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Submission #224599

# Submission time Handle Problem Language Result Execution time Memory
224599 2020-04-18T13:32:33 Z kig9981 Split the sequence (APIO14_sequence) C++17
100 / 100
 269 ms 3356 KB 
#include <bits/stdc++.h>

#ifdef NON_SUBMIT
#define TEST(n) (n)
#define tout cerr
#else
#define TEST(n) ((void)0)
#define tout cin
#endif

using namespace std;

int N, K, PS[100001], cnt[100001], P[100001];
long long D[100001];

double cross(int a, int b)
{
	if(PS[a]==PS[b]) return 0;
	return 1.*(D[b]-2LL*PS[b]*PS[b]-D[a]+2LL*PS[a]*PS[a])/(2LL*PS[a]-2LL*PS[b]);
}

pair<long long,int> solve(long long l)
{
	vector<int> S(1);
	int j=0;
	for(int i=1;i<=N;i++) {
		while(j+1<S.size() && cross(S[j],S[j+1])<PS[i]) j++;
		D[i]=D[S[j]]+2LL*(PS[i]-PS[S[j]])*PS[S[j]]-l;
		cnt[i]=cnt[S[j]]+1;
		P[i]=S[j];
		if(PS[i]==PS[S.back()] && D[i]<=D[S.back()]) continue;
		while(S.size()>j+1) {
			int c=S.back();
			S.pop_back();
			if(cross(S.back(),c)<=cross(S.back(),i)) {
				S.push_back(c);
				break;
			}
		}
		S.push_back(i);
	}
	return {D[N],cnt[N]};
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);
	TEST(freopen("input.txt","r",stdin));
	TEST(freopen("output.txt","w",stdout));
	TEST(freopen("debug.txt","w",stderr));
	long long s=0, e=1e18;
	int j=1, k2;
	vector<int> P1, P2, res(1);
	cin>>N>>K; ++K;
	for(int i=1;i<=N;i++) {
		cin>>PS[i];
		PS[i]+=PS[i-1];
	}
	while(s<=e) {
		long long m=(s+e)>>1;
		if(solve(2*m+1).second>K) s=m+1;
		else e=m-1;
	}
	solve(2*s+1);
	k2=cnt[N];
	for(int c=N;c;c=P[c]) P2.push_back(c);
	P2.push_back(0); reverse(P2.begin(),P2.end());
	solve(2*e+1);
	for(int c=N;c;c=P[c]) P1.push_back(c);
	P1.push_back(0); reverse(P1.begin(),P1.end());
	for(int i=1;i<P1.size();i++) {
		while(j<P2.size() && P1[i-1]>=P2[j]) j++;
		if(P1[i]<=P2[j] && i-j==K-k2) {
			long long ans=0;
			for(int k=1;k<i;k++) res.push_back(P1[k]);
			for(int k=j;k+1<P2.size();k++) res.push_back(P2[k]);
			for(int k=1;k<res.size();k++) ans+=1LL*(PS[N]-PS[res[k]])*(PS[res[k]]-PS[res[k-1]]);
			cout<<ans<<'\n';
			for(int k=1;k<res.size();k++) cout<<res[k]<<' ';
			return 0;
		}
	}
	return -1;
}

Compilation message

sequence.cpp: In function 'std::pair<long long int, int> solve(long long int)':
sequence.cpp:27:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(j+1<S.size() && cross(S[j],S[j+1])<PS[i]) j++;
         ~~~^~~~~~~~~
sequence.cpp:32:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(S.size()>j+1) {
         ~~~~~~~~^~~~
sequence.cpp: In function 'int main()':
sequence.cpp:72:15: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=1;i<P1.size();i++) {
              ~^~~~~~~~~~
sequence.cpp:73:10: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(j<P2.size() && P1[i-1]>=P2[j]) j++;
         ~^~~~~~~~~~
sequence.cpp:77:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    for(int k=j;k+1<P2.size();k++) res.push_back(P2[k]);
                ~~~^~~~~~~~~~
sequence.cpp:78:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    for(int k=1;k<res.size();k++) ans+=1LL*(PS[N]-PS[res[k]])*(PS[res[k]]-PS[res[k-1]]);
                ~^~~~~~~~~~~
sequence.cpp:80:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    for(int k=1;k<res.size();k++) cout<<res[k]<<' ';
                ~^~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 108 == 108
2 Correct 4 ms 384 KB contestant found the optimal answer: 999 == 999
3 Correct 5 ms 384 KB contestant found the optimal answer: 0 == 0
4 Correct 5 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 5 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 5 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 4 ms 384 KB contestant found the optimal answer: 1 == 1
8 Correct 5 ms 384 KB contestant found the optimal answer: 1 == 1
9 Correct 5 ms 384 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 5 ms 384 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 5 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 5 ms 384 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 5 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 4 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 5 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 4 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 5 ms 384 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 5 ms 384 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 4 ms 384 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 5 ms 384 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 5 ms 384 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 5 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 5 ms 384 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 5 ms 384 KB contestant found the optimal answer: 687136 == 687136
9 Correct 5 ms 384 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 5 ms 384 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 5 ms 384 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 5 ms 384 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 5 ms 384 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 5 ms 384 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 5 ms 384 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 6 ms 384 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 5 ms 384 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 6 ms 384 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 6 ms 384 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 384 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 6 ms 384 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 ms 384 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 7 ms 384 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 384 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 8 ms 384 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 7 ms 384 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 7 ms 384 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 7 ms 384 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 9 ms 384 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 640 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 20 ms 640 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 24 ms 640 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 21 ms 640 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 22 ms 640 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 22 ms 640 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 28 ms 640 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 24 ms 640 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 28 ms 640 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 34 ms 640 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 169 ms 2776 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 175 ms 2848 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 197 ms 3260 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 161 ms 2840 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 191 ms 3148 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 192 ms 3164 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 269 ms 3356 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 204 ms 3196 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 192 ms 3188 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 192 ms 3200 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845