Problem Description
Given an array of points on the X-Y plane where points[i] = [xi, yi], return the area of the largest triangle that can be formed by any three different points. Answers within 10^-5 of the actual answer will be accepted.
Key Insights
- The area of a triangle formed by three points can be calculated using the determinant method.
- The formula for the area of a triangle given by points (x1, y1), (x2, y2), and (x3, y3) is: Area = 0.5 * | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |
- We need to iterate through all combinations of three points to find the maximum area.
- The maximum number of combinations is manageable given the constraints (3 <= points.length <= 50).
Space and Time Complexity
Time Complexity: O(n^3) - We need to check all combinations of three points. Space Complexity: O(1) - We use a constant amount of space for calculations.
Solution
To solve this problem, we will use a brute-force approach by iterating over all possible combinations of three points from the given list. For each combination, we will calculate the area of the triangle they form using the determinant formula mentioned above. We will keep track of the maximum area found during these iterations.