Submission #1291873

#	Time	Username	Problem	Language	Result	Execution time	Memory
1291873		atharva0300	Knapsack (NOI18_knapsack)	C++17	100 / 100	767 ms	620 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<long long> dp(S + 1, 0);
    
    for (int idx = 0; idx < N; idx++) {
        long long V;
        int W, K;
        cin >> V >> W >> K;
        
        if (W > S) continue;
        
        K = min(K, S / W);
        
        // If K is small, use binary representation
        if (K <= 20) {
            for (int cnt = 1; K > 0; cnt *= 2) {
                int take = min(cnt, K);
                int weight = W * take;
                long long value = V * take;
                
                for (int w = S; w >= weight; w--) {
                    dp[w] = max(dp[w], dp[w - weight] + value);
                }
                K -= take;
            }
        } 
        // If K is large, use monotonic deque optimization
        else {
            vector<long long> ndp = dp;
            for (int rem = 0; rem < W; rem++) {
                deque<pair<int, long long>> dq;
                for (int j = 0; j * W + rem <= S; j++) {
                    int pos = j * W + rem;
                    long long val = dp[pos] - (long long)j * V;
                    
                    while (!dq.empty() && dq.back().second <= val) {
                        dq.pop_back();
                    }
                    dq.push_back({j, val});
                    
                    while (!dq.empty() && dq.front().first < j - K) {
                        dq.pop_front();
                    }
                    
                    ndp[pos] = dq.front().second + (long long)j * V;
                }
            }
            dp = ndp;
        }
    }
    
    cout << dp[S] << '\n';
    
    return 0;
}

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