nitial state of 8-puzzle problem,
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![2. [CLO3] Figure 3 illustrates the initial state of 8-puzzle problem,
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(a) You should use breadth first search (BFS) and illustrate the state of the search tree that
can be built down to level/depth 2 (Assume: Level/Depth 0 is the root of the tree).
(b) You should use depth first search (DFS) and illustrate the state of the search tree that can
be built down to level/depth 3 (Assume: Level/Depth 0 is the root of the tree).
*Remember to STOP once you successfully expanded one node that reaches to
level/depth 3 *](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1032527f-d436-4fb6-97b6-16b126c41cac%2Fdfc9fe39-3e0a-4b3c-84fd-d2010c81c157%2Fa78tanl_processed.jpeg&w=3840&q=75)
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- Problem 4: B-trees. In this problem the height of a tree is defined as the number of thenodes, including the root, on the longest path from the root to a leaf.(i) What is the smallest number of elements in a B-tree of order 5 and of height h =1, 2, 3, 5? Elaborate.(ii) What is the smallest number of elements in a B-tree of order b and of height h? Finda closed formula.(3) Using the following graph, draw the Minimum Spanning Tree, and by using Dijkstra’s Algorithm give the shortest path from A to F (do not confuse F with E). You may either draw the shortest path, or write out the steps needed to follow the route you find.Apply dfs technique on the below graph. Make a diagram of depth first tree. Please explanation with clear steps.
- artificial intelligence Problem 2: Consider the following game tree in which the evaluation function values are shown below each leaf node. Assume that the root node corresponds to the maximizing player and the search always visits children from left-to-right. Which nodes will not be examined by the alpha beta pruning algorithm? Please show them by double crossing on the edges of the graphDiscuss the principles and applications of Depth-First Search (DFS) algorithm in graph traversal. Include the following subparts: a) Explain the working principles and steps involved in Depth-First Search. b) Analyze the time complexity of Depth-First Search and discuss its efficiency in different types of graphs. c) Discuss the space complexity of Depth-First Search and explain the memory requirements during its execution. d) Compare Depth-First Search with Breadth-First Search (BFS) and highlight the differences in their traversal strategies.Using C/C++, implement a dynamic programming algorithm to solve the optimal binary search tree problem: define ten frequencies (summation is 1) for ten searchable objects (e.g., characters, strings, or numbers) and output: (1) the optimal binary search average comparison number; (2) the optimal binary search tree construction information (which object is in root, which is in the left child of root, which is the right child of root, … etc).
- Because many pairs of points have identical distances (e.g. dist(h,c) = dist(h,b) = dist(h,f) =sqrt(5)), the above diagram has more than one minimum-weight spanning tree. Determine the total number of minimum-weight spanning trees that exist in the above diagram. Clearly justify your answer.8. without using any standard template library Write code for DAG shortest path algorithm to find shortest path from a given source node to all other nodes using adjacency list representations Write code for DAG shortest path algorithm to find shortest path from a given source node to all other nodes using adjacency matrix representations.1) For the following graph(see image) a) Find a minimum spanning tree using Prim’s algorithm. Use A as the start point and if there are choices, use alphabetic order. b) Find a minimum spanning tree using Kruskal algorithm. Use A as the start point and if there are choices, use alphabetic order.
- (a) Describe the structure of a complete binary tree of height h with maximum number of nodes.Derive the minimum number of nodes, n(max) (h), of this tree as a function of h.(b) Describe the structure of a complete binary tree of height h with minimum number of nodes.Derive the maximum number of nodes, n(min)(h), of this tree as a function of h.(c) Derive an expression for the height of a binary tree h in terms of the number of nodes, n.Generate the shortest path tree using the Dijkstra Algorithm using the following format: Note: using link state (OSPF) Shortest path tree for node A1.Permanent list Tentative listempty A(0)2.Permanent list Tentative listA(0) B(5), C(2), D(3)3.Permanent list Tentative listA(0), C(2) B(5), D(3), E(6)4.Permanent list Tentative listA(0), C(2), D(3) B(5), D(3)5.Permanent list Tentative listA(0), C(2), D(3), B(5) D(3)6.Permanent list Tentative listA(0), C(2), D(3), B(5), D(3)…Problem 2: Consider the following game tree in which the evaluation function values are shown below each leaf node. Assume that the root node corresponds to the maximizing player and the search always visits children from left-to-right. Which nodes will not be examined by the alpha beta pruning algorithm? Please show them by double crossing on the edges of the graph