Submission #1316570

#	Time	Username	Problem	Language	Result	Execution time	Memory
1316570		ivycube	Knapsack (NOI18_knapsack)	C++20	100 / 100	36 ms	2888 KiB

knapsack

#include <iostream>
#include <algorithm>
#include <utility>
#include <vector>

using namespace std;
using ll = long long;

const int M = 1e5 + 5;
int S, N, V[M], W[M], K[M];

void solve1() {
    vector<ll> dp(S+1, 0);
    for (int i = 1; i <= N; i++) {
        // consider ith item
        for (int j = S; j >= W[i]; j--) {
            // update weight sum j backward given Wi and Ki
            for (int cnt = 1; cnt <= K[i]; cnt++) {
                int wsum = cnt * W[i];
                int vsum = cnt * V[i];
                if (wsum <= j) dp[j] = max(dp[j], dp[j - wsum] + vsum);
            }
        }
    }
    cout << dp[S] << endl;
}

void solve2() {
    vector<pair<int, int>> items_by[S+1];
    for (int i = 1; i <= N; i++)
        items_by[W[i]].push_back(make_pair(V[i], K[i]));
    
    vector<ll> dp(S+1, 0);
    for (int weight = 1; weight <= S; weight++) {
        if (items_by[weight].empty()) continue;
        sort(items_by[weight].rbegin(), items_by[weight].rend());
        
        int idx = 0;
        int cnt = 0;
        while ((++cnt)*weight <= S && idx < items_by[weight].size()) {
            int vi = items_by[weight][idx].first;
            for (int j = S; j >= weight; j--)
                dp[j] = max(dp[j], dp[j - weight] + vi);
            
            if ((--items_by[weight][idx].second) == 0) idx++;
        }
    }
    cout << dp[S] << endl;
}

int main() {
    iostream::sync_with_stdio(false);
    cin.tie(nullptr);

    cin >> S >> N;
    int maxK = 0;
    for (int i = 1; i <= N; i++) {
        cin >> V[i] >> W[i] >> K[i];
        maxK = max(maxK, K[i]);
    }
    
    if (N == 1) cout << V[1] * min(K[1], S/W[1]) << endl;
    else if (N <= 100 && maxK <= 10) solve1();
    else solve2();
    
    return 0;
}

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