Valid Boomerang

Problem

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.

Constraints

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

Solution

The problem Valid Boomerang can be solved by first checking if all points are distinct and then checking if they are in a straight line.

Implementation

static const int fast_io = []()
{
    std::ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    return 0;
}();

class Solution
{
  public:
    bool isBoomerang(vector<vector<int>> &points)
    {
        if (points[0] == points[1] || points[1] == points[2] || points[2] == points[0])
            return false;

        double old_gradient = DBL_MIN;
        for (int i = 1; i < 3; i++)
        {
            double new_gradient = points[i][0] - points[i - 1][0];
            new_gradient = new_gradient ? (points[i][1] - points[i - 1][1]) / new_gradient : DBL_MAX;

            if (old_gradient == new_gradient)
                return false;

            old_gradient = new_gradient;
        }

        return true;
    }
};