Submission #931286

#	Time	Username	Problem	Language	Result	Execution time	Memory
931286		mannshah1211	Knapsack (NOI18_knapsack)	C++17	100 / 100	66 ms	7872 KiB

knapsack

/*
 * Plat on the Open.
 */

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

#define int long long
#define f first
#define s second
#define all(x) x.begin(), x.end()
#define pb push_back

using T = pair<int, int>;

void solve() {
	int s, n;
	cin >> s >> n;
	vector<int> v(n), w(n), k(n);
	vector<vector<T>> buckets(s + 1);
	for (int i = 0; i < n; i++) {
		cin >> v[i] >> w[i] >> k[i];
		buckets[w[i]].pb({v[i], k[i]});
	}
	vector<vector<T>> items(s + 1);
	for (int i = 1; i <= s; i++) sort(all(buckets[i])), reverse(all(buckets[i]));
	for (int i = 1; i <= s; i++) {
		int sz = buckets[i].size();
		vector<int> psums_vals(sz + 1), psums_items(sz + 1);
		for (int j = 1; j <= sz; j++) {
			auto [x, y] = buckets[i][j - 1];
			psums_vals[j] = psums_vals[j - 1] + (x * y);
			psums_items[j] = psums_items[j - 1] + y;
		}
		for (int j = i; j <= min(i * psums_items[sz], s); j += i) {
			int needed_items = j / i;
			int lo = 0, hi = sz, ind = -1;
			while (lo <= hi) {
				int mid = (lo + hi) / 2;
				if (psums_items[mid] <= needed_items) {
					ind = mid;
					lo = mid + 1;
				} else {
					hi = mid - 1;
				}
			}
			if (ind != -1) {
				int x = (ind == sz) ? 0 : buckets[i][ind].f;
				int val = psums_vals[ind] + ((needed_items - psums_items[ind]) * x);
				items[i].pb(make_pair(j, val));
			} else {
				assert(0);
				int val = needed_items * buckets[i][0].f;
				items[i].pb(make_pair(j, val));
			}
		}
	}
	vector<int> dp(s + 1, 0), ndp(s + 1, 0);
	for (int i = 1; i <= s; i++) {
		for (int j = 0; j <= s; j++) {
			ndp[j] = dp[j];
			if (j >= 1) ndp[j] = max(ndp[j], ndp[j - 1]);
			for (auto& [weight, val] : items[i]) {
				if (j >= weight) {
					ndp[j] = max(ndp[j], dp[j - weight] + val);
				}
			}
		}
		swap(ndp, dp);
	}
	cout << dp[s] << '\n';
}

int32_t main() {
	ios::sync_with_stdio(false); cin.tie(0);
	int tt = 1;
	// cin >> tt;
	while (tt--) {
		solve();
	}
}

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