Find Maximum Area of a Triangle
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
2The triangle has a base of 1 and height of 2, so its area is 1 and twice the area is 2.
Example 2
Input
coords = [[1,1],[2,2],[3,3]]Output
-1The only possible triangle uses all three points, and none of its sides are parallel to the x-axis or the y-axis.
Constraints
- 1 <= n == coords.length <= 10^5
- 1 <= coords[i][0], coords[i][1] <= 10^6
- All coords[i] are unique.