Submission #265565

#	Time	Username	Problem	Language	Result	Execution time	Memory
265565		tko919	Split the sequence (APIO14_sequence)	C++17	71 / 100	2072 ms	51820 KiB

sequence

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

//template
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
//end

struct CHT{
   int n; vector<ll> xs,p,q,ids; vector<bool> used;
   CHT(vector<ll> ps){
      n=1; while(n<ps.size())n<<=1;
      used.assign(4*n,0); xs.resize(4*n,inf);
      p.resize(4*n); q.resize(4*n); ids.resize(4*n);
      rep(i,0,ps.size())xs[i]=ps[i];
   }
   void add(ll a,ll b,ll idx,int k=0,int l=0,int r=-1){
      if(r==-1)r=n;
      while(r-l>0){
         int m=(l+r)/2;
         if(!used[k]){
            p[k]=a; q[k]=b; ids[k]=idx; used[k]=1;
            return;
         }
         ll lx=xs[l],mx=xs[m],rx=xs[r-1];
         ll pk=p[k],qk=q[k];
         bool lb=(a*lx+b<pk*lx+qk);
         bool mid=(a*mx+b<pk*mx+qk);
         bool rb=(a*rx+b<pk*rx+qk);
         if(lb&&rb){p[k]=a; q[k]=b; ids[k]=idx; return;}
         if(!lb&&!rb)return;
         if(mid){swap(p[k],a); swap(q[k],b); swap(ids[k],idx);}
         if(lb!=mid){k=2*k+1; r=m;} else{k=2*k+2; l=m;}
      }
   }
   /*
   void add_segment(ll a,ll b,int l,int r){
      ll l0=l+n,r0=r+n,s0=l,t0=r,sz=1;
      while(l0<r0){
         if(r0&1){r0--; t0-=sz; add(a,b,r0-1,t0,t0+sz);}
         if(l0&1){add(a,b,l0-1,s0,s0+sz); l0++; s0+=sz;}
         l0>>=1; r0>>=1; sz<<=1;
      }
   }
   */
   pair<ll,ll> query(int i){
      int k=i+n-1,id=ids[k];
      ll x=xs[i],s=used[k]?p[k]*x+q[k]:INF;
      while(k){
         k=(k-1)/2;
         if(used[k] and chmin(s,p[k]*x+q[k]))id=ids[k];
      } return {s,id};
   }
};

ll dp[2][101010]={},pre[210][101010];

int main(){
   int n,k; cin>>n>>k;
   vector<ll> a(n),rui(n+1);
   rep(i,0,n){
      cin>>a[i]; rui[i+1]=a[i];
   }
   rep(i,0,n)rui[i+1]+=rui[i];
   rep(i,0,2)rep(j,0,n+1)dp[i][j]=-INF;
   dp[0][0]=0;
   /*
   rep(i,1,k+1)rep(j,1,n)rep(i2,0,j)if(dp[i-1][i2]>=0){
      ll add=(rui[j]-rui[i2])*(rui[n]-rui[j]);
      if(chmax(dp[i][j],dp[i-1][i2]+add))pre[i][j]=i2;
   }
   */
   unordered_map<ll,int> rev;
   rep(i,1,k+1){
      vector<ll> v;
      rep(j,1,n)v.push_back(rui[n]-rui[j]);
      sort(ALL(v)); v.erase(unique(ALL(v)),v.end());
      rev.clear();
      rep(j,0,v.size())rev[v[j]]=j;
      CHT cht(v);
      rep(j,1,n){
         if(dp[0][j-1]>=0)cht.add(rui[j-1],-dp[0][j-1],j-1);
         auto [y,x]=cht.query(rev[rui[n]-rui[j]]);
         if(y==INF)continue;
         if(chmax(dp[1][j],-y+rui[j]*(rui[n]-rui[j])))pre[i][j]=x;
      }
      swap(dp[0],dp[1]);
      rep(j,0,n+1)dp[1][j]=-INF;
   }
   ll res=-INF; int pos=-1;
   rep(i,0,n)if(chmax(res,dp[0][i]))pos=i;
   cout<<res<<endl;
   int cur=k; vector<int> ps;
   while(cur){
      ps.push_back(pos);
      pos=pre[cur][pos]; cur--;
   }
   reverse(ALL(ps));
   rep(i,0,k)cout<<ps[i]<<endl;
   return 0;
}

Compilation message (stderr)

sequence.cpp: In constructor 'CHT::CHT(std::vector<long long int>)':
sequence.cpp:17:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   17 |       n=1; while(n<ps.size())n<<=1;
      |                  ~^~~~~~~~~~

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