Examine the BST below, and recall that a tree is just an acyclic (and, in this case, undirected) graph. Let's say we start at node 15 and want to determine if a path exists to node 18. List the order in which our method will visit the nodes of the tree, assuming a) we are using breadth-first search (BFS), b) our method visits the left subtree before it visits the right subtree, and c) our method terminates when we reach node 18. This question is asking you for a single sequence of nodes that meet all three criteria. It is NOT asking for three separate sequences (one for each criterion). You do not have to list any nodes to which you "return" during your traversal. No node in your sequence should be listed more than once. (JAVA) 1 15 12 20 / \/ \ 7 14 16 22 1 18

Examine the BST below, and recall that a tree is just an acyclic (and, in this case, undirected) graph. Let's say we start at node 15 and want to determine if a path exists to node 18. List the order in which our method will visit the nodes of the tree, assuming a) we are using breadth-first search (BFS), b) our method visits the left subtree before it visits the right subtree, and c) our method terminates when we reach node 18. This question is asking you for a single sequence of nodes that meet all three criteria. It is NOT asking for three separate sequences (one for each criterion). You do not have to list any nodes to which you "return" during your traversal. No node in your sequence should be listed more than once. (JAVA) 1 15 12 20 / \/ \ 7 14 16 22 1 18

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Suppose you are given an undirected graph G and a start node s. Your task is to design an algorithm that returns FALSE if G is not a tree and returns TRUE and labels each vertex v with the number of nodes in the subtree rooted at v if G is a tree. Note that the orientation of edges is implicit given the start node. Hint: Modify DFS to solve the problem.
Please use C language to code! Question 1 (Wonderful tree) Let us think of a rooted tree. A rooted tree is a tree in which one vertex has been designated the root. In a rooted tree, the vertex u will be regarded as a parent of a vertex v if and only if there is a path (u->v). Every vertex has a unique parent except the root which has no parent. A child of a vertex v is a vertex of which v is the parent. A leaf is a vertex with no children. Among all the trees, you are invited to determine whether a given rooted tree is a wonderful tree or not. It should be recognized as a wonderful tree if its every non-leaf vertex has more than 2 (i.e., >=3) leaf children.
Answer the following questions about the rooted tree shown below. For questions in which you need to list more than one vertex, list the vertices in alphabetical order and separate them with a comma (no spaces). 1. What are the ancestor(s) of Q? 2. List the leaves of the graph. 3. How many internal vertices does graph have?
Consider the following graph. Start from vertex x, use the Depth First Search (DFS) algorithm (described in the textbook) to compute the DFS tree(s). Show intermediate results similar to the textbook example and show the final DFS tree(s). It is assumed that in the adjacency list representation, all vertices are stored according to their alphabetical order. In other words, a vertex’s neighbors should be explored by their relative alphabetical order.
Consider this algorithm (described in pseudocode): void traverse(tree_node ptr) { } if (ptr!=null) { traverse(ptr.left_child()); print(ptr.data()); traverse(ptr.right_child()); } 18. Which traversal method does this algorithm describe? 19. Apply this algorithm to the tree shown in Figure 5 and provide the result of the traversal in the text box below
Answer the following questions about the rooted tree shown. For questions in which you need to list more than one vertex, list the vertices in alphabetical order and separate them with a comma. 1) Which vertix is the root? 2) What is the height of the graph? 3) What is the level of H? 4) List the children of B. If B has no chidren, write NONE. 5) What is the parent of K? 6) What are the sibling(s) of E? 7) What are the ancestor(s) of Q? 8) What are the descendant(s) of C? 9) List the leaves of the graph. 10) How many internal vertices does the graph have?
Please show steps clearly
Based on the following undirected graph (where there are no weights assigned to the edges), draw the BFS tree (vertices and tree edges) that results when performing a BFS traversal starting at node D, also draw the DFS tree that results when performing a DFS traversal starting at node H. Include with each tree the traversal path: BSF traversal for BFS tree, and preorder traversal for DFS tree. Follow the alphabetical convention discussed in the video lectures A В D E F G H I
Write pseudo-code for a splitTree method that splits a given BST into two BSTs. Assume the method iscalled with a link (first) to the root node of the given BST, a given value x that is contained in the tree,and another link second. The method must return a link, first, to BST that does not have the value x anda link (second) to a second tree that contains the value x. Use the class definitions in the filesBSTClass.java and BinaryNode.java (from Prac1). You may not use the methods insert or remove, orcreate any new node.
Please look at image and show the answer on paper the right result!
Note, you are given the tree T and the edge e = (y, z) whose weight is changed; you are told its old weight w(e) and its new weight w~(e) (which you type in latex by widetilde{w}(e) surrounded by double dollar signs). In each case specify if the tree might change. And if it might change then give an algorithm to find the weight of the possibly new MST (just return the weight or the MST, whatever's easier). You can use the algorithms from class (DFS, Explore, BFS, Dijkstra's, SCC, Topological Sort) as black-box algorithms if you'd like. Explain your algorithm in words. Note the running time of your algorithm in terms of n and m. Part (a): e ∉ T and w~(e) > w(e): [Blank space for the answer] Part (b): e ∉ T and w~(e) < w(e): [Blank space for the answer] Part (c): e ∈ T and w~(e) < w(e): [Blank space for the answer] Part (d): e ∈ T and w~(e) > w(e): [Blank space for the answer]
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