963. Minimum Area Rectangle II

Given a set of points in the xy-plane, determine the minimum area of any rectangle formed from these points, with sides not necessarily parallel to the x and y axes.

If there isn't any rectangle, return 0.

Example 1:

Input: [[1,2],[2,1],[1,0],[0,1]]
Output: 2.00000
Explanation: The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.

Example 2:

Input: [[0,1],[2,1],[1,1],[1,0],[2,0]]
Output: 1.00000
Explanation: The minimum area rectangle occurs at [1,0],[1,1],[2,1],[2,0], with an area of 1.

Example 3:

Input: [[0,3],[1,2],[3,1],[1,3],[2,1]]
Output: 0
Explanation: There is no possible rectangle to form from these points.

Example 4:

Input: [[3,1],[1,1],[0,1],[2,1],[3,3],[3,2],[0,2],[2,3]]
Output: 2.00000
Explanation: The minimum area rectangle occurs at [2,1],[2,3],[3,3],[3,1], with an area of 2.

Note:

1. 1 <= points.length <= 50
2. 0 <= points[i][0] <= 40000
3. 0 <= points[i][1] <= 40000
4. All points are distinct.
5. Answers within 10^-5 of the actual value will be accepted as correct.

# @lc code=start
using LeetCode

function min_area_free_rect(points::Vector{Vector{Int}})
    function is_right_angle(p1, p2, p3)
        return (p1[1] - p2[1]) * (p1[1] - p3[1]) + (p1[2] - p2[2]) * (p1[2] - p3[2]) == 0
    end
    point_set = Set(points)
    res, len = Inf, length(points)
    for i in 1 : len
        for j in 1 + i : len
            for k in 1 + j : len
                flg = false
                if is_right_angle(points[i], points[j], points[k])
                    flg = true
                elseif is_right_angle(points[j], points[k], points[i])
                    flg = true
                    i, j = j, i
                elseif is_right_angle(points[k], points[i], points[j])
                    i, k = k, i
                    flg = true
                end
                if flg && (points[j] + points[k] - points[i]) in point_set
                    area = sqrt(sum((points[i] - points[j]) .^ 2) * sum((points[i] - points[k]) .^ 2))
                    (area > 0) && (res = min(res, area))
                end
            end
        end
    end
    (res == Inf) ? 0.0 : res
end
# @lc code=end

min_area_free_rect (generic function with 1 method)

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