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
}