1. What is the maximum height for a complete binary tree on S = {a, b,...
1. What is the maximum height for a complete binary tree on S = {a, b, c, d, e}?
2. the di-graphs of labeled, positional binary trees are shown. In each case we suppose that visiting a node results in printing out the label of that node. For each exercise, show the result of performing a preorder search of the tree whose digraph is shown.
Homework Answers
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1. What is the maximum height for a complete binary tree on
S = {a, b,...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of height h is 2h+1 − 1. 2. A full node is a node with two children. Prove that the number of full nodes plus one is equal to the number of leaves in a nonempty binary tree. 3. What is the minimum number of nodes in an AVL tree of height 15? 4. Show the result of inserting 14, 12, 18, 20, 27, 16,...
2. A complete binary tree is defined inductively as follows. A complete binary tree of height...
2. A complete binary tree is defined inductively as follows. A complete binary tree of height 0 consists of 1 node which is the root. A complete binary tree of height h +1 consists of two complete binary trees of height h whose roots are connected to a new root. Let T be a complete binary tree of height h. Prove that the number of leaves of the tree is 2" and the size of the tree (number of nodes...
Beginning with an empty binary search tree, what binary search tree is formed when you add the following letters in the order given?
Trees-related questionsBeginning with an empty binary search tree, what binary search
tree is formed when you add the following letters in the order
given? J, N, B, A, W, E, TRepresent the following binary tree with an array What is the result of adding 3 and 4 to the 2-3 tree shown
below?Why does a node in a red-black tree require less memory than a
node in a 2-3-4 tree?Why can’t a Red-Black Tree have a black child node with exactly...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees (left and right). In other words, all their nodes have either zero subtrees (in which case they are leaves) or two subtrees (in which case they are internal nodes). Suppose that you have a boolean function that tells you, for each node of the tree, whether it is a leaf or not (call it: leaf(n), for node n). a) Write a recursive function that...
1 Binary Search Trees (25 points) Consider the binary tree as shown in Figure 1. 9...
1 Binary Search Trees (25 points) Consider the binary tree as shown in Figure 1. 9 5 15 10 17 8 Figure 1: Binary Tree: The letter next to each node (e.g., a, b) denotes the tree node, and the number inside each node is the key. 1.1 Correctness (10 points) Is this binary tree a valid binary search tree? In other words, does it satisfy the binary search tree property? If not, which node(s) violates the binary search tree...
QUESTION 9 Consider the following binary search tree: If the root node, 50, is deleted, which node will become the new root? A 15 B 24 C 37 D 62 QUESTION 10 In the...
QUESTION 9
Consider the following binary search tree:
If the root node, 50, is deleted, which node will become the new
root?
A
15
B
24
C
37
D
62
QUESTION 10
In the following trees EXCEPT______, the left and right subtrees
of any node have heights that differ by at most 1.
A
complete trees
B
perfect full trees
C
balanced binary trees
D
binary search trees
QUESTION 11
A perfect full binary tree whose height is 5 has...
Fill a tree called Pine with 25 elements from an input file. Traverse the tree using...
Fill a tree called Pine with 25 elements from an input file. Traverse the tree using each of the following methods. Print the smallest element in the binary search tree, Pine. Find the number of edges between the root of the tree and the node that contains the smallest value in the tree. Return the count to the calling unit. Count the number of internal nodes in the original tree, Pine. Print the count and return it to the calling...
Question 1 1 pts What is the maximum height of any AVL-tree with 7 nodes? Assume...
Question 1 1 pts What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0. a N 5 Question 2 1 pts So get the sorted list from an AVL tree we need to do a postorder traversal inorder traversal preorder traversal
The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y
a. The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y. Construct the tree and determine the output of the PREORDER traversal output. b. One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1....
3. (8 points) Using the implementation of binary search tree operations we discussed in class, draw...
3. (8 points) Using the implementation of binary search tree operations we discussed in class, draw the trees that result from the following operations: (a) Inserting 142, 400, 205, 127, 100, 320, 160, 141, and 110 into an initially-empty tree (in that order). (b) Deleting 142 from the tree you drew for part (a). 4. (8 points) Draw the unique binary tree that has a preorder traversal of 4, 1, 6, 3, 7, 5, 9, 2, 8 and an inorder...
2. A complete binary tree is defined inductively as follows. A complete binary tree of height 0 consists of 1 node which is the root. A complete binary tree of height h +1 consists of two complete binary trees of height h whose roots are connected to a new root. Let T be a complete binary tree of height h. Prove that the number of leaves of the tree is 2" and the size of the tree (number of nodes...
Trees-related questionsBeginning with an empty binary search tree, what binary search
tree is formed when you add the following letters in the order
given? J, N, B, A, W, E, TRepresent the following binary tree with an array What is the result of adding 3 and 4 to the 2-3 tree shown
below?Why does a node in a red-black tree require less memory than a
node in a 2-3-4 tree?Why can’t a Red-Black Tree have a black child node with exactly...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees (left and right). In other words, all their nodes have either zero subtrees (in which case they are leaves) or two subtrees (in which case they are internal nodes). Suppose that you have a boolean function that tells you, for each node of the tree, whether it is a leaf or not (call it: leaf(n), for node n). a) Write a recursive function that...
1 Binary Search Trees (25 points) Consider the binary tree as shown in Figure 1. 9 5 15 10 17 8 Figure 1: Binary Tree: The letter next to each node (e.g., a, b) denotes the tree node, and the number inside each node is the key. 1.1 Correctness (10 points) Is this binary tree a valid binary search tree? In other words, does it satisfy the binary search tree property? If not, which node(s) violates the binary search tree...
QUESTION 9
Consider the following binary search tree:
If the root node, 50, is deleted, which node will become the new
root?
A
15
B
24
C
37
D
62
QUESTION 10
In the following trees EXCEPT______, the left and right subtrees
of any node have heights that differ by at most 1.
A
complete trees
B
perfect full trees
C
balanced binary trees
D
binary search trees
QUESTION 11
A perfect full binary tree whose height is 5 has...
Question 1 1 pts What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0. a N 5 Question 2 1 pts So get the sorted list from an AVL tree we need to do a postorder traversal inorder traversal preorder traversal
3. (8 points) Using the implementation of binary search tree operations we discussed in class, draw the trees that result from the following operations: (a) Inserting 142, 400, 205, 127, 100, 320, 160, 141, and 110 into an initially-empty tree (in that order). (b) Deleting 142 from the tree you drew for part (a). 4. (8 points) Draw the unique binary tree that has a preorder traversal of 4, 1, 6, 3, 7, 5, 9, 2, 8 and an inorder...
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