Rectangle Difference

There are two ways of defining rectangle difference:

Largest$-$cover difference, which returns the difference represented by rectangles that are as large as possible, and therefore may be overlapping.

Disjoint difference, which retums rectangles that are disjoint.

Largest$-$Cover Difference

Given two rectangles $R=(I_1,I_2,$dots,$I_n)$ and $T=(J_1,J_2,$dots,$J_n),$ their difference $R-T$ is the region $=$tilde$\frac{R}{\frac{?}{?}}$tilde$(T).$ We make the following observation: for a point to be in $R$ and not in $T,$ all it takes is that in one of the dimensions $k,$ it is in $I_k,$ but not in $J_k.$

Based on this idea, we construct a representation of $\frac{?}{\text{b}\text{a}\text{r}}\frac{R}{\frac{?}{?}}\frac{?}{\text{b}\text{a}\text{r}}(T)$ as follows. We initialize the list of result rectangles to be empty. Then, we iterate over all dimensions $k=1,2,$dots,$n,$ and for each dimension $k,$ we construct rectangles with intervals $I_1,$dots,$I_{k-1},I_k-J_k,I_{k+1},$dots,$I_n.$ where $I_k-J_k$ represents interval difference. There can be $0,1,$ or $2$ intervals in $I_k-J_k,$ and correspondinglys

$I_1,$dots,$I_{k-1},I_k-J_k,I_{k+1}$dots,$I_n$ will consist of $0,1,$ or $2$ rectangles; we add all such rectangles to the result list. Let's translate this idea into code.

Implementation of largest$-$cover difference

Fictitle Implementation of largest$-$cover difference

def rectangle$\_$difference$(r,t$ :

$"\text{'}".$"Computes the rectangle difference $r-t,$ and outputs the result

as a list of rectangles." $"$u$."$

assert ten$(r)=$len$(t),$ "Rectangles have different dimensions"

YOUR SOLUTION HERAC