Homework Answers
True.
Explanation:
A rooted tree 
is a fully connected, acyclic graph with a special node 
that is called the root of the tree. You may have studied rooted trees in your data structures class. With a root, it is possible to define a parent and children for each node. But without a root, we will regard the tree simply as a connected, acyclic graph.
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Question 2 A rooted tree always has at least one leaf. True False
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True or False? 1. In a 2-3 tree, the last node that splits is a leaf...
True or False? 1. In a 2-3 tree, the last node that splits is a leaf that already contains two entries. 2. In a red-black tree, a red node cannot have red children. 3. The vertices in a graph may only have one topological order. 4. In a weighted graph, the shortest path between two given vertices has the largest edge-weight sum.
Let T_1 be the rooted tree consisting of a single root vertex. For n greaterthanorequalto 2,...
Let T_1 be the rooted tree consisting of a single root vertex. For n greaterthanorequalto 2, let T_n be the rooted tree consisting of a root vertex with four children, where the subtree rooted at each child is the tree T_n - 1. (a) Calculate how many paths in T_n start from the root vertex and end at a leaf vertex. (b) What is the minimum number of bits (0's and 1's) required to represent a path in T_n that...
Problem E: For each of the following parts, state True or False. If true, give a short proof. If ...
Problem E: For each of the following parts, state True or False. If true, give a short proof. If false, givera counterexample: (1). Using Kruskal's algorithm, edges are (always) inserted into the MST in the same order as using Prim's (2). If an edge e is part of a TSP tour found by the quick TSP method then it must also be part of the (3). If an edge e is part of a Shortest Path Tree rooted at A...
QUESTION 6 Hill-climbing approaches to searching tree space always arrive a globally optimal solution. True False
QUESTION 6 Hill-climbing approaches to searching tree space always arrive a globally optimal solution. True False
A rooted binary tree T has 40 leaves. How many nodes in Thas exactly two children?...
A rooted binary tree T has 40 leaves. How many nodes in Thas exactly two children? (The root is always assumed to have two children.)
1. Suppose the address of vertex v in the ordered rooted tree T is 4.5.4.6. At...
1. Suppose the address of vertex v in the ordered rooted tree T is 4.5.4.6. At what level is v? What is the address of the parent of v? What is the least number of siblings v can have? What is the smallest possible number of vertices in T? If v has two children, what are their addresses? 2. Suppose the address of vertex v in the ordered rooted tree T is 4.3.5.3.4. At what level is v? What is...
True or false? Rationing health care services is always negative. 1) True 2) False Save Question...
True or false? Rationing health care services is always negative. 1) True 2) False Save Question 14 (4 points) True or false? Medical care is the process of combining certain inputs to yield an output. 1) True 2) False Save Question 15 (4 points) True or false? Both wages and noncash benefits are subject to income tax. 1) True
Answer True or False for all statements. True/False A concave mirror always forms a virtual image of...
Answer True or False for all statements. True/False A concave mirror always forms a virtual image of a real object. True/False The image produced by a convex mirror is always closer to the mirror than it would be in a plane mirror for the same object distance. True/False A concave mirror always forms an enlarged real image of a real object. True/False A virtual image formed by a concave mirror is always enlarged. True/False When an object is placed between a concave mirror and its...
Which of the following is true for a Binary Tree? Question 7 options: A binary tree...
Which of the following is true for a Binary Tree? Question 7 options: A binary tree is a tree, since no node has more than 2 children, they are known as the left child and the right child The root node is the node without a parent A leaf node is a node without child nodes All of the above
(2 points) A full binary tree has a start node, internal nodes, and leaf nodes. The...
(2 points) A full binary tree has a start node, internal nodes, and leaf nodes. The number of leaf nodes of this binary tree is 256. a) What is the height of the tree? b) How many internal nodes are in this tree?
Let T_1 be the rooted tree consisting of a single root vertex. For n greaterthanorequalto 2, let T_n be the rooted tree consisting of a root vertex with four children, where the subtree rooted at each child is the tree T_n - 1. (a) Calculate how many paths in T_n start from the root vertex and end at a leaf vertex. (b) What is the minimum number of bits (0's and 1's) required to represent a path in T_n that...
Problem E: For each of the following parts, state True or False. If true, give a short proof. If false, givera counterexample: (1). Using Kruskal's algorithm, edges are (always) inserted into the MST in the same order as using Prim's (2). If an edge e is part of a TSP tour found by the quick TSP method then it must also be part of the (3). If an edge e is part of a Shortest Path Tree rooted at A...
QUESTION 6 Hill-climbing approaches to searching tree space always arrive a globally optimal solution. True False
A rooted binary tree T has 40 leaves. How many nodes in Thas exactly two children? (The root is always assumed to have two children.)
1. Suppose the address of vertex v in the ordered rooted tree T is 4.5.4.6. At what level is v? What is the address of the parent of v? What is the least number of siblings v can have? What is the smallest possible number of vertices in T? If v has two children, what are their addresses? 2. Suppose the address of vertex v in the ordered rooted tree T is 4.3.5.3.4. At what level is v? What is...
True or false? Rationing health care services is always negative. 1) True 2) False Save Question 14 (4 points) True or false? Medical care is the process of combining certain inputs to yield an output. 1) True 2) False Save Question 15 (4 points) True or false? Both wages and noncash benefits are subject to income tax. 1) True
(2 points) A full binary tree has a start node, internal nodes, and leaf nodes. The number of leaf nodes of this binary tree is 256. a) What is the height of the tree? b) How many internal nodes are in this tree?
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