Formatted question description: https://leetcode.ca/all/812.html

812. Largest Triangle Area (Easy)

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.

 

Companies:
Google

Related Topics:
Math

Solution 1.

// OJ: https://leetcode.com/problems/largest-triangle-area/

// Time: O(N^3)
// Space: O(1)
// Ref: https://leetcode.com/problems/largest-triangle-area/solution/
class Solution {
private:
    double area (vector<int> &a, vector<int> &b, vector<int> &c) {
        return .5 * abs(a[0]*b[1] + b[0]*c[1] + c[0]*a[1]
                       -a[1]*b[0] - b[1]*c[0] - c[1]*a[0]);
    }
public:
    double largestTriangleArea(vector<vector<int>>& points) {
        double ans = 0;
        for (int i = 0, N = points.size(); i < N; ++i) {
            for (int j = i + 1; j < N; ++j) {
                for (int k = j + 1; k < N; ++k) {
                    ans = max(ans, area(points[i], points[j], points[k]));
                }
            }
        }
        return ans;
    }
};

Java

class Solution {
    public double largestTriangleArea(int[][] points) {
        double largestArea = 0;
        int length = points.length;
        for (int i = 0; i < length; i++) {
            int[] point1 = points[i];
            for (int j = i + 1; j < length; j++) {
                int[] point2 = points[j];
                for (int k = j + 1; k < length; k++) {
                    int[] point3 = points[k];
                    if (sameLine(point1, point2, point3))
                        continue;
                    double area = getArea(point1, point2, point3);
                    largestArea = Math.max(largestArea, area);
                }
            }
        }
        return largestArea;
    }

    public boolean sameLine(int[] point1, int[] point2, int[] point3) {
        int delta1X = point2[0] - point1[0], delta1Y = point2[1] - point1[1];
        int delta2X = point3[0] - point2[0], delta2Y = point3[1] - point2[1];
        return delta1X * delta2Y == delta2X * delta1Y;
    }

    public double getArea(int[] point1, int[] point2, int[] point3) {
        double side1 = getDistance(point1, point2);
        double side2 = getDistance(point2, point3);
        double side3 = getDistance(point3, point1);
        double halfPerimeter = (side1 + side2 + side3) / 2;
        double area = Math.sqrt(halfPerimeter * (halfPerimeter - side1) * (halfPerimeter - side2) * (halfPerimeter - side3));
        return area;
    }

    public double getDistance(int[] point1, int[] point2) {
        return Math.sqrt(((double) point2[0] - (double) point1[0]) * ((double) point2[0] - (double) point1[0]) + ((double) point2[1] - (double) point1[1]) * ((double) point2[1] - (double) point1[1]));
    }
}

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