Submission #404468

#	Time	Username	Problem	Language	Result	Execution time	Memory
404468		BERNARB01	Split the sequence (APIO14_sequence)	C++17	100 / 100	1806 ms	94224 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

class bag {
private:
	class line {
		public:
			long long m, b;
			int j;
			line(long long mm, long long bb, int id) {
				m = mm;
				b = bb;
				j = id;
			}
			long double taq(const line& d) const {
				return (long double) (d.b - b) / (long double) (m - d.m);
			}
	};
	int I;
	vector<pair<line, long double>> stk;
public:
	bag() {
		I = 0;
	}
	void insert_line(long long b, long long m, long long id) {
		line d(m, b, id);
		while (stk.size() > 1 && ((stk.back().first.m == m && stk.back().first.b <= b) || stk.back().second <= d.taq(stk.back().first))) {
			stk.pop_back();
		}
		if (!stk.empty() && stk.back().first.m == m) {
			if (stk.back().first.b > d.b) {
				d = stk.back().first;
			}
			stk.pop_back();
		}
		stk.push_back({d, (stk.empty() ? LLONG_MAX : d.taq(stk.back().first))});
	}
	pair<long long, int> eval(long long x) {
		I = min(I, (int) stk.size() - 1);
		while (I < (int) stk.size() && (long double) x < stk[I].second) {
			I++;
		}
		if (I >= (int) stk.size()) {
			I = stk.size() - 1;
		}
		if (x >= stk[I].second) {
			I--;
		}
		line d = stk[I].first;
		return pair<long long, int>(d.m * x + d.b, d.j);
	}
};

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n, k;
	cin >> n >> k;
	vector<int> a(n);
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	vector<long long> sum(n);
	sum[0] = a[0];
	for (int i = 1; i < n; i++) {
		sum[i] = a[i] + sum[i - 1];
	}
	vector<long long> sr(n);
	sr[n - 1] = a[n - 1];
	for (int i = n - 2; i >= 0; i--) {
		sr[i] = a[i] + sr[i + 1];
	}
	vector<long long> dp(n);
	vector<vector<int>> en(k + 1, vector<int>(n, -1));
	for (int i = 0; i < n; i++) {
		dp[i] = (sum[n - 1] - sum[i]) * (sum[i]);
	}
	for (int i = 2; i <= k; i++) {
		vector<long long> new_dp(n, 0);
		bag chL;
		chL.insert_line(dp[i - 2], sr[i - 1], i - 2);
		for (int j = i - 1; j + 1 < n; j++) {
			pair<long long, int> fromCh = chL.eval(sr[j + 1]);
			new_dp[j] = fromCh.first - sr[j + 1] * sr[j + 1];
			en[i][j] = fromCh.second;
			chL.insert_line(dp[j], sr[j + 1], j);
		}
		swap(dp, new_dp);
	}
	pair<long long, int> p = {-1, -1};
	for (int i = 0; i + 1 < n; i++) {
		p = max(p, {dp[i], i});
	}
	cout << p.first << '\n';
	int ptr = p.second;
	for (int i = k; i > 0; i--) {
		cout << ptr + 1 << " ";
		assert(en[i][ptr] < ptr);
		ptr = en[i][ptr];
	}
	cout << '\n';
	return 0;
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29