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Submission #172933

# Submission time Handle Problem Language Result Execution time Memory
172933 2020-01-02T18:30:49 Z RafaelSus Split the sequence (APIO14_sequence) C++14
71 / 100
 2000 ms 86284 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;
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<<" ";
   
}
bool bad(int f1,int f2,int f3)
{
	return (b[f3]-b[f1])*(m[f1]-m[f2])>=(b[f2]-b[f1])*(m[f1]-m[f3]);
}
 
void add(ll m_,ll b_,int id)
{
   
    
	m.push_back(m_);
	b.push_back(b_);
	idx.push_back(id);
	int sz=m.size();
	while(sz>=3 && bad(sz-3,sz-2,sz-1))
	{
		m.erase(m.end()-2);
		b.erase(b.end()-2);
		idx.erase(idx.end()-2);
		sz--;
	}
}
 
ll func(int p,ll x)
{
	return m[p]*x+b[p];
}
 
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]};
}
ll dp[N][2];
ll a[N],s[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];
		s[i]=s[i-1]+a[i];
	}
	
	
 
 
	for(int i=1;i<=n;i++)
	{
	    
	    dp[i][1]=s[i]*(s[n]-s[i]);
	    path[i][1]=0;
	    //add(-s[i],dp[i][1]);
 
	}
 
	for(int i=2;i<=k;i++)
	{
		m.clear();
		b.clear();
		idx.clear();
		int v=(i-1)%2;
		ptr=0;
		add(0,0,0);
		
	
	
	
		for(int j=1;j<=n;j++)
		{
			
			if(j<i )
			{
			    if(j==i-1)
			     add(-s[j],dp[j][v],j);
			    continue;
 
			}
		
		
			pair<ll,int> pd=get(s[n]-s[j]);
		
		
		
			dp[j][v^1]=pd.first+s[n]*s[j]-s[j]*s[j];
			path[j][i]=pd.second;
		
		    add(-s[j],dp[j][v],j);
		   
 
 
		}
		
	}
 
	ll mx=0,st=1;
	for(int i=1;i<n;i++)
	{
	    if(dp[i][k%2]>=mx)
	    {
	        mx=dp[i][k%2];
	        st=i;
	    }
	}
 
	cout<<mx<<endl;
	print(st,k);
}

Compilation message

sequence.cpp: In function 'std::pair<long long int, int> get(ll)':
sequence.cpp:57:8: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(ptr>=m.size())ptr=m.size()-1;
     ~~~^~~~~~~~~~
sequence.cpp:58:13: 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 348 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 376 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 2 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 504 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 376 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 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 1 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 3 ms 504 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 504 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 504 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 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 1144 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 1272 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 8 ms 1272 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 1272 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 9 ms 1400 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 9 ms 1144 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 9 ms 1272 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 7 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 1272 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 8952 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 12 ms 8952 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 91 ms 9080 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 15 ms 9080 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 71 ms 8952 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 80 ms 9080 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 76 ms 9176 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 60 ms 9080 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 69 ms 9080 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 88 ms 9080 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 121 ms 85784 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 121 ms 85756 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2036 ms 86284 KB Time limit exceeded
4 Halted 0 ms 0 KB -