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Submission #172907

# Submission time Handle Problem Language Result Execution time Memory
172907 2020-01-02T17:57:29 Z RafaelSus Split the sequence (APIO14_sequence) C++14
71 / 100
 2000 ms 86164 KB 
#include <bits/stdc++.h>
 
using namespace std;
const int N = 1e5 + 5;
typedef long long ll;
const ll inf=1e15;
#define pb push_back
const int INF=(0x3f3f3f3f);
 
vector<ll>m,b;
vector<int>idx;
int ptr;
 
void add(ll _m,ll _b,int _idx){
  while(m.size()>=2&&(_b-b[b.size()-2])*(m[m.size()-2]-m.back())>=(b[b.size()-2]-b.back())*(_m-m[m.size()-2])){
    m.pop_back();
    b.pop_back();
    idx.pop_back();
  }
  m.pb(_m);
  b.pb(_b);
  idx.pb(_idx);
}
 
ll func(int pos,ll x){
  return m[pos]*x+b[pos];
}
 
pair<ll,int>get(ll x){
  if(ptr>=m.size())ptr=m.size()-1;
  while(ptr+1<m.size()&&func(ptr,x)<=func(ptr+1,x))ptr++;
  return {func(ptr,x),idx[ptr]};
}
int path[N][205];
void print(int st,int k){
  if(path[st][k]==0){
    cout<<st<<' ';
    return;
  }
  print(path[st][k],k-1);
  cout<<st<<' ';
}
ll dp[2][N];
ll a[N],pref[N];
int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);cout.tie(0);
  
  int n,k;
  cin>>n>>k;
  
  for(int i=1;i<=n;i++){
    cin>>a[i];
    pref[i]=pref[i-1]+a[i];
  }
  
  for(int i=1;i<=n;i++){
    dp[1][i]=pref[i]*(pref[n]-pref[i]);
    path[i][1]=0;
  }
  for(int i=2;i<=k;i++){
    int v=(i-1)%2;
    m.clear();
    b.clear();
    idx.clear();
    ptr=0;
    add(0,0,0);
    for(int j=i-1;j<=n;j++){
      if(j==i-1){
        add(-pref[j],dp[v][j],j);
        continue;
      }
      pair<ll,int>tmp=get(pref[n]-pref[j]);
      dp[v^1][j]=tmp.first+pref[n]*pref[j]-pref[j]*pref[j];
      path[j][i]=tmp.second;
      add(-pref[j],dp[v][j],j);
    }
  }
  ll mx=0,st=1;
  for(int i=1;i<n;i++){
    if(dp[k%2][i]>mx){
      mx=dp[k%2][i];
      st=i;
    }
  }
  cout<<mx<<'\n';
  print(st,k);
}

Compilation message

sequence.cpp: In function 'std::pair<long long int, int> get(ll)':
sequence.cpp:30:9: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(ptr>=m.size())ptr=m.size()-1;
      ~~~^~~~~~~~~~
sequence.cpp:31:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(ptr+1<m.size()&&func(ptr,x)<=func(ptr+1,x))ptr++;
         ~~~~~^~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 376 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 376 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 376 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 376 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 348 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 376 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 376 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 376 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 376 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 376 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 376 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 376 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 376 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 380 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 376 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 376 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 376 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 376 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 376 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 376 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 376 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 376 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 376 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 504 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 3 ms 504 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 504 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 504 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 504 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 508 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 3 ms 504 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 504 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 484 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 504 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 1244 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 1144 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 ms 1144 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 1272 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 8 ms 1272 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 1144 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 1144 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 1144 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 1272 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 1264 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 8920 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 8976 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 90 ms 9124 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 10 ms 9080 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 57 ms 8952 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 63 ms 8996 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 70 ms 9100 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 56 ms 9080 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 63 ms 9080 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 79 ms 9080 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 101 ms 85800 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 101 ms 85776 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2058 ms 86164 KB Time limit exceeded
4 Halted 0 ms 0 KB -