812. Largest Triangle Area

Description

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.

image

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.

Solution

Iteration + Math, O(n ^ 3), S(1)

计算三角形面积是有公式的！（感觉是小学生数学题...惭愧啊）

image.png image.png

class Solution {
    public double largestTriangleArea(int[][] points) {
        double maxArea = 0;
        if (points == null || points.length < 3 || points[0].length < 2) {
            return maxArea;
        }
        
        int n = points.length;
        
        for (int i = 0; i < n - 2; ++i) {
            for (int j = i + 1; j < n - 1; ++j) {
                for (int k = j + 1; k < n; ++k) {
                    double area = area(points[i], points[j], points[k]);
                    maxArea = Math.max(area, maxArea);
                }
            }
        }
        
        return maxArea;
    }
    
    public double area(int[] P, int[] Q, int[] R) {
        return 0.5 * Math.abs(P[0]*Q[1] + Q[0]*R[1] + R[0]*P[1]
                             -P[1]*Q[0] - Q[1]*R[0] - R[1]*P[0]);
    }
}