Solution: Minimum Number of Lines to Cover Points

Statement

Given a 2D integer array, points, where points[i] $= [x_i,y_i]$ represents a point on an XY plane, find the minimum number of straight lines required to cover all the points.

Note: Straight lines will be added to the XY plane to ensure that every point is covered by at least one line.

Constraints:

• $1\leq$ points.length $\leq10$

• points[i].length $== 2$

• $-100\leq$ $x_i, y_i$ $\leq100$

• All the points are unique.

Solution

In this solution, we are solving a computational math and geometry problem of finding the minimum number of straight lines required to cover all given points in an XY plane. Let’s break down the logic, incorporating key mathematical reasoning and geometric approaches.

Slope and y-intercept

Two parameters can uniquely identify a straight line:

• Slope: Determines the line’s steepness and direction, indicating how much the line rises or falls for a given horizontal change.

• y-intercept: Specifies where the line crosses the y-axis.

For two points, $(x_1,y_1)$ and $(x_2,y_2)$, the $\text{slope}$ $a$ is calculated as:

$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\spac$ ...