Table of contents

# Problem

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C

Classify relative positions of 2 vectors into 5.

Counter-clockwise
Clockwise
Opposite directions
Same directions (p1 is further)
Same directions (p2 is further)

# Explanation

First, calculate cross product.
If cross product is negative, the answer is 1.
If positive, the answer is 2.
If 0, they are on a line and the answer is 3, 4 or 5.

Second, calculate dot product.
If dot product is negative, the answer is 3.
If not, 2 vectors are on the same direction and the answer is 4 or 5.

Finally, calculate the lengths of 2 vectors.

# Solution

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

#define EPS 0.0000000001
#define fequals(a,b) (fabs((a) - (b)) < EPS)

class Vector2 {
public:
  double x, y;
  
  Vector2(double x = 0, double y = 0): x(x), y(y) {}
  
  Vector2 operator + (const Vector2 v) const { return Vector2(x + v.x, y + v.y); }
  Vector2 operator - (const Vector2 v) const { return Vector2(x - v.x, y - v.y); }
  Vector2 operator * (const double k) const { return Vector2(x * k, y * k); }
  Vector2 operator / (const double k) const { return Vector2(x / k, y / k); }
  
  double length() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  double dot (Vector2 const v) { return x * v.x + y * v.y; }
  double cross (Vector2 const v) { return x * v.y - y * v.x; }
  
  bool parallel(Vector2 &other) {
    return fequals(0, cross(other));
  }
  
  bool orthogonal(Vector2 &other) {
    return fequals(0, dot(other));
  }
  
  bool operator < (const Vector2 &v) {
    return x != v.x ? x < v.x : y < v.y;
  }
  
  bool operator == (const Vector2 &v) {
    return fabs(x - v.x) < EPS && fabs(y - v.y) < EPS;
  }
};

ostream & operator << (ostream & out, Vector2 const & v) { 
  out<< "Vector2(" << v.x << ", " << v.y << ')';
  return out;
}

istream & operator >> (istream & in, Vector2 & v) { 
  double x, y;
  in >> x;
  in >> y;
  v.x = x;
  v.y = y;
  return in;
}

Int N;
Vector2 p0, p1, p2, v01;
string msgs[5] = {"COUNTER_CLOCKWISE", "CLOCKWISE", "ONLINE_BACK", "ONLINE_FRONT", "ON_SEGMENT"};

int clk(Vector2 &v01, Vector2 &v02) {
  double cross_ = v01.cross(v02);
  if (cross_ > 0.0) return 0;
  else if (cross_ < 0.0) return 1;

  double dot_ = v01.dot(v02);
  if (v01.dot(v02) < 0.0) return 2;
  if (v01.length() - v02.length() >= 0) return 4;
  return 3;
}

void solve() {
  Vector2 v02 = p2 - p0;
  int msg_idx = clk(v01, v02);
  cout << msgs[msg_idx] << endl;
}

void input() {
  cin >> p0 >> p1 >> N;
  v01 = p1 - p0;
  while (cin >> p2) {
    solve();
  }
}

int main() {
  cout.precision(15);
  input();
}

CGL_1_C Counter-Clockwise

# Problem

# Explanation

# Solution

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