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Grokking the Coding Interview Patterns in C++

Solution: Check If It Is a Straight Line

Understand how to verify if multiple points in a 2D plane lie on a single straight line by calculating slopes between points and using cross multiplication to handle special cases like vertical lines. This lesson helps you develop geometric problem-solving skills applicable to coding interviews, focusing on math patterns and efficient implementation.

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Statement

You are given an array, coordinates, where each element in coordinates[i] =[x,y]= [x, y] represents the coordinates of a point on a 2D\text{2D} plane. Determine whether all the points in the array lie on a single straight line in the XY plane.

Constraints:

  • 2≤2 \leq coordinates.length ≤1000\leq 1000

  • coordinates[i].length ==2== 2

  • −104≤-10^4 \leq coordinates[i][0], coordinates[i][1] ≤104\leq 10^4

  • coordinates do not contain any duplicate points.

Solution

We need to determine whether a given array of coordinates in a 2D\text{2D} plane lies in a single straight line. This problem is approached using the Math and Geometry pattern, using the slope of a straight line.

Key intuition:

The slope represents the change in y-coordinates\text{y-coordinates} relative to the change in x-coordinates\text{x-coordinates} for any two points on the line. So, the slope between two points, (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2), is defined as:

                                                 slope=ΔYΔX=y2−y1x2−x1\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\text{slope}=\dfrac{ΔY}{ΔX}=\dfrac{y_2−y_1}{x_2−x_1} ...