#codejam Qualification Round 2018, Cubic UFO (problem #4) JUDGE

cubejudge.py

#!/usr/bin/env python2

import sys
from math import acos, sqrt, pi
import numpy
from scipy.spatial import ConvexHull

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

    def mod(self):
        return sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

    def theta(self, other):
        return acos(self.x * other.x + self.y * other.y + self.z * other.z)


def equal(a, b):
    return abs(a - b) < 0.000001


def judge(A, sides):
    for v in sides:
        if not equal(v.mod(), 0.5): return "Modulus not 0.5!"

    if not equal(sides[0].theta(sides[1]), pi/2): return "0/1 not perpendicular!"
    if not equal(sides[1].theta(sides[2]), pi/2): return "1/2 not perpendicular!"
    if not equal(sides[2].theta(sides[0]), pi/2): return "2/0 not perpendicular!"

    s2v = [
        ( -1, -1, -1 ),    (  1, -1, -1 ),    ( -1,  1, -1 ),    (  1,  1, -1 ),
        ( -1, -1,  1 ),    (  1, -1,  1 ),    ( -1,  1,  1 ),    (  1,  1,  1 )
    ]
    verts = []
    for i in xrange(8):
        verts.append(Vec(
            sides[0].x * s2v[i][0] + sides[1].x * s2v[i][1] + sides[2].x * s2v[i][2],
            sides[0].y * s2v[i][0] + sides[1].y * s2v[i][1] + sides[2].y * s2v[i][2],
            sides[0].z * s2v[i][0] + sides[1].z * s2v[i][1] + sides[2].z * s2v[i][2],
        ))

    points = numpy.array( [ [v.x, v.z] for v in verts ] )
    hull = ConvexHull(points)
    a = hull.volume

    if not equal(A, a): return "area {} != {}".format(A, a)

    return "OK"

def main(argv):
    if len(argv) != 3:
        sys.stderr.write(argv[0] + " test.txt out.txt")
        exit(1)

    with open(argv[1]) as f:
        T = int(f.readline())
        AA = [ float(A.strip()) for A in f.readlines() ]

    with open(argv[2]) as f:
        for t in xrange(T):
            f.readline()
            sides = [ Vec(* ( float(c) for c in f.readline().split()) ) for _ in xrange(3) ]
            print("Case #{}: {}".format(t + 1, judge(AA[t], sides)))

if __name__ == "__main__":
    main(sys.argv)