812. Largest Triangle Area

Problem

You have a list of points in the plane. Return the area of the largest triangle that can be formed by any 3 of the points.

Example:
Input: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
Output: 2
Explanation: 
The five points are show in the figure below. The red triangle is the largest.

Notes:

• 3 <= points.length <= 50.
• No points will be duplicated.
• -50 <= points[i][j] <= 50.
• Answers within 10^-6 of the true value will be accepted as correct.

Problem Summary

Given a set containing multiple points, choose three points from it to form a triangle, and return the area of the largest triangle that can be formed.

Solution Approach

• Given a set of point coordinates, find the set of points that can form the triangle with the largest area, and output this maximum area.
• Math problem. According to the mathematical definition, calculate the areas of the triangles formed by the points that can form triangles, and finally output the maximum area.

Code

package leetcode

func largestTriangleArea(points [][]int) float64 {
	maxArea, n := 0.0, len(points)
	for i := 0; i < n; i++ {
		for j := i + 1; j < n; j++ {
			for k := j + 1; k < n; k++ {
				maxArea = max(maxArea, area(points[i], points[j], points[k]))
			}
		}
	}
	return maxArea
}

func area(p1, p2, p3 []int) float64 {
	return abs(p1[0]*p2[1]+p2[0]*p3[1]+p3[0]*p1[1]-p1[0]*p3[1]-p2[0]*p1[1]-p3[0]*p2[1]) / 2
}

func abs(num int) float64 {
	if num < 0 {
		num = -num
	}
	return float64(num)
}

func max(a, b float64) float64 {
	if a > b {
		return a
	}
	return b
}