Submission #372797

#	Time	Username	Problem	Language	Result	Execution time	Memory
372797		ogibogi2004	Aliens (IOI16_aliens)	C++14	100 / 100	222 ms	10720 KiB

aliens

#include "aliens.h"
#include<bits/stdc++.h>
using namespace std;
#define ll long long
const ll INF=1e12;
const ll MAXN=1e5+6;
struct line
{
	ll a,b;
	ll c;
	ll eval(ll x)
	{
		return x*a+b;
	}
	ll operator+(const line& other)
	{
		if(a==other.a)assert(false);
		return (other.b-b)/(a-other.a);
	}
};
struct CHT
{
	deque<line>dq;
	bool bad(line ezdp)
	{
		if(dq.size()==1)return 0;
		line l1=dq.end()[-2];
		line l2=dq.end()[-1];
		//(l1.b-ezdp.b)/(ezdp.a-l1.a)<(l1.b-l2.b)/(l2.a-l1.a)
		// <=> (l1.b-ezdp.b)*(l2.a-l1.a)/(ezdp.a-l1.a)<(l1.b-l2.b)
		return (l1.b-ezdp.b)*(l2.a-l1.a)<(l1.b-l2.b)*(ezdp.a-l1.a);
	}
	void push(line ezdp)
	{
		while(dq.size()>1&&bad(ezdp))
		{
			dq.pop_back();
		}
		dq.push_back(ezdp);
	}
	pair<ll,ll> query(ll x)
	{
		while(dq.size()>1&&(dq[0].eval(x)>dq[1].eval(x)||(dq[0].eval(x)==dq[1].eval(x)&&dq[0].c>dq[1].c)))
		{
			dq.pop_front();
		}
		//cout<<"&& "<<dq[0].a<<" "<<dq[0].b<<" "<<dq[0].c<<endl;
		return {dq[0].eval(x),dq[0].c};
	}
	void init()
	{
		dq.clear();
	}
}t;
struct poll 
{
	ll x,y;
	bool operator<(poll  const& other)const
	{
		return make_pair(x,-y)<make_pair(other.x,-other.y);
	}
};
vector<poll >v;
vector<poll >aux;
pair<ll,ll> dp[MAXN];
pair<ll,ll> calc(vector<poll >v,ll pen)
{
	t.init();
	for(ll  i=0;i<MAXN;i++)
	{
		dp[i]={INF,INF};
	}
	/*
	 const - x[i]*x[i]+pen+1+2*x[i]
	 a - -2*y[j+1]
	 b - max(x[j]-y[j+1]+1,0)*max(x[j]-y[j+1]+1,0)+dp[j]+y[j+1]*y[j+1]-2*y[j+1] 
	 c - dp[j].second
	*/
	dp[0]={(v[0].x-v[0].y+1)*(v[0].x-v[0].y+1)+pen,1};
	//cout<<"areve "<<max(v[0].x-v[1].y+1,0ll)*max(v[0].x-v[1].y+1,0ll)<<endl;
	//cout<<max(v[0].x-v[1].y+1,0ll)*max(v[0].x-v[1].y+1,0ll)+dp[0].first+v[1].y*v[1].y-2*v[1].y<<" "<<-max(v[0].x-v[1].y+1,0ll)*max(v[0].x-v[1].y+1,0ll)+dp[0].first+v[1].y*v[1].y-2*v[1].y<<endl;
	t.push({-2*v[1].y,-max(v[0].x-v[1].y+1,0ll)*max(v[0].x-v[1].y+1,0ll)+dp[0].first+v[1].y*v[1].y-2*v[1].y,1});
	//cout<<"dp\n";
	for(ll i=1;i<v.size();i++)
	{
		//cout<<"CHT is:\n";
		/*for(auto xd:t.dq)
		{
			cout<<xd.a<<" "<<xd.b<<" "<<xd.c<<endl;
		}
		cout<<"--\n";*/
		pair<ll,ll> gg=t.query(v[i].x);
		dp[i]={v[i].x*v[i].x+pen+1+2*v[i].x+gg.first,gg.second+1};
		dp[i]=min(dp[i],{(v[i].x-v[0].y+1)*(v[i].x-v[0].y+1)+pen,1});
		if(i+1<v.size())t.push({-2*v[i+1].y,-max(v[i].x-v[i+1].y+1,0ll)*max(v[i].x-v[i+1].y+1,0ll)+dp[i].first+v[i+1].y*v[i+1].y-2*v[i+1].y,dp[i].second});
		//cout<<dp[i].first<<" "<<dp[i].second<<endl;
	}
	//cout<<"----\n";
	return dp[v.size()-1];
}
long long take_photos(int  n, int  m, int  k, vector<int> r, vector<int> c) {
    for(ll i=0;i<r.size();i++)
    {
		if(r[i]<c[i])swap(r[i],c[i]);
		aux.push_back({r[i],c[i]});
	}
	sort(aux.begin(),aux.end());
	for(auto xd:aux)
	{
		while(v.size()>0&&v.back().y>=xd.y)
		{
			v.pop_back();
		}
		v.push_back(xd);
	}
	/*cout<<"v:\n";
	for(auto xd:v)
	{
		cout<<xd.x<<" "<<xd.y<<endl;
	}*/
	//cout<<"bs:\n";
	ll low=0,high=INF,mid,ans=-1;
	while(low<=high)
	{
		mid=(low+high)/2;
		ll t=calc(v,mid).second;
		//cout<<mid<<" "<<t<<endl;
		if(t<=k)
		{
			ans=mid;
			high=mid-1;
		}
		else
		{
			low=mid+1;
		}
	}
	//cout<<"------";
	pair<ll,ll> f=calc(v,ans);
	//cout<<f.first<<" "<<ans<<endl;
	return f.first-k*ans;
    return 0;
}

Compilation message (stderr)

aliens.cpp: In function 'std::pair<long long int, long long int> calc(std::vector<poll>, long long int)':
aliens.cpp:84:14: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<poll>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   84 |  for(ll i=1;i<v.size();i++)
      |             ~^~~~~~~~~
aliens.cpp:95:9: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<poll>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   95 |   if(i+1<v.size())t.push({-2*v[i+1].y,-max(v[i].x-v[i+1].y+1,0ll)*max(v[i].x-v[i+1].y+1,0ll)+dp[i].first+v[i+1].y*v[i+1].y-2*v[i+1].y,dp[i].second});
      |      ~~~^~~~~~~~~
aliens.cpp: In function 'long long int take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:102:17: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  102 |     for(ll i=0;i<r.size();i++)
      |                ~^~~~~~~~~

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40