The deadlock detection algorithm is a method used to determine whether a system is in a deadlock state. It identifies if there exists a set of processes in the system that are deadlocked, meaning they are unable to proceed and complete their execution because each process is waiting for a resource that is held by another process in the set.

The Banker's algorithm is a resource allocation and deadlock avoidance algorithm used in operating systems. It is designed to ensure that resource allocation requests from processes will not lead to a deadlock situation.

The Banker's algorithm works based on the following assumptions:

The system has a fixed number of resources of different types.

Each process declares its maximum resource requirements in advance.

The resources are allocated to processes in a way that ensures safety and avoids deadlock.

BANKERS ALGORITHM:

AVAILABLE $=<2,1,1,2>$

Step $1$:For process P$1$

Check request is less than equal to available.

$2,0,0,2<2,1,12$ true

Process P$1$ executed

Available resources $2,1,2,2+0,0,1,0$

Available $=2,1,2,2$

Step $2$:For process P$2$

Check request is less than equal to available.

$1,3,0,1<2,1,2,2$ false

Process P$2$ not executed

Step $3$:For process P$3$

Check request is less than equal to available.

$2,1,1,0<2,1,2,2$ true

Process P$3$ executed

Available resources $2,1,2,2+0,1,1,0$

Available $=2,2,3,2$

Step $4$:For process P$4$

Check request is less than equal to available.

$4,0,3,1<2,2,3,2$ false

Process P$4$ not executed

Step $5$:For process P$2$

Check request is less than equal to available.

$1,3,0,1<2,2,3,2$ true

Process P$2$ executed.

available resources $=4,2,3,3$

Step $6$:For process P$4$

Check request is less than equal to available.

$4,0,3,1<4,2,3,2$ true

Process P$4$ executed

available resources $=5,3,3,3$

SAFE SEQUENCE IS P$1,$P$3,$P$2,$P$4$