Minimum Area Rectangle II — Python

# Time:  O(n^2) ~ O(n^3)
# Space: O(n^2)

import collections
import itertools


class Solution(object):
    def minAreaFreeRect(self, points):
        """
        :type points: List[List[int]]
        :rtype: float
        """
        points.sort()
        points = [complex(*z) for z in points]
        lookup = collections.defaultdict(list)
        for P, Q in itertools.combinations(points, 2):
            lookup[P-Q].append((P+Q) / 2)

        result = float("inf")
        for A, candidates in lookup.iteritems():
            for P, Q in itertools.combinations(candidates, 2):
                if A.real * (P-Q).real + A.imag * (P-Q).imag == 0.0:
                    result = min(result, abs(A) * abs(P-Q))
        return result if result < float("inf") else 0.0