How to Solve Find Maximum Area of a Triangle Problem
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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...
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Understanding the Find Maximum Area of a Triangle Problem
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Problem Statement
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.
Find Maximum Area of a Triangle
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Examples
coords = [[1,1],[1,2],[3,2],[3,3]]
2
The triangle shown in the image has a base 1 and height 2. Hence its area is 1/2 * base * height = 1.
coords = [[1,1],[2,2],[3,3]]
-1
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
1 <= n == coords.length <= 105
1 <= coords[i][0], coords[i][1] <= 106
All coords[i] are unique.
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