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  • 2019 牛客多校第三场 H Magic Line

    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

      1 #include <bits/stdc++.h>
  2 using namespace std;
  3  
  4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  5 #define Rep(i,n) for (int i = 0; i < (n); ++i)
  6 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
  7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
  8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
  9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 12  
 13 #define pr(x) cout << #x << " = " << x << "  "
 14 #define prln(x) cout << #x << " = " << x << endl
 15  
 16 #define LOWBIT(x) ((x)&(-x))
 17  
 18 #define ALL(x) x.begin(),x.end()
 19 #define INS(x) inserter(x,x.begin())
 20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // ?? x ?????? c 
 22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 24  
 25 #define ms0(a) memset(a,0,sizeof(a))
 26 #define msI(a) memset(a,inf,sizeof(a))
 27 #define msM(a) memset(a,-1,sizeof(a))
 28 
 29 #define MP make_pair
 30 #define PB push_back
 31 #define ft first
 32 #define sd second
 33  
 34 template<typename T1, typename T2>
 35 istream &operator>>(istream &in, pair<T1, T2> &p) {
 36     in >> p.first >> p.second;
 37     return in;
 38 }
 39  
 40 template<typename T>
 41 istream &operator>>(istream &in, vector<T> &v) {
 42     for (auto &x: v)
 43         in >> x;
 44     return in;
 45 }
 46 
 47 template<typename T>
 48 ostream &operator<<(ostream &out, vector<T> &v) {
 49     Rep(i, v.size()) out << v[i] << " 
"[i == v.size()];
 50     return out;
 51 }
 52 
 53 template<typename T1, typename T2>
 54 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
 55     out << "[" << p.first << ", " << p.second << "]" << "
";
 56     return out;
 57 }
 58 
 59 inline int gc(){
 60     static const int BUF = 1e7;
 61     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 62     
 63     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
 64     return *bg++;
 65 } 
 66 
 67 inline int ri(){
 68     int x = 0, f = 1, c = gc();
 69     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
 70     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
 71     return x*f;
 72 }
 73 
 74 template<class T>
 75 inline string toString(T x) {
 76     ostringstream sout;
 77     sout << x;
 78     return sout.str();
 79 }
 80 
 81 inline int toInt(string s) {
 82     int v;
 83     istringstream sin(s);
 84     sin >> v;
 85     return v;
 86 }
 87 
 88 //min <= aim <= max
 89 template<typename T>
 90 inline bool BETWEEN(const T aim, const T min, const T max) {
 91     return min <= aim && aim <= max;
 92 }
 93  
 94 typedef long long LL;
 95 typedef unsigned long long uLL;
 96 typedef pair< double, double > PDD;
 97 typedef pair< int, int > PII;
 98 typedef pair< int, PII > PIPII;
 99 typedef pair< string, int > PSI;
100 typedef pair< int, PSI > PIPSI;
101 typedef set< int > SI;
102 typedef set< PII > SPII;
103 typedef vector< int > VI;
104 typedef vector< double > VD;
105 typedef vector< VI > VVI;
106 typedef vector< SI > VSI;
107 typedef vector< PII > VPII;
108 typedef map< int, int > MII;
109 typedef map< int, string > MIS;
110 typedef map< int, PII > MIPII;
111 typedef map< PII, int > MPIII;
112 typedef map< string, int > MSI;
113 typedef map< string, string > MSS;
114 typedef map< PII, string > MPIIS;
115 typedef map< PII, PII > MPIIPII;
116 typedef multimap< int, int > MMII;
117 typedef multimap< string, int > MMSI;
118 //typedef unordered_map< int, int > uMII;
119 typedef pair< LL, LL > PLL;
120 typedef vector< LL > VL;
121 typedef vector< VL > VVL;
122 typedef priority_queue< int > PQIMax;
123 typedef priority_queue< int, VI, greater< int > > PQIMin;
124 const double EPS = 1e-8;
125 const LL inf = 0x7fffffff;
126 const LL infLL = 0x7fffffffffffffffLL;
127 const LL mod = 1e9 + 7;
128 const int maxN = 1e3 + 7;
129 const LL ONE = 1;
130 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
131 const LL oddBits = 0x5555555555555555;
132 
133 template<typename T>
134 struct Point{
135     T X,Y;
136     Point< T >(T x = 0,T y = 0) : X(x), Y(y) {}
137     inline T setXY(T x, T y) { return X = x, Y = y; }
138     
139     inline bool operator== (const Point<T>& x) const { return X == x.X && Y == x.Y; }
140     inline bool operator< (const Point<T>& x) const {
141         if(Y == x.Y)return X < x.X;
142         return Y < x.Y;
143     }
144     inline bool operator> (const Point<T>& x)const{return x < *this;}
145         
146     inline Point<T> operator* (const T& k) { return Point<T>(k*X, k*Y); }
147     inline Point<T> operator/ (const T& k) { return Point<T>(X/k, Y/k); }
148     inline Point<T> operator+ (const Point<T>& x) { return Point<T>(X+x.X,Y+x.Y); }
149     inline Point<T> operator- (const Point<T>& x) { return Point<T>(X-x.X,Y-x.Y); }
150     
151     T operator^(const Point<T> &x) const { return X*x.Y - Y*x.X; }
152       T operator*(const Point<T> &x) const { return X*x.X + Y*x.Y; }
153 };
154 
155 template<typename T>
156 istream &operator>> (istream &in, Point<T> &x) {
157     in >> x.X >> x.Y;
158     return in;
159 }
160 
161 template<typename T>
162 ostream &operator<< (ostream &out, const Point<T> &x) {
163     out << "(" << x.X << ", " << x.Y << ")" << endl;
164     return out;
165 }
166 
167 int T, N;
168 Point< LL > p[maxN];
169 Point< LL > a(-179981887, -279985319), b;
170 
171 inline bool cmp(const Point< LL > &x, const Point< LL > &y) {
172     return ((a - x) ^ (a - y)) > 0;
173 }
174 
175 int main(){
176     //freopen("MyOutput.txt","w",stdout);
177     //freopen("input.txt","r",stdin);
178     //INIT();
179     scanf("%d", &T);
180     while(T--) {
181         scanf("%d", &N);
182         For(i, 1, N) cin >> p[i];
183         sort(p + 1, p + 1 + N, cmp);
184         
185         Point< LL > b = a * 3 - (p[N >> 1] + p[(N >> 1) + 1]);
186         
187         printf("%lld %lld %lld %lld
", a.X, a.Y, b.X, b.Y);
188     }
189     return 0;
190 }
    View Code

    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

      1 #include <bits/stdc++.h>
  2 using namespace std;
  3  
  4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  5 #define Rep(i,n) for (int i = 0; i < (n); ++i)
  6 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
  7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
  8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
  9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 12  
 13 #define pr(x) cout << #x << " = " << x << "  "
 14 #define prln(x) cout << #x << " = " << x << endl
 15  
 16 #define LOWBIT(x) ((x)&(-x))
 17  
 18 #define ALL(x) x.begin(),x.end()
 19 #define INS(x) inserter(x,x.begin())
 20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // ?? x ?????? c 
 22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 24  
 25 #define ms0(a) memset(a,0,sizeof(a))
 26 #define msI(a) memset(a,inf,sizeof(a))
 27 #define msM(a) memset(a,-1,sizeof(a))
 28 
 29 #define MP make_pair
 30 #define PB push_back
 31 #define ft first
 32 #define sd second
 33  
 34 template<typename T1, typename T2>
 35 istream &operator>>(istream &in, pair<T1, T2> &p) {
 36     in >> p.first >> p.second;
 37     return in;
 38 }
 39  
 40 template<typename T>
 41 istream &operator>>(istream &in, vector<T> &v) {
 42     for (auto &x: v)
 43         in >> x;
 44     return in;
 45 }
 46 
 47 template<typename T>
 48 ostream &operator<<(ostream &out, vector<T> &v) {
 49     Rep(i, v.size()) out << v[i] << " 
"[i == v.size()];
 50     return out;
 51 }
 52 
 53 template<typename T1, typename T2>
 54 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
 55     out << "[" << p.first << ", " << p.second << "]" << "
";
 56     return out;
 57 }
 58 
 59 inline int gc(){
 60     static const int BUF = 1e7;
 61     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 62     
 63     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
 64     return *bg++;
 65 } 
 66 
 67 inline int ri(){
 68     int x = 0, f = 1, c = gc();
 69     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
 70     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
 71     return x*f;
 72 }
 73 
 74 template<class T>
 75 inline string toString(T x) {
 76     ostringstream sout;
 77     sout << x;
 78     return sout.str();
 79 }
 80 
 81 inline int toInt(string s) {
 82     int v;
 83     istringstream sin(s);
 84     sin >> v;
 85     return v;
 86 }
 87 
 88 //min <= aim <= max
 89 template<typename T>
 90 inline bool BETWEEN(const T aim, const T min, const T max) {
 91     return min <= aim && aim <= max;
 92 }
 93  
 94 typedef long long LL;
 95 typedef unsigned long long uLL;
 96 typedef pair< double, double > PDD;
 97 typedef pair< int, int > PII;
 98 typedef pair< int, PII > PIPII;
 99 typedef pair< string, int > PSI;
100 typedef pair< int, PSI > PIPSI;
101 typedef set< int > SI;
102 typedef set< PII > SPII;
103 typedef vector< int > VI;
104 typedef vector< double > VD;
105 typedef vector< VI > VVI;
106 typedef vector< SI > VSI;
107 typedef vector< PII > VPII;
108 typedef map< int, int > MII;
109 typedef map< int, string > MIS;
110 typedef map< int, PII > MIPII;
111 typedef map< PII, int > MPIII;
112 typedef map< string, int > MSI;
113 typedef map< string, string > MSS;
114 typedef map< PII, string > MPIIS;
115 typedef map< PII, PII > MPIIPII;
116 typedef multimap< int, int > MMII;
117 typedef multimap< string, int > MMSI;
118 //typedef unordered_map< int, int > uMII;
119 typedef pair< LL, LL > PLL;
120 typedef vector< LL > VL;
121 typedef vector< VL > VVL;
122 typedef priority_queue< int > PQIMax;
123 typedef priority_queue< int, VI, greater< int > > PQIMin;
124 const double EPS = 1e-8;
125 const LL inf = 0x7fffffff;
126 const LL infLL = 0x7fffffffffffffffLL;
127 const LL mod = 1e9 + 7;
128 const int maxN = 1e3 + 7;
129 const LL ONE = 1;
130 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
131 const LL oddBits = 0x5555555555555555;
132 
133 template<typename T>
134 struct Point{
135     T X,Y;
136     Point< T >(T x = 0,T y = 0) : X(x), Y(y) {}
137     inline T setXY(T x, T y) { return X = x, Y = y; }
138     
139     inline bool operator== (const Point<T>& x) const { return X == x.X && Y == x.Y; }
140     inline bool operator< (const Point<T>& x) const {
141         if(X == x.X) return Y < x.Y;
142         return X < x.X;
143     }
144     inline bool operator> (const Point<T>& x)const{return x < *this;}
145         
146     inline Point<T> operator* (const T& k) { return Point<T>(k*X, k*Y); }
147     inline Point<T> operator/ (const T& k) { return Point<T>(X/k, Y/k); }
148     inline Point<T> operator+ (const Point<T>& x) { return Point<T>(X+x.X,Y+x.Y); }
149     inline Point<T> operator- (const Point<T>& x) { return Point<T>(X-x.X,Y-x.Y); }
150     
151     T operator^(const Point<T> &x) const { return X*x.Y - Y*x.X; }
152       T operator*(const Point<T> &x) const { return X*x.X + Y*x.Y; }
153 };
154 
155 template<typename T>
156 istream &operator>> (istream &in, Point<T> &x) {
157     in >> x.X >> x.Y;
158     return in;
159 }
160 
161 template<typename T>
162 ostream &operator<< (ostream &out, const Point<T> &x) {
163     out << "(" << x.X << ", " << x.Y << ")" << endl;
164     return out;
165 }
166 
167 int T, N;
168 Point< int > p[maxN];
169 
170 int main(){
171     //freopen("MyOutput.txt","w",stdout);
172     //freopen("input.txt","r",stdin);
173     //INIT();
174     scanf("%d", &T);
175     while(T--) {
176         scanf("%d", &N);
177         For(i, 1, N) cin >> p[i];
178         sort(p + 1, p + 1 + N);
179         
180         printf("%d %d %d %d
", p[N >> 1].X - 1, p[N >> 1].Y + (int)1e8, p[(N >> 1) + 1].X + 1, p[(N >> 1) + 1].Y - (int)1e8);
181     }
182     return 0;
183 }
    View Code
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  • 原文地址：https://www.cnblogs.com/zaq19970105/p/11246403.html
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