test/verify/aoj-2725.test.cpp

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• Last update: 2026-08-11 01:10:11+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)

Code

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

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <tuple>
#include <vector>

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

using namespace std;

constexpr int64_t kInfinity = int64_t{1} << 60;

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> t(N), p(N), f(N);
  for (int i = 0; i < N; i++) {
    tie(f[i], t[i], p[i]) = dd[i];
  }
  vector<vector<int64_t>> dp(N, vector<int64_t>(T + 1, -kInfinity));
  vector<DynamicLiChaoTree<int64_t, 0, 10000, kInfinity>> cht(T + 1);
  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] == -kInfinity) continue;
      cht[j].add_line(-2 * f[i], -(dp[i][j] - f[i] * f[i]));
    }
  }
  int64_t 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"
// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2725
// clang-format on

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <tuple>
#include <vector>

#line 2 "structure/convex-hull-trick/dynamic-li-chao-tree.hpp"

#line 4 "structure/convex-hull-trick/dynamic-li-chao-tree.hpp"
#include <utility>

/**
 * @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) {
        std::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 std::min(t->x.get(x), query(t->l, l, m, x));
    else
      return std::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 12 "test/verify/aoj-2725.test.cpp"

using namespace std;

constexpr int64_t kInfinity = int64_t{1} << 60;

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> t(N), p(N), f(N);
  for (int i = 0; i < N; i++) {
    tie(f[i], t[i], p[i]) = dd[i];
  }
  vector<vector<int64_t>> dp(N, vector<int64_t>(T + 1, -kInfinity));
  vector<DynamicLiChaoTree<int64_t, 0, 10000, kInfinity>> cht(T + 1);
  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] == -kInfinity) continue;
      cht[j].add_line(-2 * f[i], -(dp[i][j] - f[i] * f[i]));
    }
  }
  int64_t 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	2 ms	3 MB
g++	00_sample_01	AC	2 ms	4 MB
g++	00_sample_02	AC	2 ms	4 MB
g++	00_sample_03	AC	2 ms	4 MB
g++	00_sample_04	AC	2 ms	3 MB
g++	01_rando_medium_031	AC	2 ms	4 MB
g++	01_rando_medium_035	AC	2 ms	4 MB
g++	01_rando_medium_160	AC	2 ms	4 MB
g++	01_rando_medium_278	AC	2 ms	4 MB
g++	01_rando_medium_337	AC	2 ms	4 MB
g++	01_rando_medium_342	AC	2 ms	3 MB
g++	01_rando_medium_355	AC	2 ms	4 MB
g++	01_rando_medium_452	AC	2 ms	4 MB
g++	01_rando_medium_467	AC	2 ms	4 MB
g++	01_rando_medium_665	AC	2 ms	4 MB
g++	02_rando_large_000	AC	5 ms	5 MB
g++	02_rando_large_013	AC	2 ms	4 MB
g++	02_rando_large_048	AC	3 ms	4 MB
g++	02_rando_large_054	AC	7 ms	6 MB
g++	02_rando_large_083	AC	5 ms	5 MB
g++	02_rando_large_147	AC	2 ms	4 MB
g++	02_rando_large_164	AC	6 ms	6 MB
g++	02_rando_large_227	AC	6 ms	6 MB
g++	02_rando_large_283	AC	8 ms	7 MB
g++	02_rando_large_336	AC	6 ms	6 MB
g++	02_rando_large_368	AC	5 ms	5 MB
g++	05_attack_00	AC	2 ms	4 MB
g++	05_attack_01	AC	2 ms	4 MB
g++	05_attack_mi0803_00	AC	2 ms	3 MB
g++	10_random_small_000	AC	2 ms	4 MB
g++	10_random_small_001	AC	2 ms	3 MB
g++	10_random_small_002	AC	2 ms	4 MB
g++	10_random_small_003	AC	2 ms	3 MB
g++	10_random_small_004	AC	2 ms	4 MB
g++	10_random_small_005	AC	2 ms	3 MB
g++	10_random_small_006	AC	2 ms	3 MB
g++	10_random_small_007	AC	2 ms	4 MB
g++	10_random_small_008	AC	2 ms	4 MB
g++	10_random_small_009	AC	2 ms	3 MB
g++	11_rando_medium_000	AC	2 ms	4 MB
g++	11_rando_medium_001	AC	2 ms	4 MB
g++	11_rando_medium_002	AC	2 ms	3 MB
g++	11_rando_medium_003	AC	2 ms	4 MB
g++	11_rando_medium_004	AC	2 ms	4 MB
g++	11_rando_medium_005	AC	2 ms	4 MB
g++	11_rando_medium_006	AC	2 ms	4 MB
g++	11_rando_medium_007	AC	2 ms	3 MB
g++	11_rando_medium_008	AC	2 ms	4 MB
g++	11_rando_medium_009	AC	2 ms	4 MB
g++	12_random_large_000	AC	59 ms	49 MB
g++	12_random_large_001	AC	55 ms	47 MB
g++	12_random_large_002	AC	139 ms	117 MB
g++	12_random_large_003	AC	15 ms	12 MB
g++	12_random_large_004	AC	88 ms	74 MB
g++	12_random_large_005	AC	25 ms	22 MB
g++	12_random_large_006	AC	107 ms	87 MB
g++	12_random_large_007	AC	10 ms	10 MB
g++	12_random_large_008	AC	47 ms	39 MB
g++	12_random_large_009	AC	50 ms	41 MB
g++	22_shortMusics_Large_000	AC	113 ms	65 MB
g++	22_shortMusics_Large_001	AC	95 ms	56 MB
g++	22_shortMusics_Large_002	AC	174 ms	100 MB
g++	22_shortMusics_Large_003	AC	196 ms	112 MB
g++	22_shortMusics_Large_004	AC	138 ms	79 MB
g++	22_shortMusics_Large_005	AC	183 ms	103 MB
g++	22_shortMusics_Large_006	AC	134 ms	75 MB
g++	22_shortMusics_Large_007	AC	160 ms	90 MB
g++	22_shortMusics_Large_008	AC	77 ms	47 MB
g++	22_shortMusics_Large_009	AC	111 ms	63 MB
g++	41_separate_medium_000	AC	2 ms	4 MB
g++	41_separate_medium_001	AC	2 ms	4 MB
g++	41_separate_medium_002	AC	2 ms	4 MB
g++	41_separate_medium_003	AC	2 ms	4 MB
g++	41_separate_medium_004	AC	2 ms	4 MB
g++	42_separate_large_000	AC	53 ms	50 MB
g++	42_separate_large_001	AC	77 ms	71 MB
g++	42_separate_large_002	AC	55 ms	52 MB
g++	42_separate_large_003	AC	99 ms	90 MB
g++	42_separate_large_004	AC	70 ms	66 MB
clang++	00_sample_00	AC	2 ms	4 MB
clang++	00_sample_01	AC	2 ms	4 MB
clang++	00_sample_02	AC	2 ms	4 MB
clang++	00_sample_03	AC	2 ms	4 MB
clang++	00_sample_04	AC	2 ms	4 MB
clang++	01_rando_medium_031	AC	2 ms	4 MB
clang++	01_rando_medium_035	AC	2 ms	4 MB
clang++	01_rando_medium_160	AC	2 ms	4 MB
clang++	01_rando_medium_278	AC	2 ms	4 MB
clang++	01_rando_medium_337	AC	2 ms	4 MB
clang++	01_rando_medium_342	AC	2 ms	4 MB
clang++	01_rando_medium_355	AC	2 ms	4 MB
clang++	01_rando_medium_452	AC	2 ms	4 MB
clang++	01_rando_medium_467	AC	2 ms	4 MB
clang++	01_rando_medium_665	AC	2 ms	4 MB
clang++	02_rando_large_000	AC	5 ms	5 MB
clang++	02_rando_large_013	AC	2 ms	4 MB
clang++	02_rando_large_048	AC	3 ms	4 MB
clang++	02_rando_large_054	AC	7 ms	6 MB
clang++	02_rando_large_083	AC	5 ms	5 MB
clang++	02_rando_large_147	AC	2 ms	4 MB
clang++	02_rando_large_164	AC	7 ms	6 MB
clang++	02_rando_large_227	AC	6 ms	6 MB
clang++	02_rando_large_283	AC	8 ms	7 MB
clang++	02_rando_large_336	AC	7 ms	6 MB
clang++	02_rando_large_368	AC	5 ms	5 MB
clang++	05_attack_00	AC	2 ms	4 MB
clang++	05_attack_01	AC	2 ms	4 MB
clang++	05_attack_mi0803_00	AC	2 ms	4 MB
clang++	10_random_small_000	AC	2 ms	4 MB
clang++	10_random_small_001	AC	2 ms	4 MB
clang++	10_random_small_002	AC	2 ms	4 MB
clang++	10_random_small_003	AC	2 ms	4 MB
clang++	10_random_small_004	AC	2 ms	4 MB
clang++	10_random_small_005	AC	2 ms	4 MB
clang++	10_random_small_006	AC	2 ms	4 MB
clang++	10_random_small_007	AC	2 ms	4 MB
clang++	10_random_small_008	AC	2 ms	4 MB
clang++	10_random_small_009	AC	2 ms	4 MB
clang++	11_rando_medium_000	AC	2 ms	4 MB
clang++	11_rando_medium_001	AC	2 ms	4 MB
clang++	11_rando_medium_002	AC	2 ms	4 MB
clang++	11_rando_medium_003	AC	2 ms	4 MB
clang++	11_rando_medium_004	AC	2 ms	4 MB
clang++	11_rando_medium_005	AC	2 ms	4 MB
clang++	11_rando_medium_006	AC	2 ms	4 MB
clang++	11_rando_medium_007	AC	2 ms	4 MB
clang++	11_rando_medium_008	AC	2 ms	4 MB
clang++	11_rando_medium_009	AC	2 ms	4 MB
clang++	12_random_large_000	AC	72 ms	49 MB
clang++	12_random_large_001	AC	68 ms	47 MB
clang++	12_random_large_002	AC	172 ms	117 MB
clang++	12_random_large_003	AC	15 ms	12 MB
clang++	12_random_large_004	AC	110 ms	74 MB
clang++	12_random_large_005	AC	30 ms	22 MB
clang++	12_random_large_006	AC	131 ms	87 MB
clang++	12_random_large_007	AC	11 ms	10 MB
clang++	12_random_large_008	AC	56 ms	40 MB
clang++	12_random_large_009	AC	60 ms	41 MB
clang++	22_shortMusics_Large_000	AC	146 ms	65 MB
clang++	22_shortMusics_Large_001	AC	125 ms	56 MB
clang++	22_shortMusics_Large_002	AC	231 ms	100 MB
clang++	22_shortMusics_Large_003	AC	256 ms	112 MB
clang++	22_shortMusics_Large_004	AC	182 ms	80 MB
clang++	22_shortMusics_Large_005	AC	236 ms	103 MB
clang++	22_shortMusics_Large_006	AC	168 ms	75 MB
clang++	22_shortMusics_Large_007	AC	207 ms	90 MB
clang++	22_shortMusics_Large_008	AC	102 ms	46 MB
clang++	22_shortMusics_Large_009	AC	143 ms	63 MB
clang++	41_separate_medium_000	AC	2 ms	4 MB
clang++	41_separate_medium_001	AC	2 ms	4 MB
clang++	41_separate_medium_002	AC	2 ms	4 MB
clang++	41_separate_medium_003	AC	2 ms	4 MB
clang++	41_separate_medium_004	AC	2 ms	4 MB
clang++	42_separate_large_000	AC	58 ms	50 MB
clang++	42_separate_large_001	AC	85 ms	71 MB
clang++	42_separate_large_002	AC	60 ms	52 MB
clang++	42_separate_large_003	AC	109 ms	90 MB
clang++	42_separate_large_004	AC	76 ms	66 MB

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