Submission #241948

#	Time	Username	Problem	Language	Result	Execution time	Memory
241948		michao	Split the sequence (APIO14_sequence)	C++14	71 / 100	478 ms	131076 KiB

sequence

#include <bits/stdc++.h>
#define ll long long int
#define mp make_pair
#define pb push_back
#define ld long double
#define pii pair<int,int>
#define sz(x) (int)x.size()
#define piii pair<pii,pii>
#define precise cout<<fixed<<setprecision(10)
#define st first
#define nd second
#define ins insert
#define vi vector<int>
#define BOOST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
using namespace std;
const int MAX=1e5+1000;
ll dp[201][MAX];
int tab[MAX];
int pref[MAX];
ll prefix(int a,int b)
{
	return pref[b]-pref[a-1];
}

class CHT
{
public:
    deque<pair<int,ll> > D;
    void add(pair<int,ll> f)
    {
        while(true)
        {
            if(D.size()<=1)
                break;
            pair<int,ll> a=D.back();
            D.pop_back();
            pair<int,ll> b=D.back();
           // (a.nd-f.nd)/(f.st-a.st)<=(b.nd-a.nd)/(a.st-b.st);
           // (a.nd-f.nd)*(a.st-b.st)<=(b.nd-a.nd)*(f.st-a.st)
            ll x1=(a.nd-f.nd)*(a.st-b.st);
            ll x2=(b.nd-a.nd)*(f.st-a.st);
            if(x1<=x2)
                continue;
            else
            {
                D.pb(a);
                break;
            }
        }
        D.pb(f);
    }
    ll getmin(int x)
    {
        while(D.size()>1)
        {
            pair<int,ll> a=D.front();
            D.pop_front();
            pair<int,ll> b=D.front();
            ll p1=(ll)x*a.st+a.nd,p2=(ll)x*b.st+b.nd;
            if(p2>=p1)
                continue;
            else
            {
                D.push_front(a);
                break;
            }
 
        }
        pair<int,ll> a=D.front();
        return (ll)x*a.st+a.nd;
    }
};
   
vi ans;
 
int32_t main()
{
  BOOST;
  int n,k;
  cin>>n>>k;
  for (int i=1;i<=n;i++)cin>>tab[i];
  for (int i=1;i<=n;i++)pref[i]=pref[i-1]+tab[i];
  for (int i=1;i<=k;i++)
  {
  	CHT L;
  	for (int j=2;j<=n;j++)
  	{
  		L.add(mp(pref[j-1],-(ll)pref[j-1]*pref[j-1]+dp[i-1][j-1]));
  		dp[i][j]=L.getmin(pref[j]);
  	}
  }
  
  /*
  for (int i=1;i<=k;i++)
  	for (int j=1;j<=n;j++)
  		for (int l=j;l>=2;l--)
  		  dp[i][j]=max(dp[i][j],prefix(l,j)*prefix(1,l-1)+dp[i-1][l-1]);
  */
  cout<<dp[k][n]<<"\n";
  int wsk=n;
  for (int i=k;i>=1;i--)
  	for (int j=wsk;j>=2;j--)
  	{
  		if (dp[i][wsk]==prefix(j,wsk)*prefix(1,j-1)+dp[i-1][j-1])
  		{
  			wsk=j-1;
  			ans.pb(j-1);
  			break;
  		}
   }
  for (auto it:ans)cout<<it<<" ";
  return 0;
}

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