To check if points form a boomerang, verify that the points are distinct and do not lie on a straight line. This can be achieved by calculating the area of the triangle formed by the points. If the area is non-zero, the points form a boomerang.
Problem Statement
You are given an array of three points, where each point is represented as [xi, yi] in a 2D plane. Your task is to determine if these three points form a valid boomerang.
A boomerang is defined as a set of three distinct points that do not lie on a straight line. The points must form a triangle with a non-zero area, which ensures they are not collinear.
Examples
Example 1
Input: points = [[1,1],[2,3],[3,2]]
Output: true
Example details omitted.
Example 2
Input: points = [[1,1],[2,2],[3,3]]
Output: false
Example details omitted.
Constraints
- points.length == 3
- points[i].length == 2
- 0 <= xi, yi <= 100
Solution Approach
Check Collinearity Using Area
To check if three points form a valid boomerang, calculate the area of the triangle formed by the points using the determinant method. If the area is non-zero, the points are not collinear and form a boomerang.
Verify Distinct Points
Ensure that all three points are distinct. If any two points are identical, they cannot form a boomerang.
Efficient Calculation
Given the fixed size of the input (three points), the solution will have constant time complexity for both space and time, making the approach efficient and easy to implement.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Since the problem always involves exactly three points, both the time and space complexities are constant, O(1).
What Interviewers Usually Probe
- Look for efficient use of mathematical properties to solve the problem.
- Expect the candidate to explain collinearity and how the area of a triangle can help determine this.
- Candidates should confirm that all points are distinct before proceeding with further checks.
Common Pitfalls or Variants
Common pitfalls
- Confusing collinearity check with simple distance calculations, which do not guarantee non-collinearity.
- Overlooking the distinctness of the points, leading to incorrect conclusions about the boomerang formation.
- Not understanding how the area formula directly applies to this problem for determining valid boomerangs.
Follow-up variants
- Handling higher dimensions if the problem was extended to more than 2D.
- Checking for a set of points beyond three, such as determining if any subset forms a boomerang.
- Adapting the solution for larger inputs or multiple sets of points.
How GhostInterview Helps
- Provides a structured approach to solving geometry problems with simple yet effective mathematical checks.
- Helps break down complex geometric problems into manageable steps, like checking collinearity via area calculation.
- Guides candidates in avoiding common pitfalls, such as misunderstanding the importance of distinct points.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What defines a boomerang in the context of this problem?
A boomerang consists of three distinct points that do not lie on a straight line, i.e., they form a triangle with a non-zero area.
Why do we calculate the area to check for collinearity?
The area of the triangle formed by the points will be zero if they are collinear. A non-zero area confirms they are not in a straight line.
What happens if two points are the same?
If any two points are identical, the points do not form a valid boomerang, as the set must consist of distinct points.
How is this problem related to geometry?
The problem involves basic geometry concepts, particularly the area of a triangle and collinearity of points in a 2D plane.
How does GhostInterview assist with problems like this?
GhostInterview helps by offering a detailed solution approach, focusing on essential steps like checking for collinearity and distinctness, which are key to solving geometric problems efficiently.
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