Develop an algorithm that can be used to determine whether a Stack object $S$ has

exactly one element.

Develop an algorithm that adds the value val to a queue object $Q.$ The queue is

represented using an array data of size $s.$ The algorithm should assume that the queue

is not full. The most recently added item is at index $r($rear$),$ and the least recently added

item is at index $f($front$).$ If the queue is empty, $r=f=-1.$

Develop an algorithm that removes the least recently added item from a queue $Q.$ The

queue is represented using an array of size s$.$ The algorithm assumes that the queue is

not empty. The most recently added item is at index $r($rear$),$ and the least recently

added item is at index $f($front$).$ If the queue is empty, $r=f=-1.$

Develop an algorithm that computes the degree of each vertex in a graph. The graph is

represented using adjacency lists $A$;$A[i]$ is a reference to the first node in a linked list of

nodes representing the vertices adjacent to vertex $i.$ The next field in each node, except

the last, references the next node in the list. The next field of the last node is null. The

vertices are $1,2,$

Develop a recursive algorithm that returns the number of nodes in a binary tree with root

r$.$

Develop an algorithm that inserts the value val into a binary search tree with root. If the

tree is empty, root $=$ null. The algorithm returns the root of the tree containing the added

item. You should assume that "new node" creates a new node with data field data and

reference fields left $($for left child$)$ and right $($for right child$).$

Show each AVL tree created from each of the following insertion: $3,2,1,4,$

$5,6,7,16,15,14$

Show the AVL tree created by the following array $\{20,30,80,40,10,60,50,70\}$