Point in Polygon.cpp

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxN = 1001;

struct Point {
    int x, y;
    void read(){ scanf("%d %d", &x, &y); }
    Point operator +(const Point& b) const { return Point{x+b.x, y+b.y}; }
    Point operator -(const Point& b) const { return Point{x-b.x, y-b.y}; }
    ll operator *(const Point& b) const { return (ll) x * b.y - (ll) y * b.x; }
    void operator +=(const Point& b) { x += b.x; y += b.y; }
    void operator -=(const Point& b) { x -= b.x; y -= b.y; }
    void operator *=(const int k) { x *= k; y *= k; }

    ll cross(const Point& b, const Point& c) const {
        return (b - *this) * (c - *this);
    }
};

int N, M;
Point P[maxN];

bool pointlineintersect(Point P1, Point P2, Point P3){
    if(P2.cross(P1, P3) != 0)   return false;
    return (min(P2.x, P3.x) <= P1.x && P1.x <= max(P2.x, P3.x))
        && (min(P2.y, P3.y) <= P1.y && P1.y <= max(P2.y, P3.y));
}

void pointinpolygon(){
    int cnt = 0;
    bool boundary = false;
    for(int i = 1; i <= N; i++){
        int j = (i == N ? 1 : i+1);
        if(pointlineintersect(P[0], P[i], P[j]))
            boundary = true;

        if(P[i].x <= P[0].x && P[0].x < P[j].x && P[0].cross(P[i], P[j]) < 0)       cnt++;
        else if(P[j].x <= P[0].x && P[0].x < P[i].x && P[0].cross(P[j], P[i]) < 0)  cnt++;
    }

    if(boundary)    printf("BOUNDARY\n");
    else if(cnt&1)  printf("INSIDE\n");
    else            printf("OUTSIDE\n");
}

int main(){
    scanf("%d %d", &N, &M);
    for(int i = 1; i <= N; i++)
        P[i].read();
    for(int i = 0; i < M; i++){
        P[0].read();
        pointinpolygon();
    }
}