Submission #679613

#	Time	Username	Problem	Language	Result	Execution time	Memory
679613		alirezasamimi100	Aliens (IOI16_aliens)	C++17	100 / 100	242 ms	14528 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long int;
using pll = pair<ll, ll>;
using ld = long double;
using pld = pair<ld, int>;
using pdd = pair<ld, ld>;
#define pb push_back
#define F first
#define S second
const ld eps = 1e-19;
const int N = 1e5 + 10;

vector<pll> vec;
pld dp[N];
int n;
struct CHT{
  const ld INF=1e18;
  pair<ld, pair<pdd,int>> A[N];
  int L, R;
  CHT(){
    L=R=0;
  }
  inline ld Intersect(pdd a, pdd b){
    if (a.first==b.first) return (a.second>=b.second?-INF:INF);
    return (a.second-b.second)/(b.first-a.first);
  }
  inline void Add(pair<pdd,int> X){
    while (L<R && Intersect(A[R-1].second.first, X.first)<=A[R-1].first) R--;
    if (L==R) A[R++]={-INF, X};
    else A[R]={Intersect(A[R-1].second.first, X.first), X}, R++;
  }
  inline pld GetMin(ld x){
    while (L+1<R && A[L+1].first<=x) L++;
    return {A[L].second.first.first*x + A[L].second.first.second,A[L].second.second};
  }
} cht;
void solve(ld cs){
  cht.L=cht.R=0;
  for(int i=1; i<=n; i++){
    ld x=vec[i-1].S-vec[i].F+1;
    if(x>=0) x*=x;
    else x=0;
    cht.Add({{(ld)-vec[i].F,cs+dp[i-1].F+vec[i].F*vec[i].F-x},dp[i-1].S+1});
    dp[i]=cht.GetMin(2*(vec[i].S+1));
    dp[i].F+=(vec[i].S+1)*(vec[i].S+1);
  }
}
ll take_photos(int n, int m, int k, vector<int> R, vector<int> C) {
  vector<pll> tp={{-1,-1}};
  for(int i=0; i<n; i++){
    if(R[i]>C[i]) swap(R[i],C[i]);
    tp.pb({R[i],C[i]});
  }
  sort(tp.begin(),tp.end());
  for(auto [x,y] : tp){
    while(!vec.empty() && vec.back().F==x) vec.pop_back();
    if(vec.empty() || vec.back().S<y) vec.pb({x,y});
  }
  n=(int)vec.size()-1;
  ::n=n;
  ll l=0,r=1e13;
  while(r-l>1){
    ll m=(l+r)/2;
    solve(m);
    if(dp[n].S<=k) r=m;
    else l=m;
  }
  solve(l);
  int x1 = dp[n].S;
  ll y1 = dp[n].F - l * x1;
  solve(r);
  int x2 = dp[n].S;
  ll y2 = dp[n].F - r * x2;
  if(x2 == k) return y2;
  return y1 + (x1 - k) * l;
}

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