# Problem

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C

Determine given points are contained in given polygon or not.

# Explanation

See the link below for the detailed algorithm.

Polygon-Point Containment algorithm

# Solution

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 101
#define MAX_Q 1001

Int N, Q;
Vector2 polygon[MAX_N];
Vector2 point;

Int contains(Vector2 &point) {
  bool in = false;
  loop(n,0,N) {
    Vector2 a = polygon[n] - point;
    Vector2 b = polygon[(n+1) % N] - point;
    if (fabs(a.cross(b)) < EPS && a.dot(b) < EPS) return 1;
    if (a.y > b.y) swap(a, b);
    if (a.y < EPS && b.y > EPS && a.cross(b) > EPS) in = !in;
  }
  
  return in ? 2 : 0;
}

void input() {
  cin >> N;
  loop(n,0,N) cin >> polygon[n];
  cin >> Q;
  while (cin >> point) {
    cout << contains(point) << endl;
  }
}

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

Shun

Remote freelancer. A web and mobile application enginner.
Traveling around the world based on East Asia.
I'm looking forward to your job offers from all over the world!

Offer jobs or contact me!

CGL_3_C Polygon-Point Containment

# Problem

# Explanation

# Solution

Comments