{"id":55,"date":"2018-11-12T18:15:28","date_gmt":"2018-11-12T18:15:28","guid":{"rendered":"https:\/\/andybase.com\/?p=55"},"modified":"2018-11-12T18:17:07","modified_gmt":"2018-11-12T18:17:07","slug":"939-minimum-area-rectangle","status":"publish","type":"post","link":"https:\/\/andybase.com\/?p=55","title":{"rendered":"939 Minimum Area Rectangle"},"content":{"rendered":"\n

link: Minimum Area Rectangle<\/a><\/p>\n\n\n\n

Thought<\/h2>\n\n\n\n

I plan to use sweep line to solve. Firstly I put a dictionary with x-val as key, all y-val with coordinate x-val as value. Then, once I check x1, x2, if they has intersection, means there could be a rectangle. So I could enumerate all possible rectangles and record the smallest one.\u00a0<\/p>\n\n\n\n

Code<\/h2>\n\n\n\n
class Solution:
    def minAreaRect(self, points):
        \"\"\"
        :type points: List[List[int]]
        :rtype: int
        \"\"\"
        if not points or len(points) < 4:
            return 0
        res = 0
        lookup = collections.defaultdict(set)
        minimum = 2**32
        for node in points:
            lookup[node[0]].add(node[1])
        keys = list(lookup.keys())
        keys.sort()
        for j in range(len(keys)):
            for i in range(j):
                cross = list(lookup[keys[i]].intersection(lookup[keys[j]]))
                if len(cross) >= 2:
                    cross.sort()
                    for k in range(len(cross) - 1):
                        if (cross[k + 1] - cross[k]) * (keys[j] - keys[i]) < minimum:
                            minimum = (cross[k + 1] - cross[k]) * (keys[j] - keys[i])
                            res = minimum
        return res<\/pre>\n\n\n\n
Runtime<\/h2>\n\n\n\n
Time: O(n^3)
Space: O(n)<\/p>\n","protected":false},"excerpt":{"rendered":"
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