$[20$ points$]$ In the Classroom Assignment $($CA$)$ problem, you are given a collection of n class rosters R and a set of k time slots, and you need to determine whether it is possible to assign the n classes to the k time slots so that no student takes two classes at the same time. $($Each class roster lists all of the students taking that class.$)$ For example, consider the problem where we have $3$ time slots available $($say$,12$:$30,2$:$00,$ and $3$:$30)$ and the $5$ class rosters are $\{$s$1,$ s$2\},\{$s$2,$ s$3\},\{$s$3,$ s$4\},\{$s$4,$ s$5\},$ and $\{$s$1,$ s$3,$ s$5\}.$ We could assign classes $1$ and $3$ to $12$:$30,$ classes $2$ and $4$ to $2$:$00,$ and class $5$ to $3$:$30,$ and no student would take more than one class at a time, but this problem would be impossible if we only had $2$ time slots available. Give pseudocode for a greedy heuristic for CA