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

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• Last update: 2024-05-01 23:44:47+09:00
• 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)
• template/template.hpp

Code

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

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

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

int main() {
  int N;
  int64 W;
  cin >> N >> W;
  vector< int > v(N);
  vector< int64 > 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"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_I

#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/aoj-dpl-1-i.test.cpp"

#line 1 "dp/knapsack-limitations.hpp"
template <typename T, typename Compare = greater<T> >
vector<T> knapsack_limitations(const vector<int> &w, const vector<int> &m,
                               const vector<T> &v, const int &W, const T &NG,
                               const Compare &comp = Compare()) {
  const int N = (int)w.size();
  vector<T> dp(W + 1, NG), deqv(W + 1);
  dp[0] = T();
  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 2 "dp/knapsack-limitations-2.hpp"

template <typename T>
T knapsack_limitations(const vector<T> &w, const vector<T> &m,
                       const vector<int> &v, const T &W) {
  const int N = (int)w.size();
  auto v_max = *max_element(begin(v), end(v));
  if (v_max == 0) return 0;
  vector<int> ma(N);
  vector<T> mb(N);
  for (int i = 0; i < N; i++) {
    ma[i] = 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), less<>());
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord),
       [&](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 = min(mb[p], rest / w[p]);
      if (get <= 0) continue;
      cost += get * v[p];
      rest -= get * w[p];
    }
    ret = max(ret, cost);
  }
  return ret;
}
#line 6 "test/verify/aoj-dpl-1-i.test.cpp"

int main() {
  int N;
  int64 W;
  cin >> N >> W;
  vector< int > v(N);
  vector< int64 > 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.in	AC	6 ms	4 MB
g++	00_sample_01.in	AC	6 ms	4 MB
g++	00_sample_02.in	AC	6 ms	4 MB
g++	02_small_00.in	AC	8 ms	4 MB
g++	02_small_01.in	AC	14 ms	4 MB
g++	02_small_02.in	AC	6 ms	4 MB
g++	02_small_03.in	AC	11 ms	4 MB
g++	02_small_04.in	AC	6 ms	4 MB
g++	02_small_05.in	AC	11 ms	4 MB
g++	02_small_06.in	AC	7 ms	4 MB
g++	02_small_07.in	AC	12 ms	4 MB
g++	02_small_08.in	AC	12 ms	4 MB
g++	02_small_09.in	AC	9 ms	4 MB
g++	03_random_00.in	AC	7 ms	4 MB
g++	03_random_01.in	AC	29 ms	4 MB
g++	03_random_02.in	AC	6 ms	4 MB
g++	03_random_03.in	AC	11 ms	4 MB
g++	03_random_04.in	AC	6 ms	4 MB
g++	03_random_05.in	AC	10 ms	4 MB
g++	03_random_06.in	AC	7 ms	4 MB
g++	03_random_07.in	AC	12 ms	4 MB
g++	03_random_08.in	AC	13 ms	4 MB
g++	03_random_09.in	AC	8 ms	4 MB
g++	03_random_10.in	AC	9 ms	4 MB
g++	03_random_11.in	AC	9 ms	4 MB
g++	03_random_12.in	AC	6 ms	4 MB
g++	03_random_13.in	AC	14 ms	4 MB
g++	03_random_14.in	AC	6 ms	4 MB
g++	03_random_15.in	AC	11 ms	4 MB
g++	03_random_16.in	AC	10 ms	4 MB
g++	03_random_17.in	AC	9 ms	4 MB
g++	03_random_18.in	AC	8 ms	4 MB
g++	03_random_19.in	AC	8 ms	4 MB
g++	04_large_00.in	AC	8 ms	4 MB
g++	04_large_01.in	AC	14 ms	4 MB
g++	04_large_02.in	AC	6 ms	4 MB
g++	04_large_03.in	AC	15 ms	4 MB
g++	04_large_04.in	AC	7 ms	4 MB
g++	04_large_05.in	AC	11 ms	4 MB
g++	04_large_06.in	AC	7 ms	4 MB
g++	04_large_07.in	AC	12 ms	4 MB
g++	04_large_08.in	AC	13 ms	4 MB
g++	04_large_09.in	AC	8 ms	4 MB
g++	04_large_10.in	AC	8 ms	4 MB
g++	04_large_11.in	AC	8 ms	4 MB
g++	04_large_12.in	AC	6 ms	4 MB
g++	04_large_13.in	AC	14 ms	4 MB
g++	04_large_14.in	AC	6 ms	4 MB
g++	04_large_15.in	AC	11 ms	4 MB
g++	04_large_16.in	AC	9 ms	4 MB
g++	04_large_17.in	AC	9 ms	4 MB
g++	04_large_18.in	AC	9 ms	4 MB
g++	04_large_19.in	AC	8 ms	4 MB
g++	05_worst_00.in	AC	19 ms	5 MB
g++	05_worst_01.in	AC	18 ms	5 MB
g++	05_worst_02.in	AC	19 ms	5 MB
g++	06_corner_00.in	AC	6 ms	4 MB
g++	06_corner_01.in	AC	6 ms	4 MB
g++	06_corner_02.in	AC	6 ms	4 MB
g++	06_corner_03.in	AC	6 ms	4 MB
clang++	00_sample_00.in	AC	6 ms	4 MB
clang++	00_sample_01.in	AC	7 ms	4 MB
clang++	00_sample_02.in	AC	6 ms	4 MB
clang++	02_small_00.in	AC	8 ms	4 MB
clang++	02_small_01.in	AC	16 ms	5 MB
clang++	02_small_02.in	AC	6 ms	4 MB
clang++	02_small_03.in	AC	12 ms	4 MB
clang++	02_small_04.in	AC	6 ms	4 MB
clang++	02_small_05.in	AC	11 ms	4 MB
clang++	02_small_06.in	AC	7 ms	4 MB
clang++	02_small_07.in	AC	13 ms	4 MB
clang++	02_small_08.in	AC	13 ms	4 MB
clang++	02_small_09.in	AC	8 ms	4 MB
clang++	03_random_00.in	AC	8 ms	4 MB
clang++	03_random_01.in	AC	14 ms	5 MB
clang++	03_random_02.in	AC	6 ms	4 MB
clang++	03_random_03.in	AC	12 ms	4 MB
clang++	03_random_04.in	AC	6 ms	4 MB
clang++	03_random_05.in	AC	11 ms	4 MB
clang++	03_random_06.in	AC	7 ms	4 MB
clang++	03_random_07.in	AC	13 ms	4 MB
clang++	03_random_08.in	AC	13 ms	4 MB
clang++	03_random_09.in	AC	8 ms	4 MB
clang++	03_random_10.in	AC	9 ms	4 MB
clang++	03_random_11.in	AC	9 ms	4 MB
clang++	03_random_12.in	AC	6 ms	4 MB
clang++	03_random_13.in	AC	14 ms	4 MB
clang++	03_random_14.in	AC	6 ms	4 MB
clang++	03_random_15.in	AC	12 ms	4 MB
clang++	03_random_16.in	AC	10 ms	4 MB
clang++	03_random_17.in	AC	9 ms	4 MB
clang++	03_random_18.in	AC	9 ms	4 MB
clang++	03_random_19.in	AC	8 ms	4 MB
clang++	04_large_00.in	AC	7 ms	4 MB
clang++	04_large_01.in	AC	14 ms	5 MB
clang++	04_large_02.in	AC	6 ms	4 MB
clang++	04_large_03.in	AC	11 ms	4 MB
clang++	04_large_04.in	AC	6 ms	4 MB
clang++	04_large_05.in	AC	11 ms	4 MB
clang++	04_large_06.in	AC	7 ms	4 MB
clang++	04_large_07.in	AC	12 ms	4 MB
clang++	04_large_08.in	AC	13 ms	4 MB
clang++	04_large_09.in	AC	9 ms	4 MB
clang++	04_large_10.in	AC	8 ms	4 MB
clang++	04_large_11.in	AC	9 ms	4 MB
clang++	04_large_12.in	AC	6 ms	4 MB
clang++	04_large_13.in	AC	15 ms	4 MB
clang++	04_large_14.in	AC	6 ms	4 MB
clang++	04_large_15.in	AC	12 ms	4 MB
clang++	04_large_16.in	AC	10 ms	4 MB
clang++	04_large_17.in	AC	9 ms	4 MB
clang++	04_large_18.in	AC	9 ms	4 MB
clang++	04_large_19.in	AC	8 ms	4 MB
clang++	05_worst_00.in	AC	20 ms	5 MB
clang++	05_worst_01.in	AC	23 ms	5 MB
clang++	05_worst_02.in	AC	20 ms	5 MB
clang++	06_corner_00.in	AC	6 ms	4 MB
clang++	06_corner_01.in	AC	6 ms	4 MB
clang++	06_corner_02.in	AC	6 ms	4 MB
clang++	06_corner_03.in	AC	6 ms	4 MB

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