3382 - Maximum Area Rectangle With Point Constraints II.

Hard

There are n points on an infinite plane. You are given two integer arrays xCoord and yCoord where (xCoord[i], yCoord[i]) represents the coordinates of the <code>i^th</code> point.

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: xCoord = 1,1,3,3, yCoord = 1,3,1,3

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: xCoord = 1,1,3,3,2, yCoord = 1,3,1,3,2

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: xCoord = 1,1,3,3,1,3, yCoord = 1,3,1,3,2,2

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:

• <code>1 <= xCoord.length == yCoord.length <= 2 * 10⁵</code>

• <code>0 <= xCoordi, yCoordi<= 8 * 10⁷</code>

• All the given points are unique.