Exercise $8($Index sorting$)$

Create method public static int$[]$ indexSorting$($int$[]$ a$).$ It should return a table of indices

describing a sort of a$,$ but the table a should not be changed. The following example describes

an application.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}[]a=\{6,10,16,11,7,12,3,9,8,5\}$; int$[]$ index $=$

indexSorting$($a$)$; $//$ a is unchanged, index is now

$\{6,9,0,4,8,7,1,3,5,2\}.$

The result now tells us that the smallest value of a is in position $6,$ the second smallest value is

in position $9,$ and so on$.$ The largest value can then be retrieved by looking at the last element

in the index table, so max$(a)$ is therefore $a[2],$ which is $16.$

The code

for $($int $i=0$;$i$ a$.$length; $i++)$ System.out.print$($a$[$index$[$i$]]+$

should therefore print out the values of ai in ascending order.

There is no emphasis on efficiency, only that the code works. You can create

auxiliary tables if you wish $($and you must create at least one, the table to be returned$).$

The table a can have equal values, and then the solution will not be unambiguous. If$,$ for

example, the smallest value occurs twice, it does not matter which of them index$[0]$ refers to$.$

But index$[1]$ must then refer to the second of them. If a is an empty table, the returned table

must also be an empty table.