Submission #1000715

#	Time	Username	Problem	Language	Result	Execution time	Memory
1000715		shenfe1	Split the sequence (APIO14_sequence)	C++17	0 / 100	46 ms	131072 KiB

sequence

#include <bits/stdc++.h>
 
#define ll long long
#define lb lower_bound
#define pii pair<int,int>
#define pll pair<ll,ll>
#define F first
#define S second
#define ld long double
#define pb push_back
#define all(v) v.begin(),v.end()
#define in insert
#define sz(s) (int)s.size()
// #define int ll
#define ppb pop_back

using namespace std;
 
const int MAX=1e5+10;
const int inf=2e9;

int n,k;
int a[MAX];
ll dp[MAX][211];
int pr[MAX][211];
int p[MAX];

struct CHT{

  vector<pll> vec;
  vector<int> num;
  int pos;

  void init(){
    pos=0;
    vec.clear();
    num.clear();
  }

  ld inter(pll a,pll b){
    // cout<<b.F<<" "<<a.F<<"\n";
    return (0.0+a.S-b.S)/(b.F-a.F);
  }

  void add(ll k,ll x,int i){
    // cout<<k<<" "<<x<<"\n";
    while(!vec.empty()&&vec.back().F==k){
      if(vec.back().S<x){
        vec.ppb();
        num.ppb();
      }
      else{
        return;
      }
    }
    while(sz(vec)>=2&&inter(vec.back(),vec[sz(vec)-2])>=inter(vec[sz(vec)-2],{k,x})){
      vec.ppb();
      num.ppb();
    }
    vec.pb({k,x});
    num.pb(i);
    pos=min(pos,sz(vec)-1);
  }

  ll get(pll a,int x){
    return a.F*x+a.S;
  }

  ll get(ll X){
    while(pos+1<sz(vec)&&get(vec[pos],X)<=get(vec[pos+1],X))pos++;
    return get(vec[pos],X);
  }

}C;

void solve(){
  cin>>n>>k;
  for(int i=1;i<=n;i++)cin>>a[i];
  for(int i=1;i<=n;i++){
    p[i]=p[i-1]+a[i];
    dp[i][1]=0;
  }
  k++;
  for(int K=2;K<=k;K++){
    C.init();
    for(int i=K;i<=n;i++){
      C.add(p[i-1],dp[i-1][K-1]-p[i-1]*p[i-1],i-1);
      dp[i][K]=C.get(p[i]);
      pr[i][K]=C.num[C.pos];
      // cout<<i<<" "<<K<<" "<<pr[i][K]<<"\n";
    }
  }
  cout<<dp[n][k]<<"\n";
  vector<int> ans;
  int cur=n;
  while(k>0){
    ans.pb(cur);
    cur=pr[cur][k];
    k--;
  }
  sort(all(ans));
  ans.ppb();
  for(int x:ans){
    cout<<x;
    if(x!=ans.back())cout<<" ";
  }
}

// #ifdef LOCAL
signed main(){
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t=1;
  // cin>>t;
  while(t--)solve();
}
// #endif

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