Disjoint difference

We can also define a version of rectangle difference which returns a set of disjoint rectangles. The idea is this. Let the two rectangles be $R=(I_1,$dots,$I_n)$ and $S=(J_1,$dots,$J_n),$ where $I_1,$dots,$I_n$ and $J_1,$dots,$J_n$ are the intervals forming the two rectangles $R$ and $S.$

To compute the difference $\frac{R}{\frac{?}{?}}S$ as a list of disjoint rectangles, we reason by induction $($thus writing a recursive solution$).$ Consider the coordinate $k=1.$

Let $I_1-J_1=A,$ so that $A$ is a list consisting of $0,1,$ or $2$ intervals. Cleady, for any interval LinA, we have that $(L,I_2,$dots,$I_n)$ is part of the result.

As for the remaining part of the result, let $I_1{J}_1=H.H$ can be empty, or consist of one interval.

The rest of the result is given by

$\frac{H,I_2,\text{d}\text{o}\text{t}\text{s}\text{,}{I}_n}{\frac{?}{?}}(J_1,J_2,$dots,$J_n)=H[\frac{I_2,\text{d}\text{o}\text{t}\text{s}\text{,}{I}_n}{\frac{?}{?}}(J_2,$dots,$J_n)]$

It is easier thus to define a generator, which yields all the rectangles in the difference.

Computation of disjoint difference

metitle Computation of disjoint difference

def disjoint$\_$minus$(r,s$ :

$"$un$"$R and $S$ are equal$-$length lists of intervals, representing

two rectangles $R$ and $S.$ The function returns, or better, yields,

all the rectangles in the disjoint difference of $R$ and $S."$w$."$

AIHI YOUR SOLUTION MERE