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by Sumit Chourasia | Oct 01, 2020 | Category :coding | Tags : algorithm data-structure easy leetcode maths

Valid Boomerang - Math - Easy - LeetCode

Valid Boomerang - Math - Easy - LeetCode

A boomerang is a set of 3 points that are all distinct and not in a straight line.

Given a list of three points in the plane, return whether these points are a boomerang.

 

Example 1:

Input: [[1,1],[2,3],[3,2]]
Output: true
Example 2:

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

Note:

points.length == 3
points[i].length == 2
0 <= points[i][j] <= 100

public class Solution {
    public bool IsBoomerang(int[][] points) {
        return (points[0][0] - points[1][0]) * (points[0][1] - points[2][1]) != (points[0][0] - points[2][0]) * (points[0][1] - points[1][1]);
    }
}

Time Complexity: O(1)

Space Complexity: O(1)

Assuming three points are A, B, C.

The first idea is that, calculate the area of ABC.

The other idea is to calculate the slope of AB and AC.
K_AB = (p[0][0] - p[1][0]) / (p[0][1] - p[1][1])
K_AC = (p[0][0] - p[2][0]) / (p[0][1] - p[2][1])

We check if K_AB != K_AC, instead of calculating a fraction.