LeetCode 1037. Valid Boomerang Solution in Java, C++, Python & More | Explanation + Code

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.

 

Example 1:

Input: points = [[1,1],[2,3],[3,2]]
Output: true

Example 2:

Input: points = [[1,1],[2,2],[3,3]]
Output: false

 

Constraints:

• points.length == 3
• points[i].length == 2
• 0 <= xi, yi <= 100

Solutions

Solution 1: Slope Comparison

Let the three points be (x₁, y₁), (x₂, y₂), and (x₃, y₃). The formula for calculating the slope between two points is ^{y₂ - y₁}⁄_{x2 - x1}.

To ensure that the three points are not collinear, the condition ^{y₂ - y₁}⁄_{x2 - x1} ≠ ^{y₃ - y₂}⁄_{x3 - x2} must be satisfied. By transforming the equation, we get (y₂ - y₁) · (x₃ - x₂) ≠ (y₃ - y₂) · (x₂ - x₁).

Note:

1. When the slope between two points does not exist, i.e., x₁ = x₂, the transformed equation still holds.
2. If there are precision issues with division in slope comparison, it can be converted to multiplication.

Time complexity is O(1).

PythonJavaC++GoTypeScriptRust

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

class Solution { public boolean isBoomerang(int[][] points) { int x1 = points[0][0], y1 = points[0][1]; int x2 = points[1][0], y2 = points[1][1]; int x3 = points[2][0], y3 = points[2][1]; return (y2 - y1) * (x3 - x2) != (y3 - y2) * (x2 - x1); } }(code-box)

class Solution { public: bool isBoomerang(vector<vector<int>>& points) { int x1 = points[0][0], y1 = points[0][1]; int x2 = points[1][0], y2 = points[1][1]; int x3 = points[2][0], y3 = points[2][1]; return (y2 - y1) * (x3 - x2) != (y3 - y2) * (x2 - x1); } };(code-box)

func isBoomerang(points [][]int) bool { x1, y1 := points[0][0], points[0][1] x2, y2 := points[1][0], points[1][1] x3, y3 := points[2][0], points[2][1] return (y2-y1)*(x3-x2) != (y3-y2)*(x2-x1) }(code-box)

function isBoomerang(points: number[][]): boolean { const [x1, y1] = points[0]; const [x2, y2] = points[1]; const [x3, y3] = points[2]; return (x1 - x2) * (y2 - y3) !== (x2 - x3) * (y1 - y2); }(code-box)

impl Solution { pub fn is_boomerang(points: Vec<Vec<i32>>) -> bool { let (x1, y1) = (points[0][0], points[0][1]); let (x2, y2) = (points[1][0], points[1][1]); let (x3, y3) = (points[2][0], points[2][1]); (x1 - x2) * (y2 - y3) != (x2 - x3) * (y1 - y2) } }(code-box)