Submission #241937

#	Time	Username	Problem	Language	Result	Execution time	Memory
241937		michao	Split the sequence (APIO14_sequence)	C++14	71 / 100	2017 ms	54392 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+5;
ll dp[205][MAX];
ll tab[MAX];
int pref[MAX];
ll prefix(int a,int b)
{
	return pref[b]-pref[a-1];
}

struct Line {
	mutable ll k, m, p;
	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)
	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()) { x->p = inf; return false; }
		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) {
		auto z = insert({k, m, 0}), 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));
	}
	ll query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
}; 
   
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++)
  {
  	LineContainer L;
  	for (int j=2;j<=n;j++)
  	{
  		L.add(pref[j-1],-(ll)pref[j-1]*pref[j-1]+dp[i-1][j-1]);
  		dp[i][j]=L.query(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