Trouble implementing a deadlock detection algorithm

Question

I've got it all sorted out except for one specific confusion regarding:

if Allocation_i != 0, then Finish[i] := false; otherwise, Finish[i] := true.

Does this mean the sum of that particular row is zero or what?

Algorithm:

Data Structures:

• Available: A vector of length m indicates the number of available resources of each type.
• Allocation: An n x m matrix defines the number of resources of each type currently allocated to each process.
• Request: An n x m matrix indicates the current request of each process. If Request[i][j] = k, then process P_i is requesting k more instances of resource type R_j.
• Work: Vector of length m.
• Finish: Vector of length n.

Algorithm:

1. Initialize Work := Available.
   • For i = 1, 2, …, n, if Allocation_i != 0, then Finish[i] := false; otherwise, Finish[i] := true.
2. Find an index i such that both:
   • (a) Finish[i] = false
   • (b) Request_i <= Work
   • if no such i exists, go to step 4.
3. Work := Work + Allocation_i
   • Finish[i] := true
   • go to step 2
4. If Finish[i] = false, for some i, 1 <= i...n, then the system is in a deadlock state. Moreover, if Finish[i] = false, then process P_i is deadlocked. The less-than-or-equal relation (<=) between two vectors is defined as follows: let X and Y be vectors of length n. We say that X <= Y if and only if x[i] <= y[i] for all i = 1, 2, ..., n. The rows of the Allocation and Request matrices are treated as vectors and are referred to as Allocation_i and Request_i in the algorithm.

Answer 1

Since Allocation_i is a vector, "Allocation_i != 0" means to test Allocation_i against the zero vector (the vector consisting of all zeros).

In other words, "Allocation_i == 0" iff every entry in the vector is 0.