Submission #973440

#	Time	Username	Problem	Language	Result	Execution time	Memory
973440		TranGiaHuy1508	Split the sequence (APIO14_sequence)	C++17	100 / 100	726 ms	90368 KiB

sequence

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

void main_program();

signed main(){
	ios_base::sync_with_stdio(0); cin.tie(0);
	main_program();
}

using ll = long long;
const ll inf = 1e18;

struct Line {
	mutable ll k, m, p;
	int idx;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(ll x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(ll k, ll m, int idx) {
		auto z = insert({k, m, 0, idx}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	pair<ll, int> query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return {l.k * x + l.m, l.idx};
	}
};

struct StaticLineContainer : vector<Line> {
	int pt = 0;
	ll f(Line line, ll x) { return line.k * x + line.m; } 
	bool cross(Line line1, Line line2, Line line3){
		return (__int128)(line3.m - line1.m) * (line1.k - line2.k)
			<= (__int128)(line2.m - line1.m) * (line1.k - line3.k);
	}

	void add(ll k, ll m, int idx){
		push_back({k, m, 0, idx});
		int sz = size();
		while (sz >= 3 && cross(at(sz - 3), at(sz - 2), at(sz - 1))){
			erase(end() - 2); sz--;
		}
	}

	pair<ll, int> query(ll x){
		if (pt >= (int)size()) pt = (int)size() - 1;
		while (pt < (int)size() - 1 && f(at(pt), x) < f(at(pt+1), x)) pt++;
		return {f(at(pt), x), at(pt).idx};
	}
};

int n, k;
vector<ll> v, pfx;

void main_program(){
	cin >> n >> k;

	v.resize(n + 1);
	for (int i = 1; i <= n; i++) cin >> v[i];

	pfx.resize(n + 1);
	for (int i = 1; i <= n; i++) pfx[i] = pfx[i-1] + v[i];

	vector<ll> dp(n + 1, -inf);
	vector<vector<int>> trace(k + 2, vector<int>(n + 1));
	dp[0] = 0;
	for (int j = 1; j <= k + 1; j++){
		StaticLineContainer cht;
		vector<ll> newdp(n + 1, -inf);
		for (int i = 1; i <= n; i++){
			// Add line (pfx[i-1] * S + dp[i-1] - pfx[i-1]^2)
			cht.add(pfx[i-1], dp[i-1] - pfx[i-1] * pfx[i-1], i - 1);

			// Find answer
			tie(newdp[i], trace[j][i]) = cht.query(pfx[i]);
		}

		swap(dp, newdp);
	}

	cout << dp[n] << "\n";

	vector<int> splits;

	int crr = n;
	for (int j = k + 1; j > 1; j--){
		crr = trace[j][crr];
		splits.push_back(crr);
	}

	reverse(splits.begin(), splits.end());
	for (auto elem: splits) cout << elem << " ";
	cout << "\n";
}

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