1232. Check If It Is a Straight Line

• categories: Code, Interview Question, leetcode, Easy
• source: https://leetcode.com/problems/check-if-it-is-a-straight-line
• topics: Mathematics

You are given an array coordinates, coordinates[i] = [x, y], where [x, y] represents the coordinate of a point. Check if these points make a straight line in the XY plane.

EPS = 10**-4
 
class Solution(object):
    def checkStraightLine(self, coords):
        """
        :type coordinates: List[List[int]]
        :rtype: bool
        """
        # y1 = k * x1 + b => b = y1 - k * x1
        # y2 = k * x2 + b => y2 = k * x2 + y1 - k * x1 =>
        # k * (x2 - x1) = y2 - y1 =>  
        # k = (y2 - y1) / (x2 - x1) = dy / dx = const for the line
       
        if len(coords) < 2:
            return False 
        
        dx = coords[1][0] - coords[0][0]
        dy = coords[1][1] - coords[0][1]
 
        for i in range(2, len(coords)):
           dx2 = coords[i][0] - coords[0][0]
           dy2 = coords[i][1] - coords[0][1]
           if abs(dy * dx2 - dx * dy2) > EPS:
              return False
            
        return True