Submission #265370

#	Time	Username	Problem	Language	Result	Execution time	Memory
265370		amoo_safar	Split the sequence (APIO14_sequence)	C++17	0 / 100	149 ms	131076 KiB

sequence

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
 
#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define debug(x) cerr << #x << " : " << x << '\n'
 
using namespace std;
using namespace __gnu_pbds;
 
typedef long long ll;
typedef long double ld;
typedef string str;
typedef pair<ll, ll> pll;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
 
const ll Mod = 1e9 + 7;
const ll Inf = 2242545357980376863LL;
const ll Log = 20;
//const ll N = 1ll << Log;
const int Maxn = 1e5 + 10;
const int Base = 101;
 
 

typedef pair<ll, ll> Line;
typedef pair<pair<ll, Line>, int> Ty;

struct CHT{
	set < pair < Line , ll > > S;
	set < pair < ll , Line > > I;
	map< Line, int> mp;
	vector<Ty> L;

	ll INF = 4e18;
	inline void Add(Line X, ll idx){
		while(!L.empty() && Intersection(L.back().F.S, X) <= L.back().F.F)
			L.pop_back();
		L.pb({{(L.empty() ? -INF : Intersection(L.back().F.S, X)), X}, idx});
		return ;

		X.F *= -1;
		X.S *= -1;
		mp[X] = idx;
		
		ll t = -INF;
		auto it = S.lower_bound({X, -INF});
		while ((int)S.size())
		{
			if (it == S.begin())
				{t = -INF; break;}
			it --; ll r = Intersection(it->first, X);
			if (r <= it->second)
				I.erase({it->second, it->first}), it = S.erase(it);
			else
				{t = r; break;}
		}
		it = S.lower_bound({X, -INF});
		while ((int)S.size())
		{
			if (it == S.end())
				break;
			ll r = Intersection(X, it->first);
			Line Y = it->first;
			I.erase({it->second, it->first});
			it = S.erase(it);
			if (r <= t)
			{
				r = -INF;
				if (it != S.begin())
					it --, r = Intersection(it->first, Y);
				S.insert({Y, r}); I.insert({r, Y}); return ;
			}
			if (it != S.end() && it->second <= r)
				continue;
			S.insert({Y, r}); I.insert({r, Y}); break;
		}
		S.insert({X, t}); I.insert({t, X});
	}
	inline pll GetMin(ll X)
	{
		auto it = upper_bound(all(L), Ty({X, {INF, INF}}, INF)); it --;
		return pll((X * it->F.S.F + it->F.S.S), it -> S);
	}
	inline ll Intersection(Line X, Line Y)
	{
		if (X.first == Y.first && X.second <= Y.second)
			return (-INF);
		if (X.first == Y.first)
			return (INF);
		return ((X.second - Y.second) / (Y.first - X.first)) + ((X.second - Y.second) % (Y.first - X.first) > 0);
	}
};
CHT cht;
 
 
 
 
 
ll a[Maxn], mk[Maxn];
ll ps[Maxn], sf[Maxn];
 
ll dp[Maxn][203], par[Maxn][203];
vector<ll> A;
 
int main(){
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	//debug((-3) / 2);
	ll n, k;
	cin >> n >> k;
	for(int i = 0; i < n; i++) cin >> a[i];
	ps[0] = 0;
	for(int i = 1; i <= n; i++) ps[i] = ps[i - 1] + a[i - 1];
	
	for(int i = 0; i <= n; i++) dp[i][0] = ps[i] * ps[i];
	pll res;
	for(int j = 1; j <= k; j++){
		cht.I.clear();
		cht.S.clear();
		cht.mp.clear();
	
		dp[0][j] = 0;
		for(int i = 1; i <= n; i++){
			cht.Add( pll(-2LL * ps[i - 1], dp[i - 1][j - 1] + ps[i - 1]*ps[i - 1] ), i - 1);
			res = cht.GetMin(ps[i]);
			dp[i][j] = res.F + ps[i]*ps[i];
			par[i][j] = res.S;
		}
	}
	cout << ((ps[n] * ps[n]) - dp[n][k]) / 2LL << '\n';
	ll nw = n;
	for(int i = 0; i < k; i++){
		nw = par[nw][k - i];
		A.pb(nw);
	}
	reverse(all(A));
	for(auto x : A) cout << x << ' ';
	cout << '\n';
	return 0;
}
/*
7 3
4 1 3 4 0 2 3

*/

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