Point in Polygon

#include <bits/stdc++.h>

using namespace std;

typedef long long C;
typedef complex<C> P;
#define X real()
#define Y imag()

const long long INF = 1e9 + 7;

long long cross(P a, P b, P c) {
    long long cp = (conj(b-a)*(c-a)).Y;
    return (cp > 0) - (cp < 0);
}

bool comp(const P &a, const P &b) {
    return (a.X == b.X) ? (a.Y < b.Y) : (a.X < b.X);
}

bool mid(P a, P b, P c) {
    vector<P> v = {a, b, c};
    sort(v.begin(), v.end(), comp);
    return (v[1] == c);
}

bool check(P a, P b, P c, P d) {
    long long b1 = cross(a, b, c);
    long long b2 = cross(a, b, d);
    long long b3 = cross(c, d, a);
    long long b4 = cross(c, d, b);
    if (b1 * b2 < 0 && b3 * b4 < 0) return true;
    if (b3 == 0 && mid(c, d, a) && b4 < 0) return true;
    if (b4 == 0 && mid(c, d, b) && b3 < 0) return true;
    return false;
}

int main() {

    int n, m;
    cin >> n >> m;

    vector<pair<long long, long long>> vertices(n);
    vector<pair<long long, long long>> points(m);

    for (int i = 0; i < n; i++) {
        long long a, b;
        cin >> a >> b;
        vertices[i] = {a, b};
    }
    
    for (int i = 0; i < m; i++) {
        long long a, b;
        cin >> a >> b;
        points[i] = {a, b};
    }

    vector<P> polygon;

    for (long long i = 0; i < n; i++)
        polygon.push_back({vertices[i].first, vertices[i].second});
    polygon.push_back(polygon[0]);

    for (long long i = 0; i < m; i++) {
        P point = {points[i].first, points[i].second};
        P infinity = {INF, INF};
        long long intersections = 0;
        bool boundary = 0;
        for (long long j = 0; j < n; j++) {
            long long q = cross(polygon[j], polygon[j+1], point);
            if (q == 0 && mid(polygon[j], polygon[j+1], point)) {
                boundary = true;
                break;
            }
            intersections += check(polygon[j], polygon[j+1], point, infinity);
        }
        if (boundary) cout << "BOUNDARY" << endl;
        else cout << (intersections & 1 ? "INSIDE" : "OUTSIDE") << endl;
    }

}

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