Point in Polygon

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

// Structure to represent a point
struct Point {
    ll x, y;
};

// Function to check if a point is on a segment
bool is_on_segment(const Point& p, const Point& a, const Point& b) {
    // Calculate the cross product
    ll cross = (b.x - a.x) * (p.y - a.y) - (b.y - a.y) * (p.x - a.x);
    if (cross != 0)
        return false;
    // Check if p is within the bounding rectangle of a and b
    ll minx = min(a.x, b.x);
    ll maxx = max(a.x, b.x);
    ll miny = min(a.y, b.y);
    ll maxy = max(a.y, b.y);
    return (minx <= p.x && p.x <= maxx) && (miny <= p.y && p.y <= maxy);
}

// Function to determine the position of a point relative to the polygon
string point_in_polygon(const Point& p, const vector<Point>& polygon) {
    bool on_boundary = false;
    int crossings = 0;
    int n = polygon.size();
    
    for(int i = 0; i < n; ++i){
        Point a = polygon[i];
        Point b = polygon[(i+1)%n];
        
        // Check if the point is on the edge
        if(is_on_segment(p, a, b)){
            on_boundary = true;
            break;
        }
        
        // Check if the ray crosses the edge
        // We consider the ray to the right, i.e., positive x direction
        // Check if the edge crosses the horizontal line at p.y
        // and if the intersection is to the right of p.x
        // Handle cases where the edge is horizontal
        if(a.y == b.y){
            // Horizontal edge, ignore
            continue;
        }
        
        // Ensure a.y < b.y
        if(a.y > b.y){
            swap(a, b);
        }
        
        // Check if p.y is within the range [a.y, b.y)
        if(p.y >= a.y && p.y < b.y){
            // Compute the x coordinate of the intersection
            // To avoid floating point precision issues, use double
            double x_intersect = (double)(b.x - a.x) * (p.y - a.y) / (double)(b.y - a.y) + a.x;
            if(x_intersect > p.x){
                crossings++;
            }
        }
    }
    
    if(on_boundary){
        return "BOUNDARY";
    }
    else{
        return (crossings % 2 == 1) ? "INSIDE" : "OUTSIDE";
    }
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    int n, m;
    cin >> n >> m;
    
    vector<Point> polygon(n);
    for(int i = 0; i < n; ++i){
        cin >> polygon[i].x >> polygon[i].y;
    }
    
    vector<Point> points(m);
    for(int i = 0; i < m; ++i){
        cin >> points[i].x >> points[i].y;
    }
    
    for(int i = 0; i < m; ++i){
        cout << point_in_polygon(points[i], polygon) << "\n";
    }
}

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