Valid Boomerang

Valid Boomerang

What is this problem about?

The "Valid Boomerang" interview question is a geometric and mathematical problem that asks whether three given points in a 2D plane form a "boomerang." A boomerang is defined as a set of three points that are all distinct and do not lie on a single straight line. Essentially, you are tasked with verifying if three points form a valid triangle with a non-zero area.

Why is this asked in interviews?

Google and other tech giants often include the "Valid Boomerang" coding problem in their early-round interviews to check a candidate's grasp of basic coordinate geometry and edge-case handling. It tests whether you can translate a visual concept (collinearity) into a robust mathematical formula while avoiding common pitfalls like division by zero when calculating slopes.

Algorithmic pattern used

The core algorithmic pattern used is the "Math and Geometry interview pattern." Specifically, it uses the concept of the slope of a line or the cross-product of vectors. Since the slope formula (y2 - y1) / (x2 - x1) can lead to precision issues or division by zero, the preferred method is to use the cross-multiplication of the differences: (y2 - y1) * (x3 - x2) != (y3 - y2) * (x2 - x1).

Example explanation

Consider three points: A(1, 1), B(2, 3), and C(3, 2).

1. Check if they are distinct: Yes, all points are different.
2. Calculate the cross-multiplied slopes:
   • (y2 - y1) = 3 - 1 = 2
   • (x2 - x1) = 2 - 1 = 1
   • (y3 - y2) = 2 - 3 = -1
   • (x3 - x2) = 3 - 2 = 1
3. Compare: 2 * 1 vs 1 * -1. Since 2 != -1, the points are not collinear.
4. Result: This is a valid boomerang.

Common mistakes candidates make

One of the most common mistakes is attempting to use the float type to compare slopes directly, which can fail due to floating-point inaccuracies. Another error is forgetting to check if all three points are distinct; if two points are identical, they cannot form a boomerang regardless of the third point's position.

Interview preparation tip

When dealing with geometry problems like the "Valid Boomerang" coding problem, always try to convert division-based formulas into multiplication-based ones. This avoids "divide by zero" errors and keeps the logic within the realm of integers, making your solution more stable and professional.