Point in Polygon

#include <iostream>
#include <vector>

using namespace std;

bool onSegment(long long x1, long long y1, long long x2, long long y2, long long x, long long y) {
    long long cross = (x2 - x1)*(y - y1) - (x - x1)*(y2 - y1);
    if (cross != 0)
        return false;
    long long dot = (x - x1)*(x2 - x1) + (y - y1)*(y2 - y1);
    if (dot < 0)
        return false;
    long long squared_length = (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1);
    if (dot > squared_length)
        return false;
    return true;
}

int main() {
    int n, m;
    cin >> n >> m;

    vector<pair<long long, long long>> vertices(n);
    
    for (int i = 0; i < n; ++i)
        cin >> vertices[i].first >> vertices[i].second;
    
    for (int i = 0; i < m; ++i) {
        long long x, y;
        cin >> x >> y;
        
        bool boundary = false;
        int crossings = 0;
        
        for (int j = 0; j < n; ++j) {
            long long x1 = vertices[j].first;
            long long y1 = vertices[j].second;
            long long x2 = vertices[(j + 1) % n].first;
            long long y2 = vertices[(j + 1) % n].second;
            
            if (onSegment(x1, y1, x2, y2, x, y)) {
                boundary = true;
                break;
            }
            
            if ( ((y1 <= y) && (y < y2)) || ((y2 <= y) && (y < y1)) ) {
                long long intersection = (x2 - x1)*(y - y1) - (y2 - y1)*(x - x1);
                if (intersection == 0) {
                    boundary = true;
                    break;
                }
                if ( (intersection > 0 && y2 > y1) || (intersection < 0 && y2 < y1) )
                    crossings++;
            }
        }
        
        if (boundary)
            cout << "BOUNDARY" << endl;
        else if (crossings % 2 == 1)
            cout << "INSIDE" << endl;
        else 
            cout << "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