Submission #224599

#	Time	Username	Problem	Language	Result	Execution time	Memory
224599		kig9981	Split the sequence (APIO14_sequence)	C++17	100 / 100	269 ms	3356 KiB

sequence

#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 (stderr)

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