제출 #1231728

#제출 시각아이디문제언어결과실행 시간메모리
1231728mathmemonistKnapsack (NOI18_knapsack)C++20
37 / 100
1 ms328 KiB
#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;
}
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