Given the graph G from Question 2, using the Graph Breadth-First Search algorithm with a Queue, please do the following: Assume that the start node is 4 (e.g. node = 4). Demonstrate a step-by-step, manual desk-check execution of the BFS algorithm, showing the values of all variables and arrays (e.g. visited, inqueue, Q) for each step in each cycle of each loop, as demonstrated in class. [ Algorithm: Graph breadth-first search BFS (G, node) → →visited Input: G = (V, E), a graph node, the starting vertex in G Output: visited, an array of size [V] such that visited[i] is TRUE if we have visited node i, FALSE otherwise 1 Q-CreateQueue () 2 - visited CreateArray (VI) inqueue CreateArray (VI) 3 t 4 for i0 to IV do

Present an algorithm (in outline form) for inserting an element into a sorted linked list so that the list is always in sorted order. Do not utilize a sorting routine, but rather devise an insert (add) algorithm that will search the list and insert the new element in the proper place in the list so that the list is always in order.  Assume that the objects involved all properly override both the equals (==) and the compareTo (>, <, >=, and <=) methods.  The list is to be maintained in ascending order.  Assume that the add method has the following signature.  public void Add(E element)

Could you help me the following questions? Sara and her friends said they have discovered a way to get O(1) category performance for both insert and remove in a priority queue. Their description of the data structure and algorithms is as follows: They use an array implementation for the priority queue The index of the array represents the rank of an element – e.g. an element whose rank is 50 will be placed at index 49 Each element is the head node to a linked list – if a new element is inserted into the priority queue with the same rank as another element already in the queue, the new element is added to the linked list at its head Example: If an element “X” with rank 25 exists at index 24, and a new element “Y” also has a rank of 25, the linked list at index 24 is “Y” then “X” When remove is performed, the element at the highest index is removed. If there is more than one node at that index, the node at the head of the linked list there is removed Based on this description of the…

Implement two versions of the successor function for the 8-puzzle: one that generates all the successors at once by copying and editing the 8-puzzle data structure, and one that generates one new successor each time it is called and works by modifying the parent state directly (and undoing the modifications as needed). Write versions of iterative deepening depth-first search that use these functions and compare their performance.