Submission #958131

#	Time	Username	Problem	Language	Result	Execution time	Memory
958131		MinaRagy06	Split the sequence (APIO14_sequence)	C++17	100 / 100	486 ms	85292 KiB

sequence

#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
#define ll long long
 
const int N = 100'005;
const ll inf = 1e18;
int a[N];
ll prf[N];
int prv[205][N];
array<ll, 2> dp[2][N];
int main() {
	ios_base::sync_with_stdio(0), cin.tie(0);
	int n, m;
	cin >> n >> m;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		prf[i] = prf[i - 1] + a[i];
	}
	m++;
	for (int i = 1; i <= n; i++) dp[0][i] = {-inf, -1};
	for (int j = 1; j <= m; j++) {
		dp[j & 1][0] = {-inf, -1};
		auto cmp = [&] (int x, int y, int z) {
			return (__int128_t) (dp[(j - 1) & 1][x][0] - dp[(j - 1) & 1][y][0] - prf[x] * prf[x] + prf[y] * prf[y]) * (prf[z] - prf[y]) >=
				   (__int128_t) (dp[(j - 1) & 1][y][0] - dp[(j - 1) & 1][z][0] - prf[y] * prf[y] + prf[z] * prf[z]) * (prf[y] - prf[x]);
		};
		auto calc = [&] (int i, int k) {
			return dp[(j - 1) & 1][k][0] + prf[k] * (prf[i] - prf[k]);
		};
		// {x, y, z}
		deque<int> dq;
		int sz = 0;
		for (int i = 1; i <= n; i++) {
// 			cout << i << ' ' << sz << endl;
			while (sz > 1 && cmp(dq[sz - 2], dq[sz - 1], i - 1)) {
				dq.pop_back();
				sz--;
			}
			dq.push_back(i - 1);
			sz++;
			while (sz > 1 && calc(i, dq[0]) <= calc(i, dq[1])) {
				dq.pop_front();
				sz--;
			}
			dp[j & 1][i] = {calc(i, dq[0]), dq[0]};
		}
		for (int i = 1; i <= n; i++) {
			prv[j][i] = dp[j & 1][i][1];
		}
	}
	cout << dp[m & 1][n][0] << '\n';
	int j = m, i = n;
	vector<int> ans;
	while (j > 1) {
		ans.push_back(prv[j][i]);
		i = prv[j][i];
		j--;
	}
	reverse(ans.begin(), ans.end());
	for (auto x : ans) {
		cout << x << ' ';
	}
	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