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Valid Boomerang

Difficulty: Easy

Problem Description

Given an array points where points[i] = [xi, yi] 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.

Key Insights

  • The three points must be distinct from each other.
  • To determine if the points are not collinear (i.e., not in a straight line), we can use the concept of the area of the triangle formed by the points. If the area is non-zero, the points are not collinear.
  • The area can be calculated using the determinant formula for the vertices of a triangle.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To solve the problem, we will:

  1. Check for distinct points to ensure no two points are the same.
  2. Compute the area of the triangle formed by the three points using the determinant method. The formula for the area is: Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| If the area is zero, the points are collinear.

We will use an array to store the points and simple arithmetic to determine the area.

Code Solutions

def isBoomerang(points):
    # Check for distinct points
    if len(set(map(tuple, points))) < 3:
        return False
    
    # Unpack points for easier access
    (x1, y1), (x2, y2), (x3, y3) = points
    
    # Calculate area using the determinant formula
    area = x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)
    
    # Check if area is non-zero (not collinear)
    return area != 0
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