Submission #111338

#	Time	Username	Problem	Language	Result	Execution time	Memory
111338		aleksami	Split the sequence (APIO14_sequence)	C++14	71 / 100	541 ms	132096 KiB

sequence

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
#define MAXN 100005
#define MAXK 205
const ll INF = 1e18;
ll dp[MAXK][MAXN];
ll a[MAXN];
int opt[MAXK][MAXN];
deque <int> q;//deque <line> q;
//struct line {ll n;ll k;int id;};
double presekx(int x,int y,int k)
{
  if(a[x]==a[y])return INF;
  return 1.00*((dp[k][x]-a[x]*a[x])-(dp[k][y]-a[y]*a[y]))/(a[y]-a[x]);
  //if(a.k==b.k)return INF;
  //return 1.00*(a.n-b.n)/(b.k-a.k);
}

int next_front()//line next_front()
{
  int a = q.front();//line a = q.front();
  q.pop_front();
  int b = q.front();//line b = q.front();
  q.push_front(a);
  return b;
}
int prev_back()//line prev_back()
{
  int a = q.back();//line a = q.back();
  q.pop_back();
  int b = q.back();//line b = q.back();
  q.push_back(a);
  return b;
}
ll eval(int l,int k,ll x)
{
  return (a[l])*x+(dp[k][l]-a[l]*a[l]);//return l.k*x+l.n;
}

int main()
{
  ios_base::sync_with_stdio(false);
  int n,k;
  cin >> n >> k;
  for(int i = 1; i <= n; i++)cin >> a[i],a[i]+=a[i-1];
  for(int i = 1; i <= k; i++)
  {
    q.clear();
    for(int j = i; j <= n; j++)
    {
      while(1)
      {
        if(q.size()<=1)break;
        if(eval(q.front(),i-1,a[j])<=eval(next_front(),i-1,a[j])){q.pop_front();continue;}
        break;
      }
      if(q.size())
      {
        dp[i][j]=eval(q.front(),i-1,a[j]);
        opt[i][j]=q.front();//opt[i][j]=q.front().id;
      }
      int add;//line add;
      //add.k=a[j];
      //add.n=-a[j]*a[j]+dp[i-1][j];
      add=j;//add.id=j;
      while(1)
      {
        if(q.size()<=1)break;
        if(a[q.back()]==a[add]){q.pop_back();continue;}//if(q.back().k==add.k){q.pop_back();continue;}
        if(a[q.back()]==a[prev_back()]){q.pop_back();continue;}//if(q.back().k==prev_back().k){q.pop_back();continue;}
        if(presekx(prev_back(),q.back(),i-1)>=presekx(q.back(),add,i-1)){q.pop_back();continue;}//if(presekx(prev_back(),q.back())>=presekx(q.back(),add)){q.pop_back();continue;}
        break;
      }
      q.push_back(add);
    }
  }
  cout << dp[k][n] << "\n";
  int now = n;
  while(k > 0)
  {
    cout << opt[k][now] << " ";
    now=opt[k][now];
    k--;
  }
  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