1037. Valid Boomerang

Description

Given an array points where points[i] = [x_i, y_i] represents a point on the X-Y plane, return true if these points are a boomerang.

A boomerang is a set of three points that are all distinct and not in a straight line.

Example 1:

• Input: points = [[1,1],[2,3],[3,2]]
• Output: true

Example 2:

• Input: points = [[1,1],[2,2],[3,3]]
• Output: false

Constraints:

• points.length == 3
• points[i].length == 2
• 0 <= x_i, y_i <= 100

💡 Hint 1:
3 points form a boomerang if and only if the triangle formed from them has non-zero area.

Submitted Code

class Solution:
    def isBoomerang(self, points: List[List[int]]) -> bool:
        x1, y1 = points[0]
        x2, y2 = points[1]
        x3, y3 = points[2]
        area = abs((x1*y2 + x2*y3 + x3*y1) - (x2*y1 + x3*y2 + x1*y3)) * 0.5
        return area != 0

Runtime: 0 ms | Beats 100.00%
Memory: 17.64 MB | Beats 82.52%

세 점으로 만들어진 삼각형의 넓이를 신발끈 공식을 이용해서 구했다. 넓이가 0이면 삼각형이 될 수 없는 조건이다.

Other Solutions

1st

class Solution:
    def isBoomerang(self, points: List[List[int]]) -> bool:
        return (points[1][1]-points[0][1])*(points[2][0]-points[1][0]) != (points[2][1]-points[1][1])*(points[1][0]-points[0][0])

time complexity: 𝑂(1)
space complexity: 𝑂(1)

세 점이 모두 일직선상에 있는지만 확인하면 되기 때문에 두 기울기를 비교하는 방법을 사용해도 된다.

      slope1                slope2
(y2-y1) / (x2-x1)  =  (y3-y2) / (x3-x2)
                   ↓
(y2−y1) * (x3−x2)  =  (y3−y2) * (x2−x1)