Largest Triangle Area in Python

Suppose we have a list of points on a plane. We have to find the area of the largest triangle that can be formed by any 3 of the points.

So, if the input is like [[0,0],[0,1],[1,0],[0,2],[2,0]], then the output will be 2

To solve this, we will follow these steps −

• res := 0
• N := size of points list
• for i in range 0 to N - 2, do
  • for j in range i + 1 to N - 1, do
    • for k in range i + 2 to N, do
      • (x1, y1) := points[i],
      • (x2, y2) := points[j],
      • (x3, y3) := points[k]
      • res := maximum of res, 0.5 * |x1 *(y2 - y3) + x2 *(y3 - y1) + x3 *(y1 - y2)
• return res

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution:
   def largestTriangleArea(self, points):
      res = 0
      N = len(points)
      for i in range(N - 2):
         for j in range(i + 1, N - 1):
            for k in range(i + 2, N):
               (x1, y1), (x2, y2), (x3, y3) = points[i],points[j],points[k]
               res = max(res, 0.5 * abs(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)))
      return res
ob = Solution()
print(ob.largestTriangleArea([[0,0],[0,1],[1,0],[0,2],[2,0]]))

Input

[[0,0],[0,1],[1,0],[0,2],[2,0]]

Output

2.0