$($a$)$ Write an algorithm to sort a stack of integers such that the smallest

elements are on the top. You can only use one $(1)$ additional temporary stack and a constant number of

temporary integer variables. You may not copy the elements into any other data structure $($such as an

array$).$ The stack supports the following operations: push, pop, peek and isEmpty. Give pseudocode or

Java$-$like code. $($b$)$ Give the worst$-$case running time in big$-$Oh notation. You do not need to prove this,

but please show your understanding by mentioning which type of instances would give the worst case.