Home Exercise : courses $(1,2,$dots,$8)$ in the least possible number of time periods. Table $10\mathrm{.}22$ assigns $"x"$ to conflicting courses $($those that cannot be scheduled in the same time period$).$

a$)$ Express the problem as a map$-$coloring network as$($Figure $10-7).$

b$)$ Determine a starting solution using the greedy algorithm.

c$)$ Apply three SA iterations to estimate the minimum number of periods.

$\backslash$table$[[,1,2,3,4,5,6,7,8],[1,,$x$,$x$,$x$,,$x$,,],[2,$x$,,,,$x$,,$x$,$x$],[3,$x$,,,$x$,,$x$,,],[4,$x$,,$x$,,$x$,,$x$,],[5,,$x$,,$x$,,$x$,,$x$],[6,$x$,,$x$,,$x$,,$x$,$x$],[7,,$x$,,$x$,,$x$,,$x$],[8,,$x$,,,$x$,$x$,$x$,]]$

Table $10-22$ Conflicts in Course Schedules for Problem $10-22$