제출 #1261727

#제출 시각아이디문제언어결과실행 시간메모리
1261727mentariosKnapsack (NOI18_knapsack)C++20
73 / 100
1096 ms328 KiB
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define _ ios_base::sync_with_stdio(0); cin.tie(0);

struct Item {
    ll w, v;
};

int main() { _
    int S, N;
    cin >> S >> N;

    vector<ll> dp(S + 1, 0);

    for (int i = 0; i < N; i++) {
        ll v, w, k; // Valor, Peso, Quantidade
        cin >> v >> w >> k;

        // Se o item é efetivamente ilimitado
        if (k * w >= S) {
            // Aplicamos a lógica do Knapsack ILIMITADO (loop para frente)
            for (int j = w; j <= S; j++) {
                dp[j] = max(dp[j], dp[j - w] + v);
            }
        } else {
            // Se o item é realmente limitado, usamos o splitting binário
            ll c = 1;
            while (k > c) {
                k -= c;
                ll current_w = c * w;
                ll current_v = c * v;
                // Aplicamos Knapsack 0/1 para cada pacote (loop para trás)
                for (int j = S; j >= current_w; j--) {
                    dp[j] = max(dp[j], dp[j - current_w] + current_v);
                }
                c *= 2;
            }
            // Pacote final com o resto
            ll current_w = k * w;
            ll current_v = k * v;
            for (int j = S; j >= current_w; j--) {
                dp[j] = max(dp[j], dp[j - current_w] + current_v);
            }
        }
    }

    cout << dp[S] << endl;
    return 0;
}
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