F N R M H. Now suppose that, when given a choice between two or more subtrees or a given tree, you always consider them in right-to-left order, relative to what's in that diagram. (In practice, the order is not especially elevant, but, for the purposes of this question, we'll assume right-to-left ordering is required.) 1. In a complete postorder traversal of the tree, in what order would the nodes be visited? What is the maximum number of nodes that would ever be stored on the run-time stack while it runs on this tree, assuming the traversal was implemented recursively? 2. In a complete preorder traversal of the tree, in what order would the nodes be visited? What is the maximum number of nodes that would ever be stored on the run-time stack while it runs on this tree, assuming the traversal was implemented recursively? 3. In a complete breadth-first traversal of the tree, in what order would the nodes be visited? What is the maximum number of nodes that would ever be stored in the queue at any given time while it runs on this tree?

F N R M H. Now suppose that, when given a choice between two or more subtrees or a given tree, you always consider them in right-to-left order, relative to what's in that diagram. (In practice, the order is not especially elevant, but, for the purposes of this question, we'll assume right-to-left ordering is required.) 1. In a complete postorder traversal of the tree, in what order would the nodes be visited? What is the maximum number of nodes that would ever be stored on the run-time stack while it runs on this tree, assuming the traversal was implemented recursively? 2. In a complete preorder traversal of the tree, in what order would the nodes be visited? What is the maximum number of nodes that would ever be stored on the run-time stack while it runs on this tree, assuming the traversal was implemented recursively? 3. In a complete breadth-first traversal of the tree, in what order would the nodes be visited? What is the maximum number of nodes that would ever be stored in the queue at any given time while it runs on this tree?

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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Problem Description Using the binary search tree (BST) data structure, we can sort a sequence of n elements by first calling an insertion procedure for n times to maintain a BST, and then performing an INORDER-TREE-WALK on the BST to output the elements in sorted order. To insert a node, we've discussed the TREE-INSERT procedure in class (also from page 294 of the text- book). This TREE-INSERT procedure can actually be improved to reduce the number of key comparisons so that each node's key is compared with the new node's key for at most once during each insertion. For example, given the following BST, The improved insertion procedure will make • 2 comparisons to insert a node with key = 1 • 3 comparisons to insert a node with key = 3 • 2 comparisons to insert a node with key = 8 5. Program Requirements In this programming assignment, you will implement in Java this sorting algorithm using BST, by using the improved insertion procedure. Note that each node of a BST is an object…
3. In a B*-tree, there can be at most 4 search-key values in each node. Assume that the height of the B*-tree is 2. The height of the tree is the length of the path from the root to a leaf node. a) What is the maximum number of leaf nodes this tree can have? Answer: b) Let N1 be a node in the tree. N1 is neither a leaf nor the root. What is the minimum number of children that N1 can have? Answer:
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.
Match the term with each definition: In a binary tree, the left child (if any) of a node plus its descendants The number of nodes on the longest path from the root to a leaf A node on a path from a node to a leaf Set of nodes, T, such that either T is empty or T is partitioned into three disjoint sets (a single node r, called the root, and two (possibly empty) sets that are binary trees, called left and right subtrees of T). A binary tree such that for any given data item, x, in the tree, every node in the left subtree of x contains only items less than x. Every node in the right subtree of x contain only items greater than x. Nodes which have the same parent A node on the path from the root to a node A node directly "above" a node in the tree The node in a tree that has no parent If the node is the root, then the value is one. Otherwise, it's the value of one greater…
[Note: Assume height of leaf node = 0 and height of root node = h. For (a) and (b), you need to explain the number of nodes at each level of the binary tree. For answering part (c), use the results in (a) and (b)]
Scala Programming Define a polymorphic Tree data type, where a Tree is either a Node with a left subtree, a value, and a right subtree; or it is Null. Also define a companion object for the Tree data type, with the following functions: (a) [15 Points]. Three polymorphic functions -- inOrder, preOrder, and postOrder -- to traverse the tree in-order, pre-order, and post-order. Each function takes a tree and returns a list with the contents of the tree when traversed in that order. (b) [5 Points]. A polymorphic function, search, which takes two arguments — a Tree and a key — and returns a boolean result based on whether the key is found in the tree. (c) [5 Points]. A polymorphic function, replace, which takes three arguments — a Tree t, a value before, and a value after — and returns t with ALL instances of before replaced with the value after. [Hint: Model your Tree data type after the List data type]
Your second function is called “isTree". Its input is a graph G, which is a dictionary whose keys are the vertices, and whose values are lists of vertices that are adjacent to the given vertex. Its output is True if G is a tree and False if G is not a tree. Hint: You may want to make use of your "connected" function from the last coding assignment.
PLease do A,B, and C Given the following tree: A.Is the tree balanced? If not, where is the tree out of balance? B.Is it a BST? If not, where is the violation of the search tree order? C.Show the order the nodes will be visited in a preorder, inorder, and postorder traversal. Be sure to clearly indicate which traversal is which.
If n1, n, ., nk is a sequence of nodes in the tree such that n; is the parent of n41 for 1
Problem 3 Recall from lecture that a binary tree T is either: 1. null (the empty tree); or 2. a root noder with two subtrees T₁ and TR, both of which are binary trees. Consider the following algorithm numLeaves (T) that takes as input a binary tree T and returns the number of leaves in the tree. numLeaves (T): 1: if T == null then return 0 2: 3: else 4: 5: 6: 7: 8: TL, TR the left and right subtrees of T, respectively if T₁ == null and TR == null then return 1 else return numLeaves (TL) + numLeaves (TR) Prove by structural induction that for every binary tree T, numLeaves (T) returns the number of leaves of T.
What would be the appropriate kind of tree traversal to use? You're writing an analysis tool for a hierarchical organization, in which there is one person fundamentally in charge, to whom some number of people report, to each of whom some number of people report, and so on. There is a ranking in the organization, so the person in charge has rank 1, the people who report to that person have the rank 2, the people who report to the rank-2 people have the rank 3, and so on. Your input is this kind of organizational hierarchy. Your desired output is to be able to find the highest-ranking person (i.e., the person with the minimum rank number) who meets some characteristic (such as the highest-ranking person under 30 years old). Your input is a binary tree that is an expression tree, in which each non-leaf node contains a binary mathematical operator (such as +, −, ×, or ÷) and each leaf node contains a numeric value (such as 2 or 9.5). Your desired output is the value of the expression…