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A system has $n$ resources $R_0, \dots,R_{n-1}$, and $k$ processes $P_0, \dots, P_{k-1}$. The implementation of the resource request logic of each process $P_i$ is as follows:

$\text{if} (i\%2==0) \{\\ \quad\text{if} (i<n) \text{ request } R_i;\\ \quad\text{if} (i+2 < n) \text{ request } R_{i+2}; \} \\ \text{else} \{\\ \quad\text{if} (i<n) \text{ request } R_{n-i};\\ \quad\text{if} (i+2 <n) \text{ request } R_{n-i-2}; \}$

In which of the following situations is a deadlock possible?

1. $n=40,\: k=26$
2. $n=21,\:k=12$
3. $n=20,\:k=10$
4. $n=41,\:k=19$
edited | 5.5k views
+16
Deadlock iff Even and odd process request overlaps at some point. It will happen only if n is odd.

So we have only two options left (B) and (D). If you observe for even no. process resource allocation is happening from forward direction but for odd no. resource it is happening from back word direction. But in option (D) we have more then $2*k$ resources so overlap is not possible. Hence overlap will happen only in (B).

From the resource allocation logic, it's clear that even numbered processes are taking even numbered resources and all even numbered processes share no more than 1 resource. Now, if we make sure that all odd numbered processes take odd numbered resources without a cycle, then deadlock cannot occur. The "else" case of the resource allocation logic, is trying to do that. But, if n is odd, $R_{n-i}$ and $R_{n-i-2}$ will be even and there is possibility of deadlock, when two processes requests the same $R_i$ and $R_j$. So, only $B$ and $D$ are the possible answers.

Now, in $D$, we can see that $P_0$ requests $R_0$ and $R_2$, $P_2$ requests $R_2$ and $R_4$, so on until, $P_{18}$ requests $R_{18}$ and $R_{20}$. At the same time $P_1$ requests $R_{40}$ and $R_{38}$,  $P_3$ requests $R_{38}$ and $R_{36}$, so on until, $P_{17}$ requests $R_{24}$ and $R_{22}$. i.e.; there are no two processes requesting the same two resources and hence there can't be a cycle of dependencies which means, no deadlock is possible.

But for $B$, $P_8$  requests $R_8$ and $R_{10}$ and $P_{11}$ also requests $R_{10}$ and $R_8$. Hence, a deadlock is possible. (Suppose $P_8$ comes first and occupies $R_8$. Then $P_{11}$ comes and occupies $R_{10}$. Now, if $P_8$ requests $R_{10}$ and $P_{11}$ requests $R_8$, there will be deadlock)
answered by Veteran (359k points)
edited by
+5

just a small correction Sir there will be no P19 in case (D) as k=19 so P will be from 0 to 18

+2
Thanks for the correction :)
+2
+1
very clear explanation arjun sir
0
at option, B...how to reach to P8 and P11...just trial and error of any other method?
+1
check answer given by ishaan sood
+1
Thqqq soo much ..crystal clear explanation...
0
great explanation

answered by (379 points)
Option B is answer

No. of resources, n = 21
No. of processes, k = 12

Processes {P0, P1....P11}  make the following Resource requests:
{R0, R20, R2, R18, R4, R16, R6, R14, R8, R12, R10, R10}

For example P0 will request R0 (0%2 is = 0 and 0< n=21).

Similarly, P10 will request R10.

P11 will request R10 as n - i = 21 - 11 = 10.

As different processes are requesting the same resource, deadlock
may occur. 
answered by Junior (831 points)
+1 vote

(k-3) processes will take 2 resources and other 3 processes will take 1 resource each.

Total n resources. Deadlock will arise when : (((k-3) * 2) + (3*1)) = n

If k=12, n will be 21.

answered by (21 points)