812. Largest Triangle Area

Posted 2021-01-10 bernieloveslife

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.

Solution1:

class Solution:
    def largestTriangleArea(self, points):
        """
        :type points: List[List[int]]
        :rtype: float
        """
        def solve(a,b,c):
            return 0.5*abs(a[0]*b[1] + b[0]*c[1] + c[0]*a[1] - a[0]*c[1] - b[0]*a[1] - c[0]*b[1])
        l = len(points)
        res = 0
        for a in range(l):
            for b in range(a+1,l):
                for c in range(b+1,l):
                    res = max(solve(points[a],points[b],points[c]),res)
        return res

Solution2:(用itertools.combinations可以简化代码，它返回list中指定数量的所有组合)

class Solution(object):
    def largestTriangleArea(self, points):
        """
        :type points: List[List[int]]
        :rtype: float
        """
        return max(0.5*abs((y1-x1)*(z2-x2)-(z1-x1)*(y2-x2)) for (x1,x2),(y1,y2),(z1,z2) in itertools.combinations(points,3))