939. Minimum Area Rectangle

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939. Minimum Area Rectangle

Description

You are given an array of points in the X-Y plane points where points[i] = [x<sub>i</sub>, y<sub>i</sub>].

Return the minimum area of a rectangle formed from these points, with sides parallel to the X and Y axes. If there is not any such rectangle, return 0.

Example 1:

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Input: points = [[1,1],[1,3],[3,1],[3,3],[2,2]]
Output: 4

Example 2:

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Input: points = [[1,1],[1,3],[3,1],[3,3],[4,1],[4,3]]
Output: 2

Constraints:

  • 1 <= points.length <= 500
  • points[i].length == 2
  • 0 <= x<sub>i</sub>, y<sub>i</sub> <= 4 * 10^4
  • All the given points are unique .

Hints/Notes

Solution

Language: C++

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class Solution {
public:
    int minAreaRect(vector<vector<int>>& points) {
        map<int, set<int>> Xcoordinates;
        map<int, set<int>> Ycoordinates;
        for (auto& p : points) {
            int x = p[0], y = p[1];
            Xcoordinates[x].insert(y);
            Ycoordinates[y].insert(x);
        }
        int res = INT_MAX;
        for (auto& [x, s] : Xcoordinates) {
            if (s.size() < 2) {
                continue;
            }
            vector<int> yIndex(s.begin(), s.end());
            int n = yIndex.size();
            for (int i = 0; i < n; i++) {
                int y1 = yIndex[i];
                if (Ycoordinates[y1].size() < 2 || *Ycoordinates[y1].rbegin() == x) {
                    continue;
                }
                for (int j = i + 1; j < n; j++) {
                    int y2 = yIndex[j];
                    if (Ycoordinates[y2].size() < 2 || *Ycoordinates[y2].rbegin() == x) {
                        continue;
                    }
                    auto it1 = Ycoordinates[y1].lower_bound(x + 1);
                    auto it2 = Ycoordinates[y2].lower_bound(x + 1);
                    while (it1 != Ycoordinates[y1].end() && it2 != Ycoordinates[y2].end()) {
                        if (*it1 == *it2) {
                            res = min(res, (*it1 - x) * (y2 - y1));
                            it1++;
                            it2++;
                        } else if (*it1 > *it2) {
                            it2++;
                        } else {
                            it1++;
                        }
                    }
                }
            }
        }
        return res == INT_MAX ? 0 : res;
    }
};