Submission #94855

#	Time	Username	Problem	Language	Result	Execution time	Memory
94855		Origims	Split the sequence (APIO14_sequence)	C++14	71 / 100	128 ms	132096 KiB

sequence

// In The Name Of God
#include <bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

#define sqr(A) ((A) * (A))
#define X first
#define Y second
#define MP make_pair
#define bsz  __builtin_popcount
#define all(A) A.begin(), A.end()
using namespace std;
using namespace __gnu_pbds;
template < typename T >
using ordered_set = tree < T , null_type , less < T > , rb_tree_tag , tree_order_statistics_node_update >;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pii;
typedef complex<ll> point;
const int MOD = 1e9 + 7;
const int MOD2 = 1e9 + 9;
const int PR = 727;
const int INF = INT_MAX;
const ll LINF = LLONG_MAX;

struct convexHull {
	vector<point> lines;
	vector<int>   idx;
	int pos = 0;

	ll F(point p, ll x) {
		return p.real() * x + p.imag();
	}

	ld I(point p1, point p2) {
		return (ld)(p2.imag() - p1.imag()) / (ld)(p1.real() - p2.real());
	}

	void add(point p, int id) {
		if (lines.size() && p.real() == lines.back().real()) return ;
		while (lines.size()) {
			point a = lines[lines.size() - 1];
			point b = lines[lines.size() - 2];
			if (I(p, b) <= I(b, a)) {
				lines.pop_back();
				idx.pop_back();
			}
			else
				break;
		}
		lines.push_back(p);
		idx.push_back(id);
	}

	pii get(ll x) {
		while (pos + 1 < lines.size() && I(lines[pos], lines[pos + 1]) <= (ld)x) pos++;
		return MP(F(lines[pos], x), idx[pos]);
	}

	void clear() {
		lines.clear();
		idx.clear();
		pos = 0;
	}
};

const int N = 1e5 + 20;
const int K = 2e2 + 20;
ll a[N], dp[N], p[N], par[N][K], n, k;
vector<int> ans;
convexHull CHT;

int main() {
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	cin >> n >> k; k++;
	for (int i = 1; i <= n; i++)
		cin >> a[i];
	for (int i = 1; i <= n; i++) {
		p[i] = a[i] + p[i - 1];
		dp[i] = sqr(p[i]);
	}
	for (int i = 2; i <= k; i++) {
		CHT.add({p[i - 1] * -2, dp[i - 1] + sqr(p[i - 1])}, i - 1);
		for (int j = i; j <= n; j++) {
			pii tmp = CHT.get(p[j]);
			ll D = dp[j];
			dp[j] = tmp.X + sqr(p[j]);
			par[j][i] = tmp.Y;
			CHT.add({p[j] * -2, D + sqr(p[j])}, j);
		}
		CHT.clear();
	}
	int v = par[n][k];
	for (int i = k - 1; i; i--) {
		ans.push_back(v);
		v = par[v][i];
	}
//	cout << sqr(p[n]) << ' ' << dp[n] << endl;
	cout << (sqr(p[n]) - dp[n]) / 2 << endl;
	for (int i = ans.size() - 1; i >= 0; i--)
		cout << ans[i] << ' ';
	cout << endl;
}

Compilation message (stderr)

sequence.cpp: In member function 'pii convexHull::get(ll)':
sequence.cpp:56:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while (pos + 1 < lines.size() && I(lines[pos], lines[pos + 1]) <= (ld)x) pos++;
          ~~~~~~~~^~~~~~~~~~~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29