Submission #1231728

#	Time	Username	Problem	Language	Result	Execution time	Memory
1231728		mathmemonist	Knapsack (NOI18_knapsack)	C++20	37 / 100	1 ms	328 KiB

knapsack

#include <bits/stdc++.h>
using namespace std;
#define fastio ios_base::sync_with_stdio(false);cin.tie(0); cout.tie(0);
#define pb push_back
using ll = long long;

const int MAXK = 2005; // max weight capacity

int main() {
    fastio
    
    int k, n;
    cin >> k >> n;

    vector<int> value(n+1), weight(n+1), freq(n+1);
    for (int i = 1; i <= n; i++) {
        cin >> value[i] >> weight[i] >> freq[i];
    }

    // Use binary decomposition to convert bounded knapsack to 0/1 knapsack
    vector<int> new_weight, new_value;
    for (int i = 1; i <= n; i++) {
        int f = freq[i], w = weight[i], v = value[i];
        for (int j = 1; f > 0; j <<= 1) {
            int cnt = min(j, f);
            new_weight.pb(cnt * w);
            new_value.pb(cnt * v);
            f -= cnt;
        }
    }

    // Now apply 0/1 knapsack DP on new_weight/new_value
    vector<int> dp(k + 1, 0);

    for (int i = 0; i < new_weight.size(); i++) {
        for (int j = k; j >= new_weight[i]; j--) {
            dp[j] = max(dp[j], dp[j - new_weight[i]] + new_value[i]);
        }
    }

    cout << dp[k] << endl;

    return 0;
}

• Subtask 1: 0 / 12
• Subtask 2: 17 / 17
• Subtask 3: 20 / 20
• Subtask 4: 0 / 24
• Subtask 5: 0 / 27