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:

Algorithm $1$ 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$$s elements sorted in nondecreasing order

for $0$ to $1$ do

$[]0$

end for

for $0$ to $2$ do for $+1$ to $1$ do if $[]<[]$ then

$[][]+1$

else

$[][]+1$

end if

end for

end for

for $0$ to $1$ do

$[[]][]$

end for return S