There are two common traversal strategies for such trees, involving finding a walk starting at the root and containing all the verticies. Start at the root, and then for с Breadth-first search, travel to an untraversed vertex which is closest to the root. • Depth-first search, travel to an untraversed vertex that is further from the root. d e r, a, b, c, d, e, f while a depth-first search would traverse in this order r, a, c, d, b, e, f b Figure 2: Rooted binary tree In the rooted binary tree in Figure 2, we'll choose alphabetically when unsure. Then a breadth-first search would traverse in this order (a) Suppose T is the rooted binary tree in Figure 2. Let T' is its doubled version. Run Hierholzer's algorithm (alphabetic order when undecided). (b) Which search was this?

There are two common traversal strategies for such trees, involving finding a walk starting at the root and containing all the verticies. Start at the root, and then for с Breadth-first search, travel to an untraversed vertex which is closest to the root. • Depth-first search, travel to an untraversed vertex that is further from the root. d e r, a, b, c, d, e, f while a depth-first search would traverse in this order r, a, c, d, b, e, f b Figure 2: Rooted binary tree In the rooted binary tree in Figure 2, we'll choose alphabetically when unsure. Then a breadth-first search would traverse in this order (a) Suppose T is the rooted binary tree in Figure 2. Let T' is its doubled version. Run Hierholzer's algorithm (alphabetic order when undecided). (b) Which search was this?

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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50. Use the Breadth-First Spanning Tree Search Algorithm to find a spanning tree of K,. Start from vertex h. Remember, we start with vertex h being labeled 0. b K6 a. Vertices that should be labeled as step 1: b. Vertices that should be labeled as step 2: c. Vertices that should be labeled as step 3: d. Edges that need to be removed to get a spanning tree:
A complete binary tree is a graph defined through the following recur- sive definition. Basis step: A single vertex is a complete binary tree.Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the the graph formed by starting with a root r, and adding an edge from r to each of the vertices r1,r2 is also a complete binary tree.The set of leaves of a complete binary tree can also be defined recur- sively.Basis step: The root r is a leaf of the complete binary tree with exactly one vertex r.Inductive step: The set of leaves of the tree T built from trees T1, T2 is the union of the sets of leaves of T1 and the set of leaves of T2. The height h(T ) of a binary tree is defined in the class.Use structural induction to show that L(T), the number of leaves of a complete binary tree T , satisfies the following inequality L(T) ≤ 2^h(T).
1. A complete binary tree of depth d is a tree where every node has two children, except for the nodes at depth d, which have no children. Such a tree has 2' nodes at depth j, where j = 0, 1, d. What is the minimal size of a vertex cover of a complete binary tree of depth 2m + 1, where m is a nonnegative integer?
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.
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.
1 Spanning Trees. Use the Breadth-First Search Algorithm with the vertex ordering a, b, c, d, e to find a spanning tree T for the graph below. Show all steps of the algorithm. b α d e C
Kruskal's Algorithm: Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest. This algorithm is a Greedy Algorithm. The steps to find a MST using this algorithm are as follows: Sort all the edges in non-decreasing order of their weight. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it. Repeat step2 until there are (V-1) edges in the spanning tree. Example with 10 vertices and 20 weighted edges:
Delete operation makes use of the FIND MIN operation discussed in the earliersection. The delete operation is carried out as follows:D1: If the node NODE to be deleted in the k-d tree is a leaf node, then deleteNODE.D2: If the node NODE to be deleted has DISC = i, and has a right subtree, thencall FIND MIN, to obtain the node RIGHT_MIN, which has the minimum elementalong dimension i in the right subtree and replace NODE with RIGHT_MIN.Recursively delete RIGHT_MIN from the right subtree.D3: If the node NODE to be deleted has DISC = i, and has a left subtree, thencall FIND MIN to obtain the node LEFT_MIN, which has the minimum elementalong dimension i in the left subtree and replace NODE with LEFT_MIN.Recursively delete LEFT_MIN from the left subtree. Move the revised left subtreeas the right child of the current node.illustrate a recursive pseudocode description of the delete operation in a k-d tree using above statement
a) Which edges would you keep for the minimum-weight spanning tree? (Indicate as vertex-vertex — eg. “K-P”... if there were vertices K and P.) b) Describe the algorithm you used to determine the minimum-weight spanning tree above. Did you face any challenges in applying this algorithm?
A Binary Search Tree (BST) can be used to efficiently implement a sorted set. It stores uniquevalues and offers an efficient membership method (contains).A binary search tree (BST) is a binary tree with the additional binary search tree property.The binary search tree property states that for every node n in the tree1. n.data is greater than the data value of all nodes in the sub-tree rooted with n.left.2. n.data is less than the data value of all nodes in the sub-tree rooted with n.right.As we are implementing a set, all data (strings) in the tree will be unique. Every node in the treewill have its own distinct string. Strings will be compared using the canonical way (as defined bythe compareTo() method in the String class).For example, the binary tree on the left (below) IS a binary search tree and the one on the rightis NOT.You will implement several methods in the BinaryTree and BST classes. The BST class mustextend the BinaryTree class. Methods that you must complete (implement or…
(6) How many binary trees with 11 nodes (another name for vertices) are there such that the root has at least three grandchildren and at least one node has exactly one child?
Prim's minimal spanning tree algorithm makes use of a priority queue Q of vertices with an associated value on which the queue is sorted. The value on which the priority queue is ordered is the minimum weight of any edge from the vertex to a vertex already removed from Q. O True O False