Given a set of points in the plane, find the maximum possible area of any triangle formed by choosing three points.
Problem
You are given a list of points on a 2D plane. Each point is represented by its integer coordinates. Choose any three distinct points and form a triangle.
Return the largest possible area among all such triangles.
The area may be a non-integer value.
Notes
- Three points that lie on the same line form a triangle with area $0$.
- You should consider every valid triplet of points.
- The answer can be computed using the shoelace formula or an equivalent cross-product based area calculation.
Input Format
- An array of points, where each point is a pair
[x, y].
Output Format
- A single numeric value representing the maximum triangle area.
Constraints
- The number of points is at least 3.
- Coordinates are integers.
- Use a floating-point result if needed.
Hints
- A triangle's area from three coordinates can be found without computing side lengths.
- Try evaluating all triples of points and keep the maximum area found.
Input Format
- A list of 2D points
points, wherepoints[i] = [x_i, y_i]. - Each point is distinct.
Output Format
- Return the maximum area of any triangle formed by three points from the list.
Constraints
3 <= points.length- Coordinates are integers.
- The answer may be a decimal value.
Example 1
Input
points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
Output
2
Explanation
The largest triangle is formed by points [0,0], [0,2], and [2,0], which has area 2.
Example 2
Input
points = [[1,0],[0,0],[0,1]]
Output
0.5
Explanation
These three points form a right triangle with legs of length 1, so the area is 1/2.
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