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- Show the results of inserting the keys: F, L, O, R, I, D, A, U, N, V, M, Y, C, S in order into an empty B-tree with minimal degree 2. Draw only the configurations of the tree just before some node being split, and also draw the final configuration. Please make sure your tree configurations are drawn neatly and are easy to read and understand.Create a binary search tree as discussed in class, using the given numbers in the order they’re presented. State if the resulting tree is has the attributes of being FULL, BALANCED, or COMPLETE. 37, 20, 18, 56, 40, 42, 12, 5, 6, 77, 21, 54. Draw the BST constructed by inserting the values [53, 25, 11, 63, 4, 88,59, 3, 15, 82, 92, 27, 55, 14] in the order shown, into an initially emptytree. 2. Using the tree traversal algorithms and the BST from (1) above, show theoutput sequence for a (a) Preorder traversal(b) Postorder traversal3. Delete the node with value 25 and draw the resultant tree.(a) Use two methods to delete the node with value 25 and draw the resul-tant tree. (b) Briefly describe both methods that you have used.
- Consider a B Tree used as an index that has THREE levels including the root node. If a newkey is inserted in this index, then what shall be the maximum number of nodes? Explain youranswer with an example.2. We are given a complete binary tree with height h and n nodes. The link between a node and its left child is labeled as 0 and the link between a node and its right child is labeled as 1. A path from the root to each external node at the last level can be labeled by an h-tuple (X1, X2, ..., xh) of 1s and Os that lie on its links. See the following example: 0 0 1 1 0 0 1 0 (0,0,0) (0,1,1)you need to write the solutions in python and provide a brief explanation of your codes and the efficiency analysis with comments. 3. Consider a loop tree which is an undirected wighted graph formed by taking a binary tree and adding an edge from exactly one of the leaves to another node in the tree as follows: Letnbe the number of vertices in a loop tree. How long does it take Prim's or Kruskal's algorithms to find the minimum spanning tree in terms ofn? Devise a more efficient algorithm that takes an nxn adjacency weighted matrix as input, and finds the minimum spanning tree of a loop tree. 三 input1 - Not Defteri Dosya Düzenle 1078000000 700650060 800006400 060000000 050000021 006000000 004000000 060020000 000010000 output1 - Not Defteri Dosya Düzenle Görünü p 14873265 三 input2 - Not Defteri Dosya Düzenle Görünüm0210000200344010000000300000040005604005000000
- Suppose that we have a tree, and we know its pre-order and in-order traversals as follows: Pre-order traversal:1 2 4 7 3 5 6 8 In-order traversal:4 7 2 1 5 3 8 6 a) Plot this tree (tip: you can validate your tree by checking its pre-order and in-order traversals to see if they are matched to the traversals given in the question)? b) Give the post-order traversal of this tree?Let T be an arbitrary splay tree storing n elements A1, A2, . An, where A1 ≤ A2 ≤ . . . ≤ An. We perform n search operations in T, and the ith search operation looks for element Ai. That is, we search for items A1, A2, . . . , An one by one. What will T look like after all these n operations are performed? For example, what will the shape of the tree be like? Which node stores A1, which node stores A2, etc.? Prove the answer you gave for formally. Your proof should work no matter what the shape of T was like before these operations.Show the results of inserting the keys: F, L, O, R, I, D, A, U, N, V, M, Y, C, S in order into an empty B-tree with minimal degree 2. Draw only the configurations of the tree just before some node being split, and also draw the final configuration. Please make sure your tree configurations are drawn neatly and are easy to read and understand. See attached image for how the tree configurations should be presented
- Suppose we do a BFS on a connected undirected graph G and T is corresponding depth-first tree. if we remove from G all the cross edges with respecr to T the result will just be a tree. True or False?Suppose that we have an estimate ahead of time of how often search keys areto be accessed in a BST, and the freedom to insert them in any order that we desire.Should the keys be inserted into the tree in increasing order, decreasing order of likelyfrequency of access, or some other order? Explain your answerHaving read the definition of trees, which of the following graphs are trees? Why? Draw each graph to support your answer. Discuss why you think your answer satisfies the tree definition. Upload your preparations on this link.a. G=(V,E)G=(V,E) with V={a,b,c,d,e}V={a,b,c,d,e} and E={{a,b},{a,e},{b,c},{c,d},{d,e}}E={{a,b},{a,e},{b,c},{c,d},{d,e}}b. G=(V,E)G=(V,E) with V={a,b,c,d,e}V={a,b,c,d,e} and E={{a,b},{b,c},{c,d},{d,e}}E={{a,b},{b,c},{c,d},{d,e}}c. G=(V,E)G=(V,E) with V={a,b,c,d,e}V={a,b,c,d,e} and E={{a,b},{a,c},{a,d},{a,e}}E={{a,b},{a,c},{a,d},{a,e}}d. G=(V,E)G=(V,E) with V={a,b,c,d,e}V={a,b,c,d,e} and E={{a,b},{a,c},{d,e}}