Submission #553057

#	Time	Username	Problem	Language	Result	Execution time	Memory
553057		mars4	Split the sequence (APIO14_sequence)	C++17	100 / 100	865 ms	81852 KiB

sequence

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp> 

using namespace std;
using namespace __gnu_pbds; 

#define ff              first
#define ss              second
#define ll              int64_t
#define ld              long double
#define nl              cout<<"\n"
#define i128            __int128_t
#define all(v)          v.begin(),v.end()
#define mset(a,v)       memset((a),(v),sizeof(a))
#define forn(i,a,b)     for(int64_t i=int64_t(a);i<int64_t(b);++i)
#define forb(i,a,b)     for(int64_t i=int64_t(a);i>=int64_t(b);--i)
#define fastio()        ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);

#define mod         1'000'000'007
#define mod2        998'244'353 
#define inf         1'000'000'000'000'007
#define pi          3.14159265358979323846

template<class key,class cmp=std::less<key>>
using ordered_set=tree<key,null_type,cmp,rb_tree_tag,tree_order_statistics_node_update>;

template<class L,class R> ostream& operator<<(ostream& out,pair<L,R> &p)        {return out<<"("<<p.ff<<", "<<p.ss<<")";}
template<class T> ostream& operator<<(ostream& out,vector<T> &v)                {out<<"[";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())out<<", ";out<<*it;}return out<<"]";}
template<class T> ostream& operator<<(ostream& out,deque<T> &v)                 {out<<"[";for(auto it=v.begin();it!=v.end();++it){if(it!=v.begin())out<<", ";out<<*it;}return out<<"]";}
template<class T> ostream& operator<<(ostream& out,set<T> &s)                   {out<<"{";for(auto it=s.begin();it!=s.end();++it){if(it!=s.begin())out<<", ";out<<*it;}return out<<"}";}
template<class T> ostream& operator<<(ostream& out,ordered_set<T> &s)           {out<<"{";for(auto it=s.begin();it!=s.end();++it){if(it!=s.begin())out<<", ";out<<*it;}return out<<"}";}
template<class L,class R> ostream& operator<<(ostream& out,map<L,R> &m)         {out<<"{";for(auto it=m.begin();it!=m.end();++it){if(it!=m.begin())out<<", ";out<<*it;}return out<<"}";}

void dbg_out() {cerr<<"]\n";}
template<typename Head,typename... Tail> 
void dbg_out(Head H,Tail... T) {cerr<<H;if(sizeof...(Tail))cerr<<", ";dbg_out(T...);}
#ifdef LOCAL
#define dbg(...) cerr<<"["<<#__VA_ARGS__<<"] = [",dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

//---------------------------------mars4---------------------------------

const ll N=100'000;
const ll K=200;
ll a[N];
ll pre[N+1];
int v[K][N];
vector<ll> dp1;
vector<ll> dp2;

ll sum(ll l,ll r)
{
	return pre[r+1]-pre[l];
}

class CHT
{
	struct Line
	{
		ll m;
		ll c;
		ll ind;

		Line(ll m,ll c,ll ind):m(m),c(c),ind(ind) {}

		ll eval(ll x)
		{
			return m*x+c;
		}
	};

	public:
	deque<Line> cv_hull;

	void update(ll m,ll c,ll ind)
	{
		Line l=Line(m,c,ind);
		ll n=(ll)cv_hull.size();
		while(n>=2 and (l.c-cv_hull[0].c)*(cv_hull[1].m-cv_hull[0].m)>=(cv_hull[0].c-cv_hull[1].c)*(cv_hull[0].m-l.m))
		{
			cv_hull.pop_front();
			n--;
		}
		cv_hull.push_front(l);
	}
	
	pair<ll,ll> query(ll x)
	{
		ll n=(ll)cv_hull.size();
		while(n>=2 and cv_hull[n-1].eval(x)<=cv_hull[n-2].eval(x))
		{
			cv_hull.pop_back();
			n--;
		}
		return {cv_hull[n-1].eval(x),cv_hull[n-1].ind};
	}
};

int main()
{
	fastio();
	ll z,n,m,t,k,i,j,l,d,h,r;
	cin>>n>>k;
	dp1=vector<ll>(n);
	dp2=vector<ll>(n);
	forn(i,0,n)
	{
		cin>>a[i];
		pre[i+1]=pre[i]+a[i];
	}
	// dp[i][k]=dp[j][k]+(sum(j+1,n-1)-sum(r+1,n-1))*sum(r+1,n-1)
	// dp[i][k]=dp[j][k-1]+sum(j+1,n-1)*sum(r+1,n-1)-sum(r+1,n-1)*sum(r+1,n-1);
	// y=mx+c
	// m=sum(j+1,n-1), x=sum(r+1,n-1)
	// m is decreasing, x is decreasing
	forn(j,0,k)
	{
		CHT cht;
		forn(i,j,n-1)
		{
			cht.update(sum(i,n-1),i?dp1[i-1]:0,i);
			ll rsum=sum(i+1,n-1);
			auto [val,ind]=cht.query(rsum);
			dp2[i]=val-rsum*rsum;
			v[j][i]=ind;
		}
		dp1.swap(dp2);
	}
	pair<ll,ll> mval={-1,-1};
	forn(i,0,n-1)
	{
		mval=max(mval,{dp1[i],i});
	}
	vector<ll> ans;
	ll ind=mval.ss;
	forb(i,k-1,0)
	{
		ans.push_back(ind);
		ind=v[i][ind]-1;
	}
	reverse(all(ans));
	cout<<mval.ff<<"\n";
	for(ll i:ans)
	{
		cout<<i+1<<" ";
	}
	nl;
	cerr<<"\nTime elapsed: "<<1000*clock()/CLOCKS_PER_SEC<<"ms\n";
	return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:105:5: warning: unused variable 'z' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |     ^
sequence.cpp:105:9: warning: unused variable 'm' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |         ^
sequence.cpp:105:11: warning: unused variable 't' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |           ^
sequence.cpp:105:15: warning: unused variable 'i' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |               ^
sequence.cpp:105:17: warning: unused variable 'j' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |                 ^
sequence.cpp:105:19: warning: unused variable 'l' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |                   ^
sequence.cpp:105:21: warning: unused variable 'd' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |                     ^
sequence.cpp:105:23: warning: unused variable 'h' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |                       ^
sequence.cpp:105:25: warning: unused variable 'r' [-Wunused-variable]
  105 |  ll z,n,m,t,k,i,j,l,d,h,r;
      |                         ^

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29