codeingame/quadrilaterals.py

'''
> https://www.codingame.com/ide/puzzle/nature-of-quadrilaterals
@author: olivier.massot, 2019
'''
import math
import sys


class Vertex():
    def __init__(self, name_, x, y):
        self.name = name_
        self.x = int(x)
        self.y = int(y)
        self.pos = (self.x, self.y)
    
    def __repr__(self):
        return f"{self.name}{self.pos}"

class Side():
    def __init__(self, v1, v2):
        self.v1 = v1
        self.v2 = v2
        self.sqlength = (v2.x - v1.x)**2 + (v2.y - v1.y)**2
        
        self.a = (v2.x - v1.x) / (v2.y - v1.y) if v2.y != v1.y else (v2.x - v1.x) * math.inf
        self.b = -1 * self.a * v2.x + v2.y

    def ortho_to(self, s):
        if abs(self.a) == math.inf and s.a == 0:
            return True
        elif self.a == 0 and abs(s.a) == math.inf: 
            return True
        elif self.a * s.a == -1:
            return True
        return False
    
class Quadri():
    def __init__(self, *vertices):
        self.vertices = [Vertex(*v) for v in vertices]
        self.name = "".join([v.name for v in self.vertices])
        self.sides = [Side(v1, v2) for v1, v2 in list(zip(self.vertices, self.vertices[1:])) + [(self.vertices[-1], self.vertices[0])]]
    
    def __repr__(self):
        return f"<Q:{self.vertices}>"

    def nature(self):
        opposites_parallels = (abs(self.sides[0].a) == abs(self.sides[2].a) and \
                               (abs(self.sides[1].a) == abs(self.sides[3].a)))
        same_length_sides = all([s.sqlength == self.sides[0].sqlength for s in self.sides[1:]])
        right_angles = self.sides[0].ortho_to(self.sides[1]) and self.sides[1].ortho_to(self.sides[2]) and self.sides[2].ortho_to(self.sides[3])
        
        if right_angles and same_length_sides:
            return "square"
        elif right_angles:
            return "rectangle"
        elif same_length_sides:
            return "rhombus"
        elif opposites_parallels:
            return "parallelogram"
        else:
            return "quadrilateral"
        
input_ = [input().split() for _ in range(int(input()))]
quadris = [Quadri(*zip(l[::3], l[1::3], l[2::3])) for l in input_]

print(quadris, file=sys.stderr)
    
for q in quadris:
    print(f"{q.name} is a {q.nature()}.")