Point in Polygon

import sys
import math

input = sys.stdin.readline


def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a


class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __sub__(self, other):
        return Point(self.x - other.x, self.y - other.y)

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y


class Line:
    def __init__(self, a, b):
        self.a = a
        self.b = b


def cross_product(p, q):
    # x1y2 − x2y1
    return p.x * q.y - p.y * q.x


def from_the_line(p, s):
    # (p−s1)×(p−s2)
    return cross_product(p - s.a, p - s.b)


def on_the_line(p, s):
    return (cross_product(p - s.a, p - s.b) == 0 and (min(s.a.y, s.b.y) <= p.y <= max(s.a.y, s.b.y)) and
            (min(s.a.x, s.b.x) <= p.x <= max(s.a.x, s.b.x)))


def same_line(p, q):
    return on_the_line(p.a, q) or on_the_line(p.b, q) or on_the_line(q.a, p) or on_the_line(q.b, p)


def end_intersection(p, q):
    return p.a == q.a or p.a == q.b or p.b == q.b or p.b == q.a


def middle_intersection(p, q):
    return ((from_the_line(p.a, q) > 0) != (from_the_line(p.b, q) > 0) and
            (from_the_line(q.a, p) > 0) != (from_the_line(q.b, p) > 0))


n, m = map(int, input().split())
polygon_points = []
polygon_lines = []
maxx = 10**9 + 7
maxy = 10**9 + 7

x, y = map(int, input().split())
prev_p = Point(x, y)
prev_0 = prev_p

for i in range(n - 1):
    x, y = map(int, input().split())
    cur_p = Point(x, y)
    polygon_lines.append(Line(prev_p, cur_p))
    prev_p = cur_p

polygon_lines.append(Line(prev_p, prev_0))


for i in range(m):
    x, y = map(int, input().split())
    p = Point(x, y)

    on_the_border = False
    line = Line(p, Point(maxx, maxy))
    inter = 0
    for l in polygon_lines:
        if max(l.a.x, l.b.x) <= p.x or max(l.a.y, l.b.y) <= p.y:
            pass
        if on_the_line(p, l):
            on_the_border = True
            break
        if middle_intersection(line, l):
            inter += 1
    if on_the_border:
        print('BOUNDARY')
    elif inter % 2 == 0:
        print('OUTSIDE')
    else:
        print('INSIDE')

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