test/verify/aoj-dpl-1-i.test.cpp

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• Last update: 2026-08-10 10:46:05+00:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_I

Depends on

• Knapsack Limitations (個数制限つきナップサック問題) $O(N^2 \max(v_i)^2)$ (dp/knapsack-limitations-2.hpp)
• Knapsack Limitations (個数制限つきナップサック問題) $O(NW)$ (dp/knapsack-limitations.hpp)

Code

// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_I
// clang-format on

#include <iostream>
#include <vector>

#include "../../dp/knapsack-limitations-2.hpp"

using namespace std;

int main() {
  int N;
  long long W;
  cin >> N >> W;
  vector<int> v(N);
  vector<long long> w(N), m(N);
  for (int i = 0; i < N; i++) {
    cin >> v[i] >> w[i] >> m[i];
  }
  cout << knapsack_limitations(w, m, v, W) << endl;
}

#line 1 "test/verify/aoj-dpl-1-i.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_I
// clang-format on

#include <iostream>
#include <vector>

#line 2 "dp/knapsack-limitations-2.hpp"

#include <algorithm>
#include <functional>
#include <numeric>
#line 7 "dp/knapsack-limitations-2.hpp"

#line 2 "dp/knapsack-limitations.hpp"

#line 5 "dp/knapsack-limitations.hpp"

template <typename T, typename Compare = std::greater<T> >
std::vector<T> knapsack_limitations(const std::vector<int>& w,
                                    const std::vector<int>& m,
                                    const std::vector<T>& v, const int& W,
                                    const T& NG,
                                    const Compare& comp = Compare()) {
  const int N = (int)w.size();
  std::vector<T> dp(W + 1, NG), deqv(W + 1);
  dp[0] = T();
  std::vector<int> deq(W + 1);
  for (int i = 0; i < N; i++) {
    if (w[i] == 0) {
      for (int j = 0; j <= W; j++) {
        if (dp[j] != NG && comp(dp[j] + v[i] * m[i], dp[j])) {
          dp[j] = dp[j] + v[i] * m[i];
        }
      }
    } else {
      for (int a = 0; a < w[i]; a++) {
        int s = 0, t = 0;
        for (int j = 0; w[i] * j + a <= W; j++) {
          if (dp[w[i] * j + a] != NG) {
            auto val = dp[w[i] * j + a] - j * v[i];
            while (s < t && comp(val, deqv[t - 1])) --t;
            deq[t] = j;
            deqv[t++] = val;
          }
          if (s < t) {
            dp[j * w[i] + a] = deqv[s] + j * v[i];
            if (deq[s] == j - m[i]) ++s;
          }
        }
      }
    }
  }
  return dp;
}
#line 9 "dp/knapsack-limitations-2.hpp"

template <typename T>
T knapsack_limitations(const std::vector<T>& w, const std::vector<T>& m,
                       const std::vector<int>& v, const T& W) {
  const int N = (int)w.size();
  auto v_max = *std::max_element(v.begin(), v.end());
  if (v_max == 0) return 0;
  std::vector<int> ma(N);
  std::vector<T> mb(N);
  for (int i = 0; i < N; i++) {
    ma[i] = std::min<T>(m[i], v_max - 1);
    mb[i] = m[i] - ma[i];
  }
  T sum = 0;
  for (int i = 0; i < N; i++) sum += ma[i] * v[i];
  auto dp = knapsack_limitations(v, ma, w, sum, T(-1), std::less<>());
  std::vector<int> ord(N);
  std::iota(ord.begin(), ord.end(), 0);
  std::sort(ord.begin(), ord.end(),
            [&](int a, int b) { return v[a] * w[b] > v[b] * w[a]; });
  T ret = T();
  for (int i = 0; i < dp.size(); i++) {
    if (dp[i] > W || dp[i] == -1) continue;
    T rest = W - dp[i], cost = i;
    for (auto& p : ord) {
      auto get = std::min(mb[p], rest / w[p]);
      if (get <= 0) continue;
      cost += get * v[p];
      rest -= get * w[p];
    }
    ret = std::max(ret, cost);
  }
  return ret;
}
#line 9 "test/verify/aoj-dpl-1-i.test.cpp"

using namespace std;

int main() {
  int N;
  long long W;
  cin >> N >> W;
  vector<int> v(N);
  vector<long long> w(N), m(N);
  for (int i = 0; i < N; i++) {
    cin >> v[i] >> w[i] >> m[i];
  }
  cout << knapsack_limitations(w, m, v, W) << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_00	AC	2 ms	4 MB
g++	00_sample_01	AC	2 ms	4 MB
g++	00_sample_02	AC	2 ms	4 MB
g++	02_small_00	AC	4 ms	4 MB
g++	02_small_01	AC	11 ms	5 MB
g++	02_small_02	AC	2 ms	3 MB
g++	02_small_03	AC	8 ms	4 MB
g++	02_small_04	AC	2 ms	4 MB
g++	02_small_05	AC	7 ms	4 MB
g++	02_small_06	AC	3 ms	4 MB
g++	02_small_07	AC	8 ms	4 MB
g++	02_small_08	AC	10 ms	4 MB
g++	02_small_09	AC	5 ms	4 MB
g++	03_random_00	AC	4 ms	4 MB
g++	03_random_01	AC	10 ms	4 MB
g++	03_random_02	AC	2 ms	3 MB
g++	03_random_03	AC	9 ms	4 MB
g++	03_random_04	AC	2 ms	4 MB
g++	03_random_05	AC	7 ms	4 MB
g++	03_random_06	AC	3 ms	4 MB
g++	03_random_07	AC	8 ms	4 MB
g++	03_random_08	AC	9 ms	4 MB
g++	03_random_09	AC	5 ms	4 MB
g++	03_random_10	AC	5 ms	4 MB
g++	03_random_11	AC	5 ms	4 MB
g++	03_random_12	AC	2 ms	4 MB
g++	03_random_13	AC	10 ms	4 MB
g++	03_random_14	AC	2 ms	4 MB
g++	03_random_15	AC	8 ms	4 MB
g++	03_random_16	AC	7 ms	4 MB
g++	03_random_17	AC	5 ms	4 MB
g++	03_random_18	AC	5 ms	4 MB
g++	03_random_19	AC	4 ms	4 MB
g++	04_large_00	AC	4 ms	4 MB
g++	04_large_01	AC	10 ms	4 MB
g++	04_large_02	AC	2 ms	4 MB
g++	04_large_03	AC	7 ms	4 MB
g++	04_large_04	AC	2 ms	4 MB
g++	04_large_05	AC	8 ms	4 MB
g++	04_large_06	AC	3 ms	4 MB
g++	04_large_07	AC	9 ms	4 MB
g++	04_large_08	AC	11 ms	4 MB
g++	04_large_09	AC	5 ms	4 MB
g++	04_large_10	AC	4 ms	4 MB
g++	04_large_11	AC	5 ms	4 MB
g++	04_large_12	AC	2 ms	4 MB
g++	04_large_13	AC	10 ms	4 MB
g++	04_large_14	AC	2 ms	4 MB
g++	04_large_15	AC	9 ms	4 MB
g++	04_large_16	AC	6 ms	4 MB
g++	04_large_17	AC	6 ms	4 MB
g++	04_large_18	AC	5 ms	4 MB
g++	04_large_19	AC	4 ms	4 MB
g++	05_worst_00	AC	16 ms	5 MB
g++	05_worst_01	AC	15 ms	5 MB
g++	05_worst_02	AC	16 ms	5 MB
g++	06_corner_00	AC	2 ms	4 MB
g++	06_corner_01	AC	2 ms	4 MB
g++	06_corner_02	AC	2 ms	4 MB
g++	06_corner_03	AC	2 ms	4 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++	02_small_00	AC	4 ms	4 MB
clang++	02_small_01	AC	11 ms	4 MB
clang++	02_small_02	AC	2 ms	4 MB
clang++	02_small_03	AC	8 ms	4 MB
clang++	02_small_04	AC	2 ms	4 MB
clang++	02_small_05	AC	7 ms	4 MB
clang++	02_small_06	AC	3 ms	4 MB
clang++	02_small_07	AC	11 ms	4 MB
clang++	02_small_08	AC	12 ms	4 MB
clang++	02_small_09	AC	5 ms	4 MB
clang++	03_random_00	AC	4 ms	4 MB
clang++	03_random_01	AC	10 ms	4 MB
clang++	03_random_02	AC	2 ms	4 MB
clang++	03_random_03	AC	7 ms	4 MB
clang++	03_random_04	AC	2 ms	4 MB
clang++	03_random_05	AC	7 ms	4 MB
clang++	03_random_06	AC	3 ms	4 MB
clang++	03_random_07	AC	8 ms	4 MB
clang++	03_random_08	AC	10 ms	4 MB
clang++	03_random_09	AC	5 ms	4 MB
clang++	03_random_10	AC	4 ms	4 MB
clang++	03_random_11	AC	5 ms	4 MB
clang++	03_random_12	AC	2 ms	4 MB
clang++	03_random_13	AC	10 ms	4 MB
clang++	03_random_14	AC	2 ms	4 MB
clang++	03_random_15	AC	8 ms	4 MB
clang++	03_random_16	AC	6 ms	4 MB
clang++	03_random_17	AC	5 ms	4 MB
clang++	03_random_18	AC	5 ms	4 MB
clang++	03_random_19	AC	4 ms	4 MB
clang++	04_large_00	AC	4 ms	4 MB
clang++	04_large_01	AC	10 ms	4 MB
clang++	04_large_02	AC	2 ms	4 MB
clang++	04_large_03	AC	7 ms	4 MB
clang++	04_large_04	AC	2 ms	4 MB
clang++	04_large_05	AC	7 ms	4 MB
clang++	04_large_06	AC	3 ms	4 MB
clang++	04_large_07	AC	8 ms	4 MB
clang++	04_large_08	AC	10 ms	4 MB
clang++	04_large_09	AC	5 ms	4 MB
clang++	04_large_10	AC	4 ms	4 MB
clang++	04_large_11	AC	5 ms	4 MB
clang++	04_large_12	AC	2 ms	4 MB
clang++	04_large_13	AC	10 ms	4 MB
clang++	04_large_14	AC	2 ms	4 MB
clang++	04_large_15	AC	8 ms	4 MB
clang++	04_large_16	AC	6 ms	4 MB
clang++	04_large_17	AC	5 ms	4 MB
clang++	04_large_18	AC	5 ms	4 MB
clang++	04_large_19	AC	4 ms	4 MB
clang++	05_worst_00	AC	16 ms	5 MB
clang++	05_worst_01	AC	15 ms	5 MB
clang++	05_worst_02	AC	16 ms	5 MB
clang++	06_corner_00	AC	2 ms	4 MB
clang++	06_corner_01	AC	2 ms	4 MB
clang++	06_corner_02	AC	2 ms	4 MB
clang++	06_corner_03	AC	2 ms	4 MB

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