投稿日 10/29/2019最終更新日 10/29/2019

# 問題

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A

# 解説

ベクトルの内積と外積を使ってベクトル同士の平行・垂直関係を求める問題.
内積が0なら垂直、外積が0なら平行.

$V \cdot U = 0 \Leftrightarrow V \perp U$
$V \times U = 0 \Leftrightarrow V \parallel U$

ちなみに内積の絶対値がベクトルの大きさの積に等しければ平行ともいえる.

$|V \cdot U| = |V| \times |U| \Leftrightarrow V \parallel U$

# 解答

C++

// 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;
}

#define MAX_N 1001
Int N;
Vector2 a, b, c, d;

void input() {
  cin >> N;
  loop(n,0,N) {
    cin >> a >> b >> c >> d;
    a = b - a;
    c = d - c;
    if (a.parallel(c)) cout << 2 << endl;
    else if (a.orthogonal(c)) cout << 1 << endl;
    else cout << 0 << endl;
  }
}

int main() {
  input();
}