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Formatted question description: https://leetcode.ca/all/939.html

939. Minimum Area Rectangle (Medium)

Given a set of points in the xy-plane, determine the minimum area of a rectangle formed from these points, with sides parallel to the x and y axes.

If there isn’t any rectangle, return 0.

Example 1:

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

Example 2:

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

Note:

  1. 1 <= points.length <= 500
  2. 0 <= points[i][0] <= 40000
  3. 0 <= points[i][1] <= 40000
  4. All points are distinct.

Solution 1.

  • class Solution {
    public int minAreaRect(int[][] points) {
        TreeMap<Integer, List<Integer>> treeMap = new TreeMap<Integer, List<Integer>>();
        for (int[] point : points) {
            int x = point[0], y = point[1];
            List<Integer> list = treeMap.getOrDefault(x, new ArrayList<Integer>());
            list.add(y);
            treeMap.put(x, list);
        }
        int minArea = Integer.MAX_VALUE;
        HashMap<String, Integer> hashMap = new HashMap<String, Integer>();
        Set<Integer> xValuesSet = treeMap.keySet();
        for (int x : xValuesSet) {
            List<Integer> list = treeMap.get(x);
            Collections.sort(list);
            int size = list.size();
            for (int i = 0; i < size; i++) {
                int y1 = list.get(i);
                for (int j = i + 1; j < size; j++) {
                    int y2 = list.get(j);
                    String positionKey = Arrays.toString(new int[]{y1, y2});
                    if (hashMap.containsKey(positionKey))
                        minArea = Math.min(minArea, (x - hashMap.get(positionKey)) * (y2 - y1));
                    hashMap.put(positionKey, x);
                }
            }
        }
        return minArea == Integer.MAX_VALUE ? 0 : minArea;
    }
}

############

class Solution {
    public int minAreaRect(int[][] points) {
        TreeMap<Integer, List<Integer>> d = new TreeMap<>();
        for (var p : points) {
            int x = p[0], y = p[1];
            d.computeIfAbsent(x, k -> new ArrayList<>()).add(y);
        }
        Map<Integer, Integer> pos = new HashMap<>();
        int ans = 1 << 30;
        for (var e : d.entrySet()) {
            int x = e.getKey();
            var ys = e.getValue();
            Collections.sort(ys);
            int n = ys.size();
            for (int i = 0; i < n; ++i) {
                int y1 = ys.get(i);
                for (int j = i + 1; j < n; ++j) {
                    int y2 = ys.get(j);
                    int p = y1 * 40001 + y2;
                    if (pos.containsKey(p)) {
                        ans = Math.min(ans, (x - pos.get(p)) * (y2 - y1));
                    }
                    pos.put(p, x);
                }
            }
        }
        return ans == 1 << 30 ? 0 : ans;
    }
}

  • // OJ: https://leetcode.com/problems/transpose-matrix/
// Time: O(N^2logN)
//   * each point is visited only once with another point -> O(N^2)
//   * ys2.find(y) -> O(logN)
// Space: O(N)
class Solution {
public:
    int minAreaRect(vector<vector<int>>& points) {
        int ans = INT_MAX;
        unordered_map<int, set<int>> m;
        for (auto &p : points) m[p[0]].insert(p[1]);
        for (auto i = m.begin(); i != m.end(); ++i) {
            auto &ys1 = i->second;
            for (auto j = next(i); j != m.end(); ++j) {
                auto &ys2 = j->second;
                int xDist = abs(i->first - j->first);
                int prevY = INT_MIN;
                int minYDist = INT_MAX;
                for (auto &y : ys1) {
                    if (ys2.find(y) == ys2.end()) continue;
                    if (prevY != INT_MIN) {
                        minYDist = min(minYDist, y - prevY);
                    }
                    prevY = y;
                }
                if (minYDist != INT_MAX) ans = min(ans, xDist * minYDist);
            }
        }
        return ans == INT_MAX ? 0 : ans;
    }
};

  • class Solution:
    def minAreaRect(self, points: List[List[int]]) -> int:
        d = defaultdict(list)
        for x, y in points:
            d[x].append(y)
        pos = {}
        ans = inf
        for x in sorted(d):
            ys = d[x]
            ys.sort()
            n = len(ys)
            for i, y1 in enumerate(ys):
                for y2 in ys[i + 1 :]:
                    if (y1, y2) in pos:
                        ans = min(ans, (x - pos[(y1, y2)]) * (y2 - y1))
                    pos[(y1, y2)] = x
        return 0 if ans == inf else ans

############

class Solution(object):
    def minAreaRect(self, points):
        """
        :type points: List[List[int]]
        :rtype: int
        """
        points = map(tuple, points)
        points.sort()
        pset = set(points)
        N = len(points)
        res = float('inf')
        for i in range(N - 1):
            p1 = points[i]
            for j in range(i + 1, N):
                p4 = points[j]
                if p4[0] == p1[0] or p4[1] == p1[1]:
                    continue
                p2 = (p1[0], p4[1])
                p3 = (p4[0], p1[1])
                if p2 in pset and p3 in pset:
                    res = min(res, abs(p3[0] - p1[0]) * abs(p2[1] - p1[1]))
        return res if res != float("inf") else 0

  • func minAreaRect(points [][]int) int {
	d := map[int][]int{}
	xs := []int{}
	for _, p := range points {
		x, y := p[0], p[1]
		d[x] = append(d[x], y)
	}
	for x := range d {
		xs = append(xs, x)
	}
	sort.Ints(xs)
	type pair struct{ x, y int }
	pos := map[pair]int{}
	ans := 1 << 30
	for _, x := range xs {
		ys := d[x]
		sort.Ints(ys)
		for i, y1 := range ys {
			for _, y2 := range ys[i+1:] {
				p := pair{y1, y2}
				if x1, ok := pos[p]; ok {
					ans = min(ans, (x-x1)*(y2-y1))
				}
				pos[p] = x
			}
		}
	}
	if ans == 1<<30 {
		return 0
	}
	return ans
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

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