Submission #91855

#	Time	Username	Problem	Language	Result	Execution time	Memory
91855		Abelyan	Split the sequence (APIO14_sequence)	C++17	100 / 100	617 ms	84904 KiB

sequence

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


#define FOR(i,a) for (int i=0;i<(a);++i)
#define FORR(i,a) for (int i=(a)-1;i>=0;i--)
#define FORT(i,a,b) for (int i=(a);i<=(b);++i)
#define FORTR(i,a,b) for (int i=(b);i>=(a);--i)
#define trav(i,v) for (auto i : v)
#define fr first
#define sc second
#define x real
#define y imag

typedef long long ll;
typedef long double ld;
typedef complex<ll> point;

const int N = 2e5+6;
const int K = 406;


class conv_hull{
public:
	vector<point> lines;
	vector<int> ind;
	int pos=0;
	ll f(point a,  ll x) {
	    return a.x()*x+a.y();
	}
	ld inter(point a,point b){
		ll k=a.x()-b.x();
		ll c=b.y()-a.y();
		//cout<<k<<endl;
		//cout<<c/k<<endl;
		return (ld)c/k;
	}
	void add_line(point nw,int index){
		if (!lines.empty() && nw.x()==lines.back().x()){
			return;
		}
		while (lines.size()>1){
		 	//cout<<1<<endl;
		 	point a=lines.back();
		 	point b=lines[lines.size()-2];
		 	//cout<<1<<endl;
		 	if (inter(nw,b)<=inter(b,a)){
				lines.pop_back();
				ind.pop_back();
			}
		 	else break;
		}
		lines.push_back(nw);
		ind.push_back(index);
	}
	pair<ll,int> get(ll x){
		//cout<<pos<<" "<<lines.size()<<endl;
		while(pos<lines.size()-1 && inter(lines[pos],lines[pos+1])<=(ld)x){
			pos++;
		}
		//cout<<lines[pos]<<endl;
		return {f(lines[pos],x),ind[pos]};
	}
	void del(){
		lines.clear();
		ind.clear();
		pos=0;
	}
};
ll a[N],dp[N],pref[N];
int nax[K][N];
int main(){
	ios_base::sync_with_stdio(false);
	//cout<<"hi"<<endl;
	int n,k;
	cin>>n>>k;k++;
	FORT (i,1,n){
		cin>>a[i];
		pref[i]=pref[i-1]+a[i];
	}
	FORT(i,1,n){
		dp[i]=pref[i]*pref[i];
	}
	conv_hull t;
	FORT(i,2,k){
		t.add_line({-2ll*pref[i-1],dp[i-1]+pref[i-1]*pref[i-1]},i-1);
		//cout<<-pref[i-1]<<" "<<dp[i-1][i-1]+pref[i-1]*pref[i-1]<<endl;
		FORT(j,i,n){
			ll z=dp[j];
			pair<ll,int> tv=t.get(pref[j]);
			dp[j]=tv.fr+pref[j]*pref[j];
			nax[i][j]=tv.sc;
			t.add_line({-2ll*pref[j],z+pref[j]*pref[j]},j);
			//cout<<-2ll*pref[j]<<" "<<dp[i-1][j]+pref[j]*pref[j]<<endl;
		}
		t.del();
		//cout<<endl;
	}
	cout<<(pref[n]*pref[n]-dp[n])/2ll<<endl;
	int tv=nax[k][n];
	vector<int> v;
	FORTR(i,1,k-1){
		v.push_back(tv);
		tv=nax[i][tv];
	}
	reverse(v.begin(),v.end());
	trav(ans,v)cout<<ans<<" ";
	return 0;
}
/*
7 3
4 1 3 4 0 2 3
*/

Compilation message (stderr)

sequence.cpp: In member function 'std::pair<long long int, int> conv_hull::get(ll)':
sequence.cpp:58:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(pos<lines.size()-1 && inter(lines[pos],lines[pos+1])<=(ld)x){
         ~~~^~~~~~~~~~~~~~~

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