# Largest Triangle Area Problem

## Description

LeetCode Problem 812.

Given an array of points on the X-Y plane points where points[i] = [x_i, y_i], return the area of the largest triangle that can be formed by any three different points. Answers within 10^-5 of the actual answer will be accepted.

Example 1:

``````1
2
3
Input: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
Output: 2.00000
Explanation: The five points are shown in the above figure. The red triangle is the largest.
``````

Example 2:

``````1
2
Input: points = [[1,0],[0,0],[0,1]]
Output: 0.50000
``````

Constraints:

• 3 <= points.length <= 50
• -50 <= x_i, y_i <= 50
• All the given points are unique.

## Sample C++ Code

``````1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
class Solution {
public:
double largestTriangleArea(vector<vector<int>>& points) {
double ans = 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 ){
double a = sqrt(pow(points[i] - points[j], 2) + pow(points[i] - points[j], 2)),
b = sqrt(pow(points[j] - points[k], 2) + pow(points[j] - points[k], 2)),
c = sqrt(pow(points[k] - points[i], 2) + pow(points[k] - points[i], 2)),
s = (a + b + c)/2;
ans = max(ans, sqrt(s * (s-a) * (s-b) * (s-c)));
}
}
}
return ans;
}
};
``````