ALGORITHM AND DATA STRUCTURES Question Question 1: Convert the following binary tree into a heap using...
ALGORITHM AND DATA STRUCTURES Question
Question 1: Convert the following binary tree into a heap using
the Heapify algorithm. Draw the diagrams of the tree step by step
after every alteration.
Question 2: Show the heap that results when the items are
inserted into the heap one by one, starting with one that is
empty.
7, 3, 8, 1, 4, 20, 11, 33, 45, 23, 6
Question 3. Draw the 2-3-4 tree that results when values are
inserted in the order given :
44, 11, 22, 55, 33, 99, 77, 88, 66
Question 4: Construct a Red-Black tree for the list of numbers
given below:
45, 23, 11, 36, 34, 21, 78, 43, 88, 76
Question 5: For the tree given below, write the balance factor
of each vertex. Is the tree an AVL-tree? If not, convert it into an
AVL tree.
Homework Answers
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ALGORITHM AND DATA STRUCTURES Question
Question 1: Convert the following binary tree into a heap using...
In above picture is simple binary tree. Convert this binary tree into "Max Heap" Using below...
In above picture is simple binary tree. Convert this
binary tree into "Max Heap" Using below mentioned
algorithm.
Perform each step complete dry run. All swaping
occurence show in another step. for example 5 swaping. show 5 steps
and 1 swaping in each step. And mention the algorithm line what
happen what line are execute in this step. algorithm mention
below:-
In swaping algorithm line mentioned what line is
executed. complete dry run. only one swaping in one
step.
9...
You are given a binary tree of the form: Each node in the tree has a...
You are given a binary tree of the form:
Each node in the tree has a left child and a right child. Each
of the children will be extended as a linked list. Every node has
the following attributes: key, left node, right node, and next
node. The next node allows a node, that is a part of the tree, to
be extended as a linked list. The diamonds represent the next
nodes, which are part of the linked list...
Discrete Mathematics Time Complexity Analysis Due: May 9th, 2019 Math 4 6026 Heap Sort Another algorithm for sorting uses a specialized tree structure called a "heap." Specifically, we wi...
Discrete Mathematics
Time Complexity Analysis Due: May 9th, 2019 Math 4 6026 Heap Sort Another algorithm for sorting uses a specialized tree structure called a "heap." Specifically, we will use a binary heap, which is like a binary tree with hierarchy. Here is an example of a binary heap structure 1. 2. There is a top vertex, called the parent vertex (aka node). The top parent vertex connects to two vertices a level below. These vertices are the "left child"...
[DSW] Create a balanced binary tree from the tree in figure 1 using DSW algorithm. Show...
[DSW] Create a balanced binary tree from the
tree in figure 1 using DSW algorithm. Show step-by-step process
including the process of
creating backbone and
perfectly balanced tree
[AVL]
Delete node 9 from tree in figure 1, then determine balance
factor for each remaining node, and create a balanced AVL tree from
it.
Delete node 3 from tree in figure 1 by using Delete-by-Copying
procedure, determine balance factor for each remaining node, and
create a balanced AVL tree...
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,...
Tree & Hash Table & Heap Use the following integer keys 73, 58, 91, 42, 60, 130, 64, 87 to perform the followings: a) Binary Search Tree - Draw a binary search tree - Retrieve the integers ke...
Tree & Hash Table & Heap Use the following integer keys 73, 58, 91, 42, 60, 130, 64, 87 to perform the followings: a) Binary Search Tree - Draw a binary search tree - Retrieve the integers keys in post-order - Retrieve the integers keys in pre-order - Draw a binary search tree after node 58 is deleted b) Create a Hash Table using the methods described below. Show the final array after all integer keys are inserted. Assumes that...
Data structures Exercises: For the following binary tree (Index-Value): 0 1 2 3 4 5 6...
Data structures Exercises: For the following binary tree (Index-Value): 0 1 2 3 4 5 6 7 8 9 A C E G B P D X F H Give the pre-order traversal. Give the post-order traversal. Give the in-order traversal. Determine the height of the tree. Using these values: 8 6 4 3 5 9 2 1 6 Build a binary search tree. Build an AVL Tree. Build a 2-3 Tree. Build a min-heap. Build a max-heap. Apply a...
QUESTION 16 Show the first pass of sorting the following array-based binary tree max-heap. In other...
QUESTION 16 Show the first pass of sorting the following array-based binary tree max-heap. In other words, show the first step in sorting, then re-heap the remaining tree into a max-heap. For answers that are not used, put null. You may use scratch paper to draw the trees if you wish. (You will not need all the columns)
Using C++, data structures, C++ STL, inputs and expected outputs are shown below. Max Heap Heap...
Using C++, data structures, C++ STL, inputs and expected
outputs are shown below.
Max Heap Heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either > (in a max heap) or s (in a min heap) the key of C. The node at the "top" of the heap (with no parents) is called the root node. In binary-tree based heap, it...
In above picture is simple binary tree. Convert this
binary tree into "Max Heap" Using below mentioned
algorithm.
Perform each step complete dry run. All swaping
occurence show in another step. for example 5 swaping. show 5 steps
and 1 swaping in each step. And mention the algorithm line what
happen what line are execute in this step. algorithm mention
below:-
In swaping algorithm line mentioned what line is
executed. complete dry run. only one swaping in one
step.
9...
You are given a binary tree of the form:
Each node in the tree has a left child and a right child. Each
of the children will be extended as a linked list. Every node has
the following attributes: key, left node, right node, and next
node. The next node allows a node, that is a part of the tree, to
be extended as a linked list. The diamonds represent the next
nodes, which are part of the linked list...
Discrete Mathematics
Time Complexity Analysis Due: May 9th, 2019 Math 4 6026 Heap Sort Another algorithm for sorting uses a specialized tree structure called a "heap." Specifically, we will use a binary heap, which is like a binary tree with hierarchy. Here is an example of a binary heap structure 1. 2. There is a top vertex, called the parent vertex (aka node). The top parent vertex connects to two vertices a level below. These vertices are the "left child"...
[DSW] Create a balanced binary tree from the
tree in figure 1 using DSW algorithm. Show step-by-step process
including the process of
creating backbone and
perfectly balanced tree
[AVL]
Delete node 9 from tree in figure 1, then determine balance
factor for each remaining node, and create a balanced AVL tree from
it.
Delete node 3 from tree in figure 1 by using Delete-by-Copying
procedure, determine balance factor for each remaining node, and
create a balanced AVL tree...
QUESTION 16 Show the first pass of sorting the following array-based binary tree max-heap. In other words, show the first step in sorting, then re-heap the remaining tree into a max-heap. For answers that are not used, put null. You may use scratch paper to draw the trees if you wish. (You will not need all the columns)
Using C++, data structures, C++ STL, inputs and expected
outputs are shown below.
Max Heap Heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either > (in a max heap) or s (in a min heap) the key of C. The node at the "top" of the heap (with no parents) is called the root node. In binary-tree based heap, it...
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