Gate Fever, flash12
Yes, for a single process ( X=1 ) Circular wait condition is not hold so deadlock can not occur. But , this question have other conditions , like : These are three key conditions : Minimum number of thread and lock All locks in the program are Non-reentrant . ( key Point ) " If a thread is unable to acquire a lock, it blocks until the lock becomes available."
Means thread gets block if another lock is unavailable . Re entrant means it can again acquire a lock but question says about Non re entrant , non re-entrant process cant own same lock multiple times, so if process tries to acquire already owned lock, will get blocked , and deadlock will happen.
Also, Question asked for minimum value of X and Y require, so if a single thread with a single lock can not acquire any other locks other than the lock which it already acquire , this situation leads to deadlock ( as in the question it says If a thread is unable to acquire a lock, it blocks until the lock becomes available. )
so for X=1 ( a single thread ) and Y=1 ( a single lock ) deadlock is possible when we consider given situations in question.
The main point is : With 1 thread and 1 lock , a thread after acquire a lock enter into it's critical section then come out of CS, again looking for another lock but due to a single lock available, that thread acquire that same lock again and again and get blocked .
So the possibility of Deadlock is there with single thread .
Hope you get it now !!