3588 - Find Maximum Area of a Triangle.

Medium

You are given a 2D array coords of size n x 2, representing the coordinates of n points in an infinite Cartesian plane.

Find twice the maximum area of a triangle with its corners at any three elements from coords, such that at least one side of this triangle is parallel to the x-axis or y-axis. Formally, if the maximum area of such a triangle is A, return 2 * A.

If no such triangle exists, return -1.

Note that a triangle cannot have zero area.

Example 1:

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

Output: 2

Explanation:

The triangle shown in the image has a base 1 and height 2. Hence its area is 1/2 * base * height = 1.

Example 2:

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

Output: \-1

Explanation:

The only possible triangle has corners (1, 1), (2, 2), and (3, 3). None of its sides are parallel to the x-axis or the y-axis.

Constraints:

• <code>1 <= n == coords.length <= 10⁵</code>

• <code>1 <= coords0, coords1<= 10⁶</code>

• All coords[i] are unique.