The left figure illustrates a direct network topology for a $9-$computer architecture. Using message$-$driven structure for given architecture

a$.$ Develop a barrier algorithm $($if your number is unique$)$

b$.$ Show that the barrier algorithm you have developed works in the same topology as $4$x$4($if your number is unique$)$

c$.$ Develop an All$-$reduce algorithm $($if your number is even$)$

d$.$ Show that the all$-$reduce algorithm you have developed works in the same topology as $4$x$4($if your number is even$)$