Consider the algorithm for the sorting problem that sorts an array by counting, for each of its elements,

the number of smaller elements and then uses this information to put the element in its appropriate

position in the sorted array:

ComparisonCountingSort $(A[0..n-1])$

$//$Sorts an array by comparison counting

$//$Input: Array $A[0..n-1]$ of orderable values

$//$Output: Array $S[0,n-1]$ of $A\text{'}$s elements sorted in nondecreasing order

for ilarr$0$ to $n-1$ do

Count $[i]larr0$

for ilarr$0$ to $n-2$ do

for jlarri$+1$ to $n-1$ do

if $[j]larr[j]+1$Count$[i]larrCount[i]+1$ilarr$0n-1[i]S\{6,5,13,8,14,23\}A[i]$

Count $[j]larr$ Count $[j]+1$

else Count$[i]larrCount[i]+1$

for ilarr$0ton-1do$

$S[$ Count $[i]]larrA[i]$

return $S$

$a.$ Apply this algorithm $to$ sorting the list $\{6,5,13,8,14,23\}.$ Show intermediate results.

$b.Is$ this algorithm stable? Justify your answer.

$c.Isitin-$place? Justify your answer.