题目链接：https://ac.nowcoder.com/acm/contest/883/H

题目大意

　　给定 N 个不同的整数点，N 为偶数，求一条直线，这条直线能把这 N 个点对半分开，输出这条直线经过的两个整点坐标。

分析1

　　在无穷远处选一个点（我选两个互质的质数），设为$(x, y)$，然后极角排序，然后取最中间两个点的中点，设为$(\frac{a}{2}, \frac{b}{2})$，由于题目要求整数点，通过求出直线方程，可以发现整数点$(3x - a, 3y - b)$也在直线上，于是答案就出来了。

代码如下

 #include <bits/stdc++.h>

 using namespace std;

 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);

 #define Rep(i,n) for (int i = 0; i < (n); ++i)

 #define For(i,s,t) for (int i = (s); i <= (t); ++i)

 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)

 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)

 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)

 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)

 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)

 #define pr(x) cout << #x << " = " << x << "  "

 #define prln(x) cout << #x << " = " << x << endl

 #define LOWBIT(x) ((x)&(-x))

 #define ALL(x) x.begin(),x.end()

 #define INS(x) inserter(x,x.begin())

 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())

 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // ?? x ?????? c

 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);

 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);

 #define ms0(a) memset(a,0,sizeof(a))

 #define msI(a) memset(a,inf,sizeof(a))

 #define msM(a) memset(a,-1,sizeof(a))

 #define MP make_pair

 #define PB push_back

 #define ft first

 #define sd second

 template<typename T1, typename T2>

 istream &operator>>(istream &in, pair<T1, T2> &p) {

     in >> p.first >> p.second;

     return in;

 }

 template<typename T>

 istream &operator>>(istream &in, vector<T> &v) {

     for (auto &x: v)

         in >> x;

     return in;

 }

 template<typename T>

 ostream &operator<<(ostream &out, vector<T> &v) {

     Rep(i, v.size()) out << v[i] << " \n"[i == v.size()];

     return out;

 }

 template<typename T1, typename T2>

 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {

     out << "[" << p.first << ", " << p.second << "]" << "\n";

     return out;

 }

 inline int gc(){

     static const int BUF = 1e7;

     static char buf[BUF], *bg = buf + BUF, *ed = bg;

     if(bg == ed) fread(bg = buf, , BUF, stdin);

     return *bg++;

 } 

 inline int ri(){

     int x = , f = , c = gc();

     for(; c<||c>; f = c=='-'?-:f, c=gc());

     for(; c>&&c<; x = x* + c - , c=gc());

     return x*f;

 }

 template<class T>

 inline string toString(T x) {

     ostringstream sout;

     sout << x;

     return sout.str();

 }

 inline int toInt(string s) {

     int v;

     istringstream sin(s);

     sin >> v;

     return v;

 }

 //min <= aim <= max

 template<typename T>

 inline bool BETWEEN(const T aim, const T min, const T max) {

     return min <= aim && aim <= max;

 }

 typedef long long LL;

 typedef unsigned long long uLL;

 typedef pair< double, double > PDD;

 typedef pair< int, int > PII;

 typedef pair< int, PII > PIPII;

 typedef pair< string, int > PSI;

 typedef pair< int, PSI > PIPSI;

 typedef set< int > SI;

 typedef set< PII > SPII;

 typedef vector< int > VI;

 typedef vector< double > VD;

 typedef vector< VI > VVI;

 typedef vector< SI > VSI;

 typedef vector< PII > VPII;

 typedef map< int, int > MII;

 typedef map< int, string > MIS;

 typedef map< int, PII > MIPII;

 typedef map< PII, int > MPIII;

 typedef map< string, int > MSI;

 typedef map< string, string > MSS;

 typedef map< PII, string > MPIIS;

 typedef map< PII, PII > MPIIPII;

 typedef multimap< int, int > MMII;

 typedef multimap< string, int > MMSI;

 //typedef unordered_map< int, int > uMII;

 typedef pair< LL, LL > PLL;

 typedef vector< LL > VL;

 typedef vector< VL > VVL;

 typedef priority_queue< int > PQIMax;

 typedef priority_queue< int, VI, greater< int > > PQIMin;

 const double EPS = 1e-;

 const LL inf = 0x7fffffff;

 const LL infLL = 0x7fffffffffffffffLL;

 const LL mod = 1e9 + ;

 const int maxN = 1e3 + ;

 const LL ONE = ;

 const LL evenBits = 0xaaaaaaaaaaaaaaaa;

 const LL oddBits = 0x5555555555555555;

 template<typename T>

 struct Point{

     T X,Y;

     Point< T >(T x = ,T y = ) : X(x), Y(y) {}

     inline T setXY(T x, T y) { return X = x, Y = y; }

     inline bool operator== (const Point<T>& x) const { return X == x.X && Y == x.Y; }

     inline bool operator< (const Point<T>& x) const {

         if(Y == x.Y)return X < x.X;

         return Y < x.Y;

     }

     inline bool operator> (const Point<T>& x)const{return x < *this;}

     inline Point<T> operator* (const T& k) { return Point<T>(k*X, k*Y); }

     inline Point<T> operator/ (const T& k) { return Point<T>(X/k, Y/k); }

     inline Point<T> operator+ (const Point<T>& x) { return Point<T>(X+x.X,Y+x.Y); }

     inline Point<T> operator- (const Point<T>& x) { return Point<T>(X-x.X,Y-x.Y); }

     T operator^(const Point<T> &x) const { return X*x.Y - Y*x.X; }

       T operator*(const Point<T> &x) const { return X*x.X + Y*x.Y; }

 };

 template<typename T>

 istream &operator>> (istream &in, Point<T> &x) {

     in >> x.X >> x.Y;

     return in;

 }

 template<typename T>

 ostream &operator<< (ostream &out, const Point<T> &x) {

     out << "(" << x.X << ", " << x.Y << ")" << endl;

     return out;

 }

 int T, N;

 Point< LL > p[maxN];

 Point< LL > a(-, -), b;

 inline bool cmp(const Point< LL > &x, const Point< LL > &y) {

     return ((a - x) ^ (a - y)) > ;

 }

 int main(){

     //freopen("MyOutput.txt","w",stdout);

     //freopen("input.txt","r",stdin);

     //INIT();

     scanf("%d", &T);

     while(T--) {

         scanf("%d", &N);

         For(i, , N) cin >> p[i];

         sort(p + , p +  + N, cmp);

         Point< LL > b = a *  - (p[N >> ] + p[(N >> ) + ]);

         printf("%lld %lld %lld %lld\n", a.X, a.Y, b.X, b.Y);

     }

     return ;

 }

分析2（正解）

　　其实没必要极角排序，只要进行一次二维偏序排序，选中间两个点，直接构造直线即可。

代码如下

 #include <bits/stdc++.h>

 using namespace std;

 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);

 #define Rep(i,n) for (int i = 0; i < (n); ++i)

 #define For(i,s,t) for (int i = (s); i <= (t); ++i)

 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)

 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)

 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)

 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)

 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)

 #define pr(x) cout << #x << " = " << x << "  "

 #define prln(x) cout << #x << " = " << x << endl

 #define LOWBIT(x) ((x)&(-x))

 #define ALL(x) x.begin(),x.end()

 #define INS(x) inserter(x,x.begin())

 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())

 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // ?? x ?????? c

 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);

 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);

 #define ms0(a) memset(a,0,sizeof(a))

 #define msI(a) memset(a,inf,sizeof(a))

 #define msM(a) memset(a,-1,sizeof(a))

 #define MP make_pair

 #define PB push_back

 #define ft first

 #define sd second

 template<typename T1, typename T2>

 istream &operator>>(istream &in, pair<T1, T2> &p) {

     in >> p.first >> p.second;

     return in;

 }

 template<typename T>

 istream &operator>>(istream &in, vector<T> &v) {

     for (auto &x: v)

         in >> x;

     return in;

 }

 template<typename T>

 ostream &operator<<(ostream &out, vector<T> &v) {

     Rep(i, v.size()) out << v[i] << " \n"[i == v.size()];

     return out;

 }

 template<typename T1, typename T2>

 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {

     out << "[" << p.first << ", " << p.second << "]" << "\n";

     return out;

 }

 inline int gc(){

     static const int BUF = 1e7;

     static char buf[BUF], *bg = buf + BUF, *ed = bg;

     if(bg == ed) fread(bg = buf, , BUF, stdin);

     return *bg++;

 } 

 inline int ri(){

     int x = , f = , c = gc();

     for(; c<||c>; f = c=='-'?-:f, c=gc());

     for(; c>&&c<; x = x* + c - , c=gc());

     return x*f;

 }

 template<class T>

 inline string toString(T x) {

     ostringstream sout;

     sout << x;

     return sout.str();

 }

 inline int toInt(string s) {

     int v;

     istringstream sin(s);

     sin >> v;

     return v;

 }

 //min <= aim <= max

 template<typename T>

 inline bool BETWEEN(const T aim, const T min, const T max) {

     return min <= aim && aim <= max;

 }

 typedef long long LL;

 typedef unsigned long long uLL;

 typedef pair< double, double > PDD;

 typedef pair< int, int > PII;

 typedef pair< int, PII > PIPII;

 typedef pair< string, int > PSI;

 typedef pair< int, PSI > PIPSI;

 typedef set< int > SI;

 typedef set< PII > SPII;

 typedef vector< int > VI;

 typedef vector< double > VD;

 typedef vector< VI > VVI;

 typedef vector< SI > VSI;

 typedef vector< PII > VPII;

 typedef map< int, int > MII;

 typedef map< int, string > MIS;

 typedef map< int, PII > MIPII;

 typedef map< PII, int > MPIII;

 typedef map< string, int > MSI;

 typedef map< string, string > MSS;

 typedef map< PII, string > MPIIS;

 typedef map< PII, PII > MPIIPII;

 typedef multimap< int, int > MMII;

 typedef multimap< string, int > MMSI;

 //typedef unordered_map< int, int > uMII;

 typedef pair< LL, LL > PLL;

 typedef vector< LL > VL;

 typedef vector< VL > VVL;

 typedef priority_queue< int > PQIMax;

 typedef priority_queue< int, VI, greater< int > > PQIMin;

 const double EPS = 1e-;

 const LL inf = 0x7fffffff;

 const LL infLL = 0x7fffffffffffffffLL;

 const LL mod = 1e9 + ;

 const int maxN = 1e3 + ;

 const LL ONE = ;

 const LL evenBits = 0xaaaaaaaaaaaaaaaa;

 const LL oddBits = 0x5555555555555555;

 template<typename T>

 struct Point{

     T X,Y;

     Point< T >(T x = ,T y = ) : X(x), Y(y) {}

     inline T setXY(T x, T y) { return X = x, Y = y; }

     inline bool operator== (const Point<T>& x) const { return X == x.X && Y == x.Y; }

     inline bool operator< (const Point<T>& x) const {

         if(X == x.X) return Y < x.Y;

         return X < x.X;

     }

     inline bool operator> (const Point<T>& x)const{return x < *this;}

     inline Point<T> operator* (const T& k) { return Point<T>(k*X, k*Y); }

     inline Point<T> operator/ (const T& k) { return Point<T>(X/k, Y/k); }

     inline Point<T> operator+ (const Point<T>& x) { return Point<T>(X+x.X,Y+x.Y); }

     inline Point<T> operator- (const Point<T>& x) { return Point<T>(X-x.X,Y-x.Y); }

     T operator^(const Point<T> &x) const { return X*x.Y - Y*x.X; }

       T operator*(const Point<T> &x) const { return X*x.X + Y*x.Y; }

 };

 template<typename T>

 istream &operator>> (istream &in, Point<T> &x) {

     in >> x.X >> x.Y;

     return in;

 }

 template<typename T>

 ostream &operator<< (ostream &out, const Point<T> &x) {

     out << "(" << x.X << ", " << x.Y << ")" << endl;

     return out;

 }

 int T, N;

 Point< int > p[maxN];

 int main(){

     //freopen("MyOutput.txt","w",stdout);

     //freopen("input.txt","r",stdin);

     //INIT();

     scanf("%d", &T);

     while(T--) {

         scanf("%d", &N);

         For(i, , N) cin >> p[i];

         sort(p + , p +  + N);

         printf("%d %d %d %d\n", p[N >> ].X - , p[N >> ].Y + (int)1e8, p[(N >> ) + ].X + , p[(N >> ) + ].Y - (int)1e8);

     }

     return ;

 }

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