Point in Polygon

#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for(int i=a;i<(b);++i)
#define all(x) begin(x),end(x)
#define sz(x) int((x).size())
using ll = long long;
using pii = pair<int,int>;
using vi = vector<int>;

/**
 * Author: Ulf Lundstrom
 * Date: 2009-02-26
 * License: CC0
 * Source: My head with inspiration from tinyKACTL
 * Description: Class to handle points in the plane.
 * 	T can be e.g. double or long long. (Avoid int.)
 * Status: Works fine, used a lot
 */
template <class T> int sgn(T x) { return (x > 0) - (x < 0); }
template<class T>
struct Point {
	typedef Point P;
	T x, y;
	explicit Point(T x=0, T y=0) : x(x), y(y) {}
	bool operator<(P p) const { return tie(x,y) < tie(p.x,p.y); }
	bool operator==(P p) const { return tie(x,y)==tie(p.x,p.y); }
	P operator+(P p) const { return P(x+p.x, y+p.y); }
	P operator-(P p) const { return P(x-p.x, y-p.y); }
	P operator*(T d) const { return P(x*d, y*d); }
	P operator/(T d) const { return P(x/d, y/d); }
	T dot(P p) const { return x*p.x + y*p.y; }
	T cross(P p) const { return x*p.y - y*p.x; }
	T cross(P a, P b) const { return (a-*this).cross(b-*this); }
	T dist2() const { return x*x + y*y; }
	double dist() const { return sqrt((double)dist2()); }
	// angle to x-axis in interval [-pi, pi]
	double angle() const { return atan2(y, x); }
	P unit() const { return *this/dist(); } // makes dist()=1
	P perp() const { return P(-y, x); } // rotates +90 degrees
	P normal() const { return perp().unit(); }
	// returns point rotated 'a' radians ccw around the origin
	P rotate(double a) const {
		return P(x*cos(a)-y*sin(a),x*sin(a)+y*cos(a)); }
  friend istream& operator>>(istream& os, P& p) {
		return os >> p.x >> p.y; }
	friend ostream& operator<<(ostream& os, P p) {
		return os << '(' << p.x << ',' << p.y << ')'; }
};
using pd = Point<ll>;

template<class P> bool onSegment(P s, P e, P p) {
	return p.cross(s, e) == 0 && (s - p).dot(e - p) <= 0;
}

/**
 * Author: Victor Lecomte, chilli
 * Date: 2019-04-26
 * License: CC0
 * Source: https://vlecomte.github.io/cp-geo.pdf
 * Description: Returns true if p lies within the polygon. If strict is true,
 * it returns false for points on the boundary. The algorithm uses
 * products in intermediate steps so watch out for overflow.
 * Time: O(n)
 * Usage:
 * vector<P> v = {P{4,4}, P{1,2}, P{2,1}};
 * bool in = inPolygon(v, P{3, 3}, false);
 * Status: stress-tested and tested on kattis:pointinpolygon
 */

template<class P>
void inPolygon(vector<P> &p, P a) {
	int cnt = 0, n = sz(p);
	rep(i,0,n) {
		P q = p[(i + 1) % n];
		if (onSegment(p[i], q, a)) {
      cout << "BOUNDARY\n";
      return;
    }
		//or: if (segDist(p[i], q, a) <= eps) return !strict;
		cnt ^= ((a.y<p[i].y) - (a.y<q.y)) * a.cross(p[i], q) > 0;
	}
  cout << (cnt ? "INSIDE\n" : "OUTSIDE\n");
}

int main() {
  int n, m;
  cin >> n >> m;
  vector<pd> P(n);
  rep(i,0,n) {
    cin >> P[i];
  }
  rep(i,0,m) {
    pd p;
    cin >> p;
    inPolygon(P,p);
  }
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED