Point in Polygon

#include<bits/stdc++.h>
using namespace std;
 
#define ll long long
#define endl '\n'
 
#define P complex<ll>
 
#define X real()
 
#define Y imag()
 
const ll INF = 1e9 + 7;
 
ll cross(P a, P b, P c) {
    P u = b - a;
    P v = c - a;
    ll cp = (conj(u)*v).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) {
    ll cp1 = cross(a, b, c);
    ll cp2 = cross(a, b, d);
    ll cp3 = cross(c, d, a);
    ll cp4 = cross(c, d, b);
    if (cp1 * cp2 < 0 && cp3 * cp4 < 0) return true;
    if (cp3 == 0 && mid(c, d, a) && cp4 < 0) return true;
    if (cp4 == 0 && mid(c, d, b) && cp3 < 0) return true;
    return false;
}
 
int main(){
 
    ll n,m;
    cin >> n >> m;
    vector<pair<ll,ll>> vertices(n);
    vector<pair<ll,ll>> points(m);
    vector<P> polygon;
    for(ll i = 0; i < n; ++i){
        ll a,b;
        cin >> a >> b;
        vertices[i] =  make_pair(a,b);
    }
 
    for(ll i = 0; i < m; ++i){
        ll a,b;
        cin >> a >> b;
        points[i] =  make_pair(a,b);
    }
    for (ll i = 0; i < n; i++) {
        polygon.push_back({vertices[i].first, vertices[i].second});
    }
 
    polygon.push_back(polygon[0]);
 
    for (ll i = 0; i < m; i++) {
        P point = {points[i].first, points[i].second};
        P infinity = {INF, INF};
        ll cnt = 0;
        ll flag = 0;
        for (ll j = 0; j < n; j++) {
            ll cp = cross(polygon[j], polygon[j+1], point);
            if (cp == 0 && mid(polygon[j], polygon[j+1], point)) {
                flag = 1;
                break;
            }
            cnt += check(polygon[j], polygon[j+1], point, infinity);
        }
        if (flag) cout << "BOUNDARY" << endl;
        else cout << (cnt & 1 ? "INSIDE" : "OUTSIDE") << endl;
    }
 
    return 0;
}

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