Submission #386218

#	Time	Username	Problem	Language	Result	Execution time	Memory
386218		tko919	Aliens (IOI16_aliens)	C++17	100 / 100	1355 ms	22380 KiB

aliens

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
 
//template
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
using ll=long long int;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
//end

struct CHT{
   int n; vector<ll> xs,p,q; vector<bool> used;
   CHT(const vector<ll>& ps){
      n=1; while(n<(int)ps.size())n<<=1;
      used.assign(4*n,0); xs.resize(4*n,inf);
      p.resize(4*n); q.resize(4*n);
      rep(i,0,ps.size())xs[i]=ps[i];
   }
   void add(ll a,ll b,int k=0,int l=0,int r=-1){
      if(r==-1)r=n;
      while(r-l>0){
         int m=(l+r)>>1;
         if(!used[k]){
            p[k]=a; q[k]=b; used[k]=1;
            return;
         }
         ll lx=xs[l],mx=xs[m],rx=xs[r-1];
         ll pk=p[k],qk=q[k];
         bool lb=(a*lx+b<pk*lx+qk);
         bool mid=(a*mx+b<pk*mx+qk);
         bool rb=(a*rx+b<pk*rx+qk);
         if(lb&&rb){p[k]=a; q[k]=b; return;}
         if(!lb&&!rb)return;
         if(mid){swap(p[k],a); swap(q[k],b);}
         if(lb!=mid){k=2*k+1; r=m;} else{k=2*k+2; l=m;}
      }
   }
   void add_segment(ll a,ll b,int l,int r){
      ll l0=l+n,r0=r+n,s0=l,t0=r,sz=1;
      while(l0<r0){
         if(r0&1){r0--; t0-=sz; add(a,b,r0-1,t0,t0+sz);}
         if(l0&1){add(a,b,l0-1,s0,s0+sz); l0++; s0+=sz;}
         l0>>=1; r0>>=1; sz<<=1;
      }
   }
   pair<ll,ll> query(int i){
      int k=i+n-1;
      ll ami=-1,x=xs[i],s=INF;
      if(used[k]){
         s=p[k]*x+q[k];
         ami=p[k];
      }
      while(k){
         k=(k-1)>>1;
         if(used[k]){
            if(chmin(s,p[k]*x+q[k]))ami=p[k];
         }
      } return {s,ami};
   }
};
 
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
   using P=pair<ll,ll>;
   vector<P> pos,used;
   rep(i,0,n){
      if(r[i]>c[i])swap(r[i],c[i]);
      c[i]++;
      pos.push_back({r[i],c[i]});
   }
   sort(ALL(pos),[](P& a,P& b){
      if(a.first==b.first)return a.second>b.second;
      else return a.first<b.first;
   });
   ll mx=-1;
   rep(i,0,n){
      if(!chmax(mx,pos[i].second))continue;
      used.push_back(pos[i]);
   }
   n=used.size();
   r.clear();
   c.clear();
   for(auto& [x,y]:used){
      r.push_back(x);
      c.push_back(y);
   }
   
   auto get=[&](ll pena)->P{
      vector<ll> ps,dp(n+10),dp2(n+10);
      dp[0]=dp2[0]=0;
      
      rep(i,0,n)ps.push_back(c[i]);
      CHT cht(ps);
      rep(i,0,n){
         ll b=dp[i]+ll(r[i])*r[i];
         if(i and c[i-1]>r[i])b-=ll(c[i-1]-r[i])*(c[i-1]-r[i]);
         cht.add(-2LL*r[i],b);
         auto [v,a]=cht.query(i);
         int pre=lower_bound(ALL(r),-(a/2))-r.begin();
         dp[i+1]=v+ll(c[i])*c[i]+pena;
         dp2[i+1]=dp2[pre]+1;
      }
      return {dp[n],dp2[n]};
   };

   chmin(k,n);
   ll lb=-1,rb=1e13;
   while(rb-lb>1){
      ll mid=(lb+rb)/2;
      if(get(mid).second<=k)rb=mid;
      else lb=mid;
   }
   auto p1=get(lb),p2=get(rb);
   ll x1=p1.first-lb*p1.second;
   ll x2=p2.first-rb*p2.second;
   ll s=p1.second-k,t=k-p2.second;
   if(t==0)return x2;
   else return (x1*t+x2*s)/(s+t);
}
 
/*
int main() {
    int n, m, k;
    assert(3 == scanf("%d %d %d", &n, &m, &k));
    std::vector<int> r(n), c(n);
    for (int i = 0; i < n; i++) {
        assert(2 == scanf("%d %d", &r[i], &c[i]));
    }
    long long ans = take_photos(n, m, k, r, c);
    
    
    printf("%lld\n", ans);
    return 0;
}
//*/

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