3380 - Maximum Area Rectangle With Point Constraints I.

Medium

You are given an array points where <code>pointsi = x_i, y_i</code> represents the coordinates of a point on an infinite plane.

Your task is to find the maximum area of a rectangle that:

• Can be formed using four of these points as its corners.

• Does not contain any other point inside or on its border.

• Has its edges parallel to the axes.

Return the maximum area that you can obtain or -1 if no such rectangle is possible.

Example 1:

Input: points = [1,1,1,3,3,1,3,3]

Output: 4

Explanation:

We can make a rectangle with these 4 points as corners and there is no other point that lies inside or on the border. Hence, the maximum possible area would be 4.

Example 2:

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

Output: \-1

Explanation:

There is only one rectangle possible is with points [1,1], [1,3], [3,1] and [3,3] but [2,2] will always lie inside it. Hence, returning -1.

Example 3:

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

Output: 2

Explanation:

The maximum area rectangle is formed by the points [1,3], [1,2], [3,2], [3,3], which has an area of 2. Additionally, the points [1,1], [1,2], [3,1], [3,2] also form a valid rectangle with the same area.

Constraints:

• 1 <= points.length <= 10

• points[i].length == 2

• <code>0 <= x_i, y_i<= 100</code>

• All the given points are unique.