Submission #404385

#	Time	Username	Problem	Language	Result	Execution time	Memory
404385		BERNARB01	Split the sequence (APIO14_sequence)	C++17	71 / 100	2067 ms	92792 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

const long long is_query = -(1LL<<62);

struct line {
	long long m, b;
	int id;
	mutable function<const line*()> succ;
	bool operator<(const line& rhs) const {
		if (rhs.b != is_query) return m < rhs.m;
		const line* s = succ();
		if (!s) return 0;
		long long x = rhs.m;
		return b - s->b < (s->m - m) * x;
	}
};

struct dynamic_hull : public multiset<line> {
	const long long inf = LLONG_MAX;
	bool bad(iterator y) {
		auto z = next(y);
		if (y == begin()) {
			if (z == end()) return 0;
			return y->m == z->m && y->b <= z->b;
		}
		auto x = prev(y);
		if (z == end()) return y->m == x->m && y->b <= x->b;
		long long v1 = (x->b - y->b);
		if (y->m == x->m) v1 = x->b > y->b ? inf : -inf;
		else v1 /= (y->m - x->m);
		long long v2 = (y->b - z->b);
		if (z->m == y->m) v2 = y->b > z->b ? inf : -inf;
		else v2 /= (z->m - y->m);
		return v1 >= v2;
	}
	void insert_line(long long b, long long m, int id) {
		auto y = insert({ m, b, id });
		y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
		if (bad(y)) { erase(y); return; }
		while (next(y) != end() && bad(next(y))) erase(next(y));
		while (y != begin() && bad(prev(y))) erase(prev(y));
	}
	pair<long long, int> eval(long long x) {
		auto l = *lower_bound((line) { x, is_query });
		return pair<long long, int>(l.m * x + l.b, l.id);
	}
};

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);
		dynamic_hull 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: 0 / 29