Solution: Max Points on a Line

Let’s solve the Max Points on a Line problem using the Math and Geometry pattern.

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Statement

Given an integer array of points where points[i]=[xi,yi]\text{points}[i] = [x_i, y_i] represents a point on the X–Y plane, your task is to return the maximum number of points on the same straight line.

Constraints:

  • 1≤1 \leq points.length ≤300\leq 300

  • points[i].length =2= 2

  • −104≤xi,yi≤104-10^4 \leq x_i, y_i \leq 10^4

  • All the points are unique.

Solution

The problem is finding the largest number of points on the same straight line. To solve this, we’ll use the concept of slopes. In a 2D plane, a line can be identified by its slope, which helps us group points that share the same slope with a reference point. This approach relies on the Math and Geometry pattern, making it easier to identify collinear points efficiently.

How do slopes help measure the count of maximum points on a straight line?

The slope of a line measures its steepness. Mathematically, the slope is calculated as the change in yy (vertical) divided by the change in xx (horizontal) between two points:

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