Submission #447765

#	Time	Username	Problem	Language	Result	Execution time	Memory
447765		Neos	Knapsack (NOI18_knapsack)	C++14	100 / 100	75 ms	5196 KiB

knapsack

#include <bits/stdc++.h>
 
using namespace std;
 
typedef vector<pair<long long, long long>> vii;
 
#define pb push_back
#define all(x) x.begin(), x.end()
 
const int V = 1e6 + 7;
const int N = 1e5 + 7;
const int S = 2e3 + 7;
const int inf = 1e9;
 
long long s, n, v[N], w[N], k[N];
 
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
 
  #ifndef ONLINE_JUDGE
  // freopen("test.inp", "r", stdin);
  //freopen("test.out", "w", stdout);
  #endif
 
  cin >> s >> n;
  for (int i = 1; i <= n; i++) cin >> v[i] >> w[i] >> k[i];
 
  int mx = *max_element(k, k + n);
  // Subtask 1
  if (n == 1) {
    cout << v[1] * min(s / w[1], k[1]) << endl;
  }
  // Subtask 2 & 3: Normal knapsack
  else if (1 <= n && n <= 100 && mx <= 10) {
    long long dp[2001];
    memset(dp, 0, sizeof dp);
    for (int i = 1; i <= n; i++) 
      for (int j = s; j >= w[i]; j--)
        for (int t = 0; t <= k[i]; t++)
          if (j >= w[i] * t) {
            dp[j] = max(dp[j], dp[j - w[i] * t] + v[i] * t);
          }
    cout << dp[s] << endl;
  }
  // Subtask 4 & 5: knapsack with observation
  else if (1 <= n && n <= 1e5 && mx <= 1e9) {
 
    /*
      Observation: The numbers of taken product must less than S since 1 <= Wi <= S -> maximum taken product: S / W[i]
      -> consider the top valued S/W[i] items for each W[i]
    */
    vii obj[S];
    long long dp[2001];
    memset(dp, 0, sizeof dp);
    for (int i = 1; i <= n; i++) {
      obj[w[i]].pb({v[i], k[i]});
    }
 
    for (int i = 0; i <= s; i++) {
      if (obj[i].size() == 0) continue;
      sort(all(obj[i]), greater<pair<int, int>>());
 
      int id = 0;
      for (int j = 0; j * i < s; j++) {
        if (id >= obj[i].size()) break;
        for (int k = s; k >= i; k--) {
          dp[k] = max(dp[k], dp[k - i] + obj[i][id].first);
        }
        --obj[i][id].second;
        if (obj[i][id].second == 0) ++id;
      }
    }
    cout << dp[s] << endl;
  } 
}

Compilation message (stderr)

knapsack.cpp: In function 'int main()':
knapsack.cpp:66:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   66 |         if (id >= obj[i].size()) break;
      |             ~~~^~~~~~~~~~~~~~~~

• Subtask 1: 12 / 12
• Subtask 2: 17 / 17
• Subtask 3: 20 / 20
• Subtask 4: 24 / 24
• Subtask 5: 27 / 27