Submission #1219975

#	Time	Username	Problem	Language	Result	Execution time	Memory
1219975		brito.joao	Knapsack (NOI18_knapsack)	C++20	37 / 100	1 ms	328 KiB

knapsack

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

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    int S, N;
    cin >> S >> N;
    
    vector<int> dp(S + 1, 0);
    
    for (int i = 0; i < N; i++) {
        int V, W, K;
        cin >> V >> W >> K;
        
        // Binary lifting optimization for large K values
        vector<pair<int, int>> items; // {weight, value}
        
        int power = 1;
        while (power < K) {
            items.push_back({W * power, V * power});
            K -= power;
            power *= 2;
        }
        if (K > 0) {
            items.push_back({W * K, V * K});
        }
        
        // Process each binary representation item
        for (auto& item : items) {
            int weight = item.first;
            int value = item.second;
            
            // Standard 0/1 knapsack for each item (reverse iteration)
            for (int w = S; w >= weight; w--) {
                dp[w] = max(dp[w], dp[w - weight] + value);
            }
        }
    }
    
    cout << dp[S] << endl;
    
    return 0;
}

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