Write a function to reverse a singly linked list. The function should return the new head of the

reversed list. $(5$pts$)$

Input: $1->2->3->4->$ null

Output: $4->3->2->1->$ null

$$ Given a singly linked list, write a function to detect if there is a loop $($cycle$)$ in the list. Remove

the loop and return the list without the cycle if a loop is found. $(5$pts$)$

Input: $1->2->3->4->5->2($cycle at node $2)$

Output: $1->2->3->4->5->$ null

$$ Write a function to insert a new node in a doubly linked list at a specified position. You should

adjust the pointers accordingly to maintain the doubly linked structure. $(5$pts$)$

Input: List $=10<->20<->30<->$ null, data $=25,$ pos $=2$