139 ms	87 MB
clang++	12_random_large_007	AC	14 ms	10 MB
clang++	12_random_large_008	AC	61 ms	39 MB
clang++	12_random_large_009	AC	64 ms	41 MB
clang++	22_shortMusics_Large_000	AC	159 ms	65 MB
clang++	22_shortMusics_Large_001	AC	134 ms	55 MB
clang++	22_shortMusics_Large_002	AC	248 ms	100 MB
clang++	22_shortMusics_Large_003	AC	274 ms	112 MB
clang++	22_shortMusics_Large_004	AC	193 ms	79 MB
clang++	22_shortMusics_Large_005	AC	253 ms	103 MB
clang++	22_shortMusics_Large_006	AC	181 ms	75 MB
clang++	22_shortMusics_Large_007	AC	218 ms	90 MB
clang++	22_shortMusics_Large_008	AC	110 ms	46 MB
clang++	22_shortMusics_Large_009	AC	150 ms	63 MB
clang++	41_separate_medium_000	AC	5 ms	4 MB
clang++	41_separate_medium_001	AC	5 ms	4 MB
clang++	41_separate_medium_002	AC	4 ms	4 MB
clang++	41_separate_medium_003	AC	4 ms	4 MB
clang++	41_separate_medium_004	AC	4 ms	4 MB
clang++	42_separate_large_000	AC	60 ms	50 MB
clang++	42_separate_large_001	AC	90 ms	71 MB
clang++	42_separate_large_002	AC	63 ms	52 MB
clang++	42_separate_large_003	AC	114 ms	90 MB
clang++	42_separate_large_004	AC	81 ms	66 MB

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