The algorithm which is prone to deadlock is —

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Correct answer: A — Concept: Among distributed mutual-exclusion algorithms, deadlock can arise when processes end up waiting on each other's permissions in a cycle. A design that forces a single global (typically timestamp-based) order on all pending requests avoids such a cycle — every request is eventually served in that order. A permission/voting-based design in which each process instead waits on only an overlapping subset of the others, without imposing that kind of global order, can still allow a cycle unless it adds an explicit priority or timestamp rule to break ties. 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 a conflicting request unless its own pending request carries an earlier timestamp, in which case it defers the reply until its own request is served. 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 a conflicting request unless its own pending request carries an earlier timestamp, in which case it defers the reply until its own request is served.	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.