LeetCode 1037: Valid Boomerang

Problem Restatement

We are given three points in the 2D plane: points[0], points[1], points[2].

A boomerang is a set of three points that are all distinct and not collinear.

Return true if the three points form a boomerang.

The official constraints state that points.length == 3 and 0 <= points[i][j] <= 100.

Input and Output

Function shape:

def isBoomerang(points: list[list[int]]) -> bool:
    ...

Examples

Example 1:

points = [[1,1],[2,3],[3,2]]

Non-collinear. Answer: True.

Example 2:

points = [[1,1],[2,2],[3,3]]

Collinear (all on the line y = x). Answer: False.

Key Insight

Three points are collinear if and only if the cross product of vectors AB and AC is zero.

AB = (B[0] - A[0], B[1] - A[1])
AC = (C[0] - A[0], C[1] - A[1])
cross = AB[0] * AC[1] - AB[1] * AC[0]

If cross == 0, points are collinear (or two are identical). If cross != 0, they form a valid boomerang.

Correctness

The cross product of two 2D vectors is zero if and only if they are parallel (or one is zero). Three points are collinear if the vectors from the first point to the other two are parallel.

Using the cross product avoids division and handles all edge cases including identical points.

Edge Cases

• Check the minimum input size allowed by the constraints.
• Verify duplicate values or tie cases if the input can contain them.
• Keep the return value aligned with the exact failure case in the statement.

Complexity

Common Pitfalls

• Do not optimize away the invariant; the code should still make it clear what condition is being maintained.
• Prefer problem-specific names over one-letter variables once the logic becomes stateful.

Implementation

class Solution:
    def isBoomerang(self, points: list[list[int]]) -> bool:
        (x1, y1), (x2, y2), (x3, y3) = points
        return (x2 - x1) * (y3 - y1) != (x3 - x1) * (y2 - y1)

Testing

def run_tests():
    s = Solution()

    assert s.isBoomerang([[1,1],[2,3],[3,2]]) == True
    assert s.isBoomerang([[1,1],[2,2],[3,3]]) == False
    assert s.isBoomerang([[0,0],[0,0],[1,1]]) == False
    assert s.isBoomerang([[0,0],[1,0],[2,1]]) == True

    print("all tests passed")

run_tests()