Submission #478231

#	Time	Username	Problem	Language	Result	Execution time	Memory
478231		dennisstar	Split the sequence (APIO14_sequence)	C++17	100 / 100	342 ms	9400 KiB

sequence

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using i128 = __int128;

struct line {
	ll a, b; int ind;
	ll get(ll x) { return a*x+b; }
	line() {}
	line(ll a, ll b, ll i) : a(a), b(b), ind(i) {}
};
 
struct cht {
	vector<line> l;
	int t;
	cht() : t(0) {}
	void upd(line v) {
		while (t+1<l.size() && (l.back().b<=v.b || (i128)(l[l.size()-2].b-v.b)*(l.back().a-l[l.size()-2].a)<=(i128)(l[l.size()-2].b-l.back().b)*(v.a-l[l.size()-2].a))) l.pop_back();
		l.emplace_back(v);
	}
	pair<ll, ll> get(ll x) {
		while (t+1<l.size() && l[t].get(x)<l[t+1].get(x)) t++;
		return {l[t].get(x), l[t].ind};
	}
};

vector<int> rt, ans;

pair<ll, ll> sol(vector<ll> &a, ll s, bool q=false) {
	int n=a.size();
	vector<ll> d(n), l(n), c(n);
	cht st;
	st.upd(line(2*a[n-1], 0, -1));
	for (int i=0; i<n; i++) {
		auto [v, j]=st.get(a[i]);
		d[i]=v-2*a[i]*a[i]+s;
		l[i]=j;
		c[i]=(j<0?0:c[j])+1;
		st.upd(line(2*(a[i]+a[n-1]), d[i]-2*a[i]*a[n-1], i));
	}

	if (q) {
		rt.clear();
		for (int i=n-1; i!=-1; i=l[i]) rt.emplace_back(i);
		reverse(rt.begin(), rt.end());
	}

	return {d[n-1], c[n-1]};
}

void track(vector<ll> &a, ll s, int p) {
	sol(a, -(2*s+1), true);
	auto l=rt;
	sol(a, -(2*s-1), true);
	auto r=rt;
	if (l.size()==p) { ans=l; return ; }
	if (r.size()==p) { ans=r; return ; }
	for (int i=0, j=0; i+1<r.size(); i++) {
		while (l[j]<=r[i]) j++;
		if (r[i+1]<=l[j]&&i+1+l.size()-j==p) {
			for (int k=0; k<=i; k++) ans.emplace_back(r[k]);
			for (int k=j; k<l.size(); k++) ans.emplace_back(l[k]);
			return ;
		}
	}
	puts("fuck");
	assert(0);
}

int main() {
	cin.tie(0)->sync_with_stdio(0);

	int n, k;
	cin>>n>>k;
	k++;
	vector<ll> a(n);
	for (auto &i:a) cin>>i;
	for (int i=1; i<n; i++) a[i]+=a[i-1];

	ll s=0, e=1e18;
	while (s<e) {
		ll m=(s+e)/2;
		auto c=sol(a, -(2*m+1)).second;
		if (c>k) s=m+1;
		else e=m;
	}

	track(a, s, k);
	ll v=0;
	for (int i=0; i<k-1; i++) v+=(a[n-1]-a[ans[i]])*(a[ans[i]]-(i?a[ans[i-1]]:0));
	cout<<v<<'\n';
	for (int i=0; i<k-1; i++) cout<<ans[i]+1<<' ';

	return 0;
}

Compilation message (stderr)

sequence.cpp: In member function 'void cht::upd(line)':
sequence.cpp:19:13: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   19 |   while (t+1<l.size() && (l.back().b<=v.b || (i128)(l[l.size()-2].b-v.b)*(l.back().a-l[l.size()-2].a)<=(i128)(l[l.size()-2].b-l.back().b)*(v.a-l[l.size()-2].a))) l.pop_back();
      |          ~~~^~~~~~~~~
sequence.cpp: In member function 'std::pair<long long int, long long int> cht::get(ll)':
sequence.cpp:23:13: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   23 |   while (t+1<l.size() && l[t].get(x)<l[t+1].get(x)) t++;
      |          ~~~^~~~~~~~~
sequence.cpp: In function 'void track(std::vector<long long int>&, ll, int)':
sequence.cpp:57:14: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   57 |  if (l.size()==p) { ans=l; return ; }
      |      ~~~~~~~~^~~
sequence.cpp:58:14: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   58 |  if (r.size()==p) { ans=r; return ; }
      |      ~~~~~~~~^~~
sequence.cpp:59:24: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   59 |  for (int i=0, j=0; i+1<r.size(); i++) {
      |                     ~~~^~~~~~~~~
sequence.cpp:61:35: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   61 |   if (r[i+1]<=l[j]&&i+1+l.size()-j==p) {
      |                     ~~~~~~~~~~~~~~^~~
sequence.cpp:63:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   63 |    for (int k=j; k<l.size(); k++) ans.emplace_back(l[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