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Submission #265565

# Submission time Handle Problem Language Result Execution time Memory
265565 2020-08-15T01:35:22 Z tko919 Split the sequence (APIO14_sequence) C++17
71 / 100
 2000 ms 51820 KB 
#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

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
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1920 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 1920 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 1920 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 1920 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 3 ms 1920 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 1920 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 1920 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 1920 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 1920 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 1920 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 1920 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 1920 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 1920 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 1920 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 1920 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 1920 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 1920 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1920 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 1952 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 8 ms 2176 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 1920 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 3 ms 1920 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 1920 KB contestant found the optimal answer: 933702 == 933702
7 Correct 5 ms 2048 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 4 ms 1920 KB contestant found the optimal answer: 687136 == 687136
9 Correct 3 ms 1920 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 4 ms 2048 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1920 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 1920 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 38 ms 3192 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 1920 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 24 ms 2816 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 29 ms 3064 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 33 ms 3192 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 9 ms 2304 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 7 ms 2176 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 11 ms 2304 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2168 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 2172 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 80 ms 4592 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 2168 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 71 ms 4588 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 63 ms 4264 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 79 ms 4584 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 78 ms 4584 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 17 ms 2648 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 32 ms 3200 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 3872 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 3872 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 932 ms 21376 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 18 ms 5024 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 368 ms 13712 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 428 ms 15368 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 692 ms 17228 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 538 ms 14916 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 651 ms 16536 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 842 ms 19672 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 150 ms 27672 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 133 ms 27576 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2072 ms 51820 KB Time limit exceeded
4 Halted 0 ms 0 KB -