Submission #1195423

#	Time	Username	Problem	Language	Result	Execution time	Memory
1195423		timeflew	Knapsack (NOI18_knapsack)	C++20	73 / 100	1093 ms	2632 KiB

knapsack

//test by gpt 4
#include <bits/stdc++.h>
using namespace std;

#define ll long long

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

    int S, N;
    cin >> S >> N;

    struct Item { ll v, w, k; };
    vector<Item> items(N);
    for (int i = 0; i < N; i++) {
        cin >> items[i].v >> items[i].w >> items[i].k;
    }

    // dp[x] = max total value with weight exactly x
    const ll NEG_INF = LLONG_MIN / 4;
    vector<ll> dp(S+1, NEG_INF);
    dp[0] = 0;

    for (auto &it : items) {
        ll V = it.v, W = it.w, K = it.k;
        ll rem = K;
        // binary‐split the K copies into sums of powers of two
        for (ll batch = 1; rem > 0; batch <<= 1) {
            ll take = min(batch, rem);
            rem -= take;
            ll weight = take * W;
            ll value  = take * V;
            if (weight > S) 
                continue;
            // 0–1 knapsack for this “batch” chunk
            for (int x = S; x >= weight; x--) {
                if (dp[x - weight] != NEG_INF) {
                    dp[x] = max(dp[x], dp[x - weight] + value);
                }
            }
        }
    }

    // answer = best over all weights ≤ S
    ll ans = 0;
    for (int x = 0; x <= S; x++) {
        ans = max(ans, dp[x]);
    }
    cout << ans << "\n";

    return 0;
}

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