How do you solve Valid Boomerang on LeetCode?

Valid Boomerang (LeetCode #1037) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: Three points must be distinct to form a boomerang.

What is the time complexity of Valid Boomerang?

The optimal solution for Valid Boomerang runs in O(1) time and uses O(1) space. The complexity remains constant since we are only working with three points.

What is the brute force solution for Valid Boomerang?

The brute force approach for Valid Boomerang is Brute Force, with O(1) time complexity and O(1) space complexity. To determine if three points form a boomerang, we can check if they are distinct and if they do not lie on a straight line. This is done by calculating the area of the triangle they form. If the area is non-zero, they are not collinear. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Valid Boomerang?

Valid Boomerang uses the following concepts: Array, Math, Geometry. The recommended patterns to study are: Geometry, Set operations.

What are the interview tips for Valid Boomerang?

Always clarify the definition of terms like 'distinct' and 'collinear' before starting. Think about edge cases, such as points being the same or lying on a straight line. Explain your thought process clearly while coding; it helps the interviewer understand your logic.

What are common mistakes when solving Valid Boomerang?

Not checking for distinct points before calculating the area. Confusing the area calculation, leading to incorrect results.

#1037

Valid Boomerang

Easy

ArrayMathGeometryGeometrySet operations

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(1)	O(1)
Space	O(1)	O(1)

💡

Intuition

Time O(1)Space O(1)

The optimal solution leverages the same area calculation but ensures that we check for distinct points in a single step, making the solution cleaner and more efficient.

⚙️

Algorithm

3 steps

1Step 1: Use a set to check if all three points are distinct.
2Step 2: Calculate the area using the same formula as before.
3Step 3: Return true if the area is greater than 0; otherwise, return false.

solution.py6 lines

1def isBoomerang(points):
2    if len(set(map(tuple, points))) != 3:
3        return False
4    return (points[0][0] * (points[1][1] - points[2][1]) +
5            points[1][0] * (points[2][1] - points[0][1]) +
6            points[2][0] * (points[0][1] - points[1][1])) != 0

ℹ

Complexity note: The complexity remains constant since we are only working with three points.

1Three points must be distinct to form a boomerang.
2The area of the triangle formed by the points must be non-zero to ensure they are not collinear.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.