Problem Description
You are given an array of points in the X-Y plane where points[i] = [xi, yi]. Return the minimum area of any rectangle formed from these points, with sides not necessarily parallel to the X and Y axes. If there is not any such rectangle, return 0. Answers within 10^-5 of the actual answer will be accepted.
Key Insights
- A rectangle can be defined by four points.
- To form a rectangle, the diagonals should intersect at their midpoints.
- The area of the rectangle can be computed using the distance between two opposite corners.
- We can use a set for quick look-up of points to verify if the required opposite points exist.
Space and Time Complexity
Time Complexity: O(n^2) - We need to check pairs of points to find possible rectangles. Space Complexity: O(n) - We use a set to store points for quick access.
Solution
To solve this problem, we will iterate through each pair of points and treat them as potential diagonal corners of a rectangle. For each pair, we can calculate the other two corner points that would form the rectangle. We then check if these points exist in our original set of points. If they do, we calculate the area of the rectangle using the distance formula and keep track of the minimum area found.
We will utilize a HashSet to store the points for O(1) average time complexity look-up. The area can be calculated using the formula: area = |x1 - x2| * |y1 - y2|, where (x1, y1) and (x2, y2) are the coordinates of the diagonal corners.