830. Largest Triangle Area

• Difficulty: Easy

• Topics: Math

• Similar Questions:

  • Largest Perimeter Triangle

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.

Solutions:

class Solution {
public:
    double largestTriangleArea(vector<vector<int>>& points) {
        int n = points.size();
        double ret = 0;
        for (int i = 0; i < points.size(); ++i) {
            for (int j = i + 1; j < points.size(); ++j) {
                for (int k = j + 1; k < points.size(); ++k) {
                    ret = max(ret, area(points[i], points[j], points[k]));     
                }
            }
        }

        return ret;
    }

private:
    inline double area(vector<int>& p1, vector<int>& p2, vector<int>& p3) {
        // (p2[0] - p1[0], p2[1] - p1[1]) cross product (p3[0] - p1[0], p3[1] - p1[1])
        return 0.5 * abs(((p2[0] - p1[0]) * (p3[1] - p1[1])) - ((p2[1] - p1[1]) * (p3[0] - p1[0])));
    }

};