$5.(14\backslash \%)$ Zookeeper.

The following pseudo$-$code lists the implementation of the distributed read$/$write lock using Zookeeper $($only the lock function is shown$).$

Write lock:

$1.$ n $=$ create$(1+"/$write$-",$ EPHEMERAL$\_$SEQUENTIAL$)$

$2.\backslash (\backslash$mathrm$\{$C$\}=\backslash$operatorname$\{$getChildren$\}(1\backslash ),$ false $\backslash ()\backslash )$

$3.$ if $\backslash ($ n $\backslash )$ is lowest znode in C $,$ exit

$4.\backslash (\backslash$mathrm$\{$p$\}=\backslash )$ znode in C ordered just before n

$5.$ if exists$($p$,$ true$)$ wait for watch event

$6.$ goto $2$

Read lock:

$1.$ n $=$ create$(1+"/$read$-",$ EPHEMERAL$\_$SEQUENTIAL$)$

$2.\backslash (\backslash$mathrm$\{$C$\}=\backslash )$ getChildren$(1,$ false$)$

$3.$ if no write znodes lower than n in C $,$ exit

$4.\backslash (\backslash$mathrm$\{$p$\}=\backslash )$ znode in C ordered just before n

$5.$ if exists$($p$,$ true$)$ wait for event

$6.$ goto $2$

$($a$)(4\backslash \%)$ The above pseudo$-$code unfortunately is known to have one bug. Can you identify the bug, explain how the bug creates incorrect results, and explain how the bug should be fixed?

$($b$)(4\backslash \%)$ Suppose that the bug in Part $($a$)$ is fixed. Suppose that there are five client requests of the read$/$write lock in the following order: Write, Write, Read, Read, and Write. Say $\backslash ($ l$=$z o o $\backslash ).$ Draw the lock chain of znodes that shows how each lock request monitors the availability of locks.

$($c$)(6\backslash \%)$ We want to modify the above pseudocode, such that a writer can acquire the write lock as long as no writer exists, while a reader can acquire the read lock only when no writer exists. Thus, a writer is always given a higher priority to obtain a lock than any reader. Show how you revise the above pseudo$-$code.