結果

問題 No.2012 Largest Triangle
コンテスト
ユーザー tute7627
提出日時 2022-08-26 19:59:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 302 ms / 2,500 ms
コード長 10,990 bytes
コンパイル時間 2,542 ms
コンパイル使用メモリ 208,480 KB
最終ジャッジ日時 2025-01-31 04:08:10
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 41
権限があれば一括ダウンロードができます

ソースコード

diff # 

//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
template<typename T> vector<int> ascend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});
  return ord;
}
template<typename T> vector<int> descend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});
  return ord;
}
template<typename T> vector<T> inv_perm(const vector<T>&ord){
  vector<T>inv(ord.size());
  for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
  return inv;
}
ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
ll modulo(ll n,ll d){return (n%d+d)%d;};
template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
template< typename T = int >
struct edge {
  int to;
  T cost;
  int id;
  edge():id(-1){};
  edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
  operator int() const { return to; }
};

template<typename T>
using Graph = vector<vector<edge<T>>>;
template<typename T>
Graph<T>revgraph(const Graph<T> &g){
  Graph<T>ret(g.size());
  for(int i=0;i<g.size();i++){
    for(auto e:g[i]){
      int to = e.to;
      e.to = i;
      ret[to].push_back(e);
    }
  }
  return ret;
}
template<typename T>
Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
  Graph<T> ret(n);
  for(int es = 0; es < m; es++){
    int u,v;
    T w=1;
    cin>>u>>v;u-=indexed,v-=indexed;
    if(weighted)cin>>w;
    ret[u].emplace_back(v,w,es);
    if(!directed)ret[v].emplace_back(u,w,es);
  }
  return ret;
}
template<typename T>
Graph<T> readParent(int n,int indexed=1,bool directed=true){
  Graph<T>ret(n);
  for(int i=1;i<n;i++){
    int p;cin>>p;
    p-=indexed;
    ret[p].emplace_back(i);
    if(!directed)ret[i].emplace_back(p);
  }
  return ret;
}
struct IncrementalConvexHull{
  struct Lower{
    mutable int x,y,dx,dy;
    bool operator<(const Lower& p) const{return make_pair(x,y) < make_pair(p.x,p.y);}
    bool operator<(pair<int, int>p)const{return (long long)dy * p.first < (long long)dx * p.second;}
  };
  struct Upper{
    mutable int x,y,dx,dy;
    bool operator<(const Upper& p) const{return make_pair(x,-y) < make_pair(p.x,-p.y);}
    bool operator<(pair<int, int>p)const{return (long long)dy * p.first > (long long)dx * p.second;}
  };
  multiset<Lower, less<>>lower;
  multiset<Upper, less<>>upper;
  const int inf = 2e9;
  void add(int x, int y){
    add_lower(x,y);
    add_upper(x,y);
  }
  template<typename Itr>
  bool check_lower(Itr it){
    auto nxt = next(it);
    if(nxt != lower.end()){
      it->dx = nxt->x - it->x; 
      it->dy = nxt->y - it->y;
    } 
    else{
      it->dx = 0;
      it->dy = 1;
    }
    if(it == lower.begin())return false;
    auto pre = prev(it);
    pre->dx = it->x - pre->x;
    pre->dy = it->y - pre->y;
    if(nxt == lower.end())return false;
    if((long long)pre->dy * it->dx >= (long long)pre->dx * it->dy){
      if(nxt != lower.end()){
        pre->dx = nxt->x - pre->x; 
        pre->dy = nxt->y - pre->y;
      } 
      else{
        pre->dx = 0;
        pre->dy = 1;
      }
      return true;
    }
    return false;
  }
  void add_lower(int ax,int ay){
    if(lower.find(Lower{ax,ay,0,0}) != lower.end())return; 
    auto it = lower.find(Lower{ax,ay,0,0});
    auto l = lower.insert(Lower{ax,ay,0,0});
    if(check_lower(l)){
      lower.erase(l);
      return;
    }
    auto r = next(l);
    while(l != lower.begin() && check_lower(--l))l = lower.erase(l);
    while(r != lower.end() && check_lower(r))r = lower.erase(r);
  }
  template<typename Itr>
  bool check_upper(Itr it){
    auto nxt = next(it);
    if(nxt != upper.end()){
      it->dx = nxt->x - it->x; 
      it->dy = nxt->y - it->y;
    } 
    else{
      it->dx = 0;
      it->dy = -1;
    }
    if(it == upper.begin())return false;
    auto pre = prev(it);
    pre->dx = it->x - pre->x;
    pre->dy = it->y - pre->y;
    if(nxt == upper.end())return false;
    if((long long)pre->dy * it->dx <= (long long)pre->dx * it->dy){
      if(nxt != upper.end()){
        pre->dx = nxt->x - pre->x; 
        pre->dy = nxt->y - pre->y;
      } 
      else{
        pre->dx = 0;
        pre->dy = 1;
      }
      return true;
    }
    return false;
  }
  void add_upper(int ax,int ay){
    if(upper.find(Upper{ax,ay,0,0}) != upper.end())return; 
    auto it = upper.find(Upper{ax,ay,0,0});
    auto l = upper.insert(Upper{ax,ay,0,0});
    if(check_upper(l)){
      upper.erase(l);
      return;
    }
    auto r = next(l);
    while(l != upper.begin() && check_upper(--l))l = upper.erase(l);
    while(r != upper.end() && check_upper(r))r = upper.erase(r);
  }
  //cross((x,y), 点集合内の一点)の最大値
  long long maximum_cross(int x,int y){
    int sx = x, sy = y;
    if(sx < 0)sx *= -1, sy *= -1;
    auto itl = lower.lower_bound(make_pair(sx, sy));
    auto itr = upper.lower_bound(make_pair(sx, sy));
    if(itl == lower.end())itl--;
    if(itr == upper.end())itr--;
    return max((long long)x * itl->y - (long long)y * itl->x, (long long)x * itr->y - (long long)y * itr->x);
  };
  long long minimum_cross(int x,int y){
    return -maximum_cross(-x, -y);
  };
  long long maximum_dot(int x,int y){
    return maximum_cross(y, -x);
  }
  void print(){
    cout << "lower" << endl;
    for(auto [x, y, dx, dy]: lower){
      cout << "(" << x << "," << y << ")"<<endl;
    }
    cout << "upper" << endl;
    for(auto [x, y, dx, dy]: upper){
      cout << "(" << x << "," << y << ")"<<endl;
    }
  }
};

int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n;cin>>n;
  IncrementalConvexHull ch;
  rep(i,0,n){
    ll x,y;cin>>x>>y;
    ch.add(x,y);
    chmax(res,ch.maximum_cross(x,y));
    chmax(res,-ch.minimum_cross(x,y));
  }
  cout<<res<<endl;
  return 0;
}
0