Solution to Question 8.9
========================

To show that the system is dead-lock free, we show that a circular
wait is not possible.

We argue by contradiction.  Suppose that we have a circular wait.

Let Alloc[i]=number of resources allocated to Pi.  

Then:

Alloc[0]+Alloc[1]+...+Alloc[n-1]=m  (*)

since otherwise there would be free resources and hence no dead-lock
yet.   We assume that Alloc[i]>0 for all i, since if for some i
Alloc[i]=0, then we can ignore that process since it is not part of
the circular wait anyways.

Let Req[i]=number of resources requested by Pi.  

It must be the case that Req[i]>0 for all i, since if some allocated
process was making no request, once it was done with its resources, it
would let them free, and thay could be re-assigned.

By (b) we know that:

(Alloc[0]+Req[0])+(Alloc[1]+Req[1])+...+(Alloc[n]+Req[n])<m+n (**)

so by (*) we know from (**) that:

Req[0]+Req[1]+...+Req[n]<n

But if each Req[i]>0, this is a contradiction.  Note that condition
(a) is there to ensure that no process requests more than m resources
(so there is no single process dead-lock).