Submission #698995

#	Time	Username	Problem	Language	Result	Execution time	Memory
698995		NemanjaSo2005	Aliens (IOI16_aliens)	C++14	100 / 100	569 ms	9532 KiB

aliens

#include "aliens.h"
#include<bits/stdc++.h>
#define ll long long
#define ld long double
using namespace std;
ll N,M,K;
ll dp[100005],c1=0,v1,c2=1e6,v2,cnt[100005];
struct tacka{
   ll x,y;/// X i Y su kao u matematici
} tniz[100005],niz[100005],tpp;
stack<tacka> S;
bool pox(tacka a,tacka b){
   if(a.x<b.x)
      return true;
   if(a.x>b.x)
      return false;
   return a.y<b.y;
}
ll koliko(ll x,ll y,ll px){
   ll r=abs(x-y);
   ll d=r+1;
   if((x-px)>=d)
      return d*d;
   ll a=d*d-(d-(x-px))*(d-(x-px));
   return a;
}
struct funk{
   ll offset,slope;
   int id;
   ll evaluiraj(ll gde){
      return gde*slope+offset;
   }
}pp;
deque<funk> C;
ld presek(funk a,funk b){
   return (ld)(b.offset-a.offset)/(a.slope-b.slope);
}
void dodaj(funk x){
   funk p1,p2;
   while(C.size()>=2){
      p1=C.back();
      C.pop_back();
      p2=C.back();
      if(presek(x,p2)>=presek(p1,p2)){
         C.push_back(p1);
         break;
      }
   }
   C.push_back(x);
}
funk koja(ll gde){
   funk p1,p2;
   while(C.size()>1){
      p1=C.front();
      C.pop_front();
      p2=C.front();
      if(p1.evaluiraj(gde)<p2.evaluiraj(gde)){
         C.push_front(p1);
         break;
      }
   }
   return C[0];
}
ll izracunaj(ll lmb){
   C.clear();
   dp[0]=0;
   cnt[0]=0;
   for(ll i=1;i<=N;i++){
      dp[i]=dp[i-1]+koliko(niz[i].x,niz[i].y,niz[i-1].x)-lmb;
      cnt[i]=cnt[i-1]+1;
      ll mvred=1e18,gde=0;
      //C.clear();
      if(i!=1){
         funk ff=koja(niz[i].x);
         mvred=ff.evaluiraj(niz[i].x);
         gde=ff.id;

         if(mvred+niz[i].x*niz[i].x<dp[i]){
            dp[i]=mvred+niz[i].x*niz[i].x;
            cnt[i]=cnt[gde-1]+1;
         }
      }

      pp.slope=-2*(niz[i].y-1);
      pp.id=i;
      if(-niz[i-1].x>=-niz[i].y+1)
         pp.offset=(niz[i].y-1)*(niz[i].y-1)+dp[i-1]-lmb;
      else
         pp.offset=(niz[i].y-1)*(niz[i].y-1) - (-niz[i].y+1+niz[i-1].x)*(-niz[i].y+1+niz[i-1].x)+dp[i-1]-lmb;
      dodaj(pp);
   }
   if(cnt[N]<=K and cnt[N]>c1){
      c1=cnt[N];
      v1=dp[N]+lmb*cnt[N];
   }
   if(cnt[N]>K and cnt[N]<c2){
      c2=cnt[N];
      v2=dp[N]+lmb*cnt[N];
   }
   return dp[N]+lmb*cnt[N];
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
   /*while(true){
      ll a,b,c,d;
      cin>>a>>b>>c>>d;
      cout<<koliko(a,b,c,d)<<endl;
   }*/
   N=n;
   M=m;
   K=k;
   for(ll i=1;i<=N;i++){
      tniz[i].x=c[i-1]+1;
      tniz[i].y=r[i-1]+1;
   }
   for(ll i=1;i<=N;i++)
      if(tniz[i].x<tniz[i].y)
         swap(tniz[i].x,tniz[i].y);
   sort(tniz+1,tniz+1+N,pox);
   tpp.x=-1;
   tpp.y=-1e9;
   S.push(tpp);
  // cout<<N<<endl;
   //for(ll i=1;i<=N;i++)
    //  cout<<tniz[i].x<<" "<<tniz[i].y<<endl;
   for(ll i=1;i<=N;i++){
      if(S.top().x==tniz[i].x)
         continue;
      while(S.top().y>=tniz[i].y)
         S.pop();
      S.push(tniz[i]);
   }
   for(ll i=1;i<=N;i++){
      niz[i].x=0;
      niz[i].y=0;
   }
   N=S.size()-1;
   for(ll i=N;i>=1;i--){
      niz[i]=S.top();
      S.pop();
   }
   //cout<<N<<endl;
   //for(ll i=1;i<=N;i++)
    //  cout<<niz[i].x<<" "<<niz[i].y<<endl;
   if(K>N)
      K=N;
   niz[0].x=niz[0].y=-1e9;
/*   izracunaj(-8);
   cout<<cnt[N]<<" "<<dp[N]<<endl;
   return 0;*/
   ll dg=-M*M,ret=0,gg=0,sred;
   while(dg<=gg){
      sred=(dg+gg)/2;
      izracunaj(sred);
      if(cnt[N]<=K){
         dg=sred+1;
         ret=dg;
      }
      else
         gg=sred-1;
   }
 //  cout<<sred<<endl;
   ll res=v1;
   res=min(res,v1+((v2-v1)/(c2-c1))*(K-c1));
   dg=-M*M;
   gg=ret;
   ll v1,v2;
   while(dg<=gg){
      sred=(dg+gg)/2;
      v1=izracunaj(sred-1);
      v2=izracunaj(sred);
      res=min(res,v1);
      res=min(res,v2);
      if(v2<v1)
         dg=sred+1;
      else
         gg=sred-1;
   }
   return res;
}

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