Table of contents

# Problem

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B

Determin if 2 segments intersect each other.

# Solution

Define the return value of function cw

1: Counter-clockwise
-1: Clockwise
0: On segment
other integer $x$ : on a line, but out of segment

The result of the product of the 2 cw means:

1: no intersection.
-1: They intersect.
0: They intersect. 4 points on a line. Either vertex of segment is on the other segment
$x^2$ : no intersection. 4 points on a line, but no common part.

// 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, p3;

int cw(Vector2 v01, Vector2 v02) {
  double cross_ = v01.cross(v02);
  if (cross_ > EPS) return 1; // above segment
  else if (cross_ < -EPS) return -1; // beneath segment
  if (v01.dot(v02) < 0) return 2; // opposite
  if (v01.length() - v02.length() >= 0) return 0; // on segment
  return -2; // out of segment
}

void solve() {
  int cw1 = cw(p1 - p0, p2 - p0) * cw(p1 - p0, p3 - p0);
  int cw2 = cw(p3 - p2, p1 - p2) * cw(p3 - p2, p0 - p2);
  if (cw1 <= 0 && cw2 <= 0) cout << 1 << endl;
  else cout << 0 << endl;
}

void input() {
  cin >> N;
  while (cin >> p0 >> p1 >> p2 >> p3) {
    solve();
  }
}

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

CGL_2_B Intersection

# Problem

# Solution

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