The algorithm which is prone to deadlock is —

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Accepted Answer

Correct answer: A — Concept: A distributed mutual-exclusion algorithm is deadlock-free only if it forces one global order on all pending requests, so no set of processes can end up circularly waiting on each other's permissions. Timestamp-based total-ordering schemes guarantee this; permission/voting-based schemes in which each process waits on only an overlapping subset of the others do not guarantee it unless extra ordering or priority rules are added. Algorithm How permission is granted Deadlock-free? Lamport's algorithm Every request is placed on one shared logical-timestamp-ordered queue; a process enters its critical section only when its own request is at the head everywhere. Yes — a single total order rules out any circular wait. Ricart–Agrawala's algorithm A process replies immediately to any request whose timestamp is later than its own pending request, and defers only requests it must logically precede. Yes — the same timestamp ordering rules out any cycle. Maekawa's algorithm A process needs permission from only a subset of processes (its voting set); voting sets overlap pairwise but are not globally ordered. No — in its basic form, two processes can each hold part of the other's needed votes and wait on each other, forming a cycle. Cross-check: Lamport's and Ricart–Agrawala's algorithms are both provably deadlock-free because of their total ordering, and among the given choices only one other named algorithm remains besides “none of these” — so the deadlock-prone one must be that remaining algorithm, which also rules out “none of these.” Therefore, the algorithm prone to deadlock is Maekawa's algorithm.

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A. Maekawa's algorithm

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B. Ricart–Agrawala's algorithm

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C. Lamport’s algorithm

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D. None of these

Algorithm	How permission is granted	Deadlock-free?
Lamport's algorithm	Every request is placed on one shared logical-timestamp-ordered queue; a process enters its critical section only when its own request is at the head everywhere.	Yes — a single total order rules out any circular wait.
Ricart–Agrawala's algorithm	A process replies immediately to any request whose timestamp is later than its own pending request, and defers only requests it must logically precede.	Yes — the same timestamp ordering rules out any cycle.
Maekawa's algorithm	A process needs permission from only a subset of processes (its voting set); voting sets overlap pairwise but are not globally ordered.	No — in its basic form, two processes can each hold part of the other's needed votes and wait on each other, forming a cycle.