Submission #1145700

#	Time	Username	Problem	Language	Result	Execution time	Memory
1145700		poltanos	Knapsack (NOI18_knapsack)	C++20	100 / 100	66 ms	34376 KiB

knapsack

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

const int inf = 1e18;

// Try to accurately compute the time complexity
// Also remember 1/1 + 1/2 + 1/3 + ... + 1/n = log(n) [approx]

void solve(){
    int limit, type_num;
    cin >> limit >> type_num;

    map<int, vector<pair<int, int>>> by_weight;
    for(int t = 0; t < type_num; t++){
        int val, wt, amt;
        cin >> val >> wt >> amt;

        if(wt <= limit && amt > 0) by_weight[wt].push_back({val, amt});
    }

    /*
	*   best[i][j] contains the most value we can
	*   get using j weight and the first i weight types
	*/
    vector<vector<int>> best(by_weight.size() + 1, vector<int> (limit + 1, -inf));
    best[0][0] = 0;
    int at = 1;

    for(auto &[wt, items] : by_weight){
        sort(items.begin(), items.end(), greater<pair<int, int>>());

        for(int i = 0; i <= limit; i++){
            best[at][i] = best[at - 1][i];

            int copies = 0, type_at = 0, curr_used = 0, profit = 0;
            while((copies + 1)*wt <= i && type_at < items.size()){
                copies++;
                profit += items[type_at].first;

                if(best[at - 1][i - copies*wt] != -inf){
                    best[at][i] = max(best[at][i], best[at - 1][i - copies*wt] + profit);
                }

                curr_used++;
                if(curr_used == items[type_at].second){
                    curr_used = 0;
                    type_at++;
                }
            }
        }

        at++;
    }

    cout << *max_element(best.back().begin(), best.back().end()) << endl;
}

signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t = 1;
    while(t--) solve();

    return 0;
}

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