Submission #1291871

#	Time	Username	Problem	Language	Result	Execution time	Memory
1291871		atharva0300	Knapsack (NOI18_knapsack)	C++20	73 / 100	1097 ms	16904 KiB

knapsack

#include <bits/stdc++.h>
using namespace std;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    
    int S, N;
    cin >> S >> N;
    
    vector<pair<int, long long>> items; // {weight, value}
    
    for (int i = 0; i < N; i++) {
        long long V;
        int W, K;
        cin >> V >> W >> K;
        
        // Skip if single item is too heavy
        if (W > S) continue;
        
        // Binary representation optimization
        int cnt = 1;
        while (cnt <= K) {
            if ((long long)W * cnt > S) break; // Stop if weight exceeds capacity
            items.push_back({W * cnt, V * cnt});
            K -= cnt;
            cnt *= 2;
        }
        // Add remainder if it fits
        if (K > 0 && (long long)W * K <= S) {
            items.push_back({W * K, V * K});
        }
    }
    
    // Standard 0/1 knapsack with space optimization
    vector<long long> dp(S + 1, 0);
    
    for (auto& [weight, value] : items) {
        for (int w = S; w >= weight; w--) {
            dp[w] = max(dp[w], dp[w - weight] + value);
        }
    }
    
    cout << dp[S] << '\n';
    
    return 0;
}

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