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Project 03 - Trees, Trees, and more Trees
Project 03 - Trees, Trees, and more Trees
Introduction
You are required to implement three tree data structures: a general tree, a heap
tree, and an AVL tree. No tree should contain duplicate values. You are also
required to create UML diagrams for each of the classes that you implement.
Finally, you have to provide the means to test your system by developing a
menu program that allows the user to manipulate your structures.
It is strictly prohibited to use the structures and/or algorithms defined in
the C++ standard library (STL). So, if your design requires a list, queue, stack,
or a hash table, you can only use your own implementations.
Underflow exceptions might be generated in some of the functions you implement. Make sure exceptions are thrown and caught where appropriate.
Deliverables
• A 1 page report with your UML diagrams that explains the design of your
data structures. Please include what each teammate did and approximate
hours spent on the project.
• An implementation of a general tree.
• An implementation of a heap tree.
• An implementation of an AVL tree.
• A menu program to test the implemented data structures.
1 General Tree
In this part of the project, you need to implement two classes, a TreeNode Class
and a LinkedTree Class; create their respective UML diagrams. Your TreeNode
class can be used for all trees (not all trees will use all data members). If you
would like to include further data members you may although it is not necessary.
Some of the methods are the same but have different names, you may feel free
to rename them as you see fit as long as they are descriptive. Calculate the
running time of your functions and include them in your report.
1
1.1 Description Trees, Trees, and more Trees
1.1 Description
A tree is a structure that is formed by Nodes (vertices) and Edges (arcs). Edges
connect nodes together. Any two nodes in the tree are connected by one and
only one path.
1.2 Data Members
Specify all the data members your implementation needs. You are required to
instantiate a TreeNode object for each of the nodes in the tree. Each node has a
key(int) - for Heap tree only, value (Type), balanceFactor (short int: -1 for
right high, 0 for balanced, 1 for left high) - for AVL tree only, and a parent,
left and right child (pointers for General and AVL tree, unused for Heap tree
because it is an array implementation).
1.3 Member Functions
Constructors
defines constructor.
Destructor
defines destructor.
Accessors
getRoot() returns the root of the tree.
getSize() returns number of elements in the tree.
getHeight() returns the height of the three.
getHeight(node) returns the height of the node in the argument (from
the root).
empty() returns true if the tree is empty, false otherwise.
leaves() returns the number of leaves in the tree.
siblings(node) returns the number of siblings of the node in the argument.
findNode(data) returns a pointer to a node that holds the data in the
argument.
2
1.3 Member Functions Trees, Trees, and more Trees
preorder() performs preorder traversal.
postorder() performs postorder traversal.
inorder() performs in order traversal.
Mutators
clear() removes all the elements in the tree
insert(data) inserts data in the tree.
del(data) removes data from the tree.
Friends
no friends for this class.
3
Trees, Trees, and more Trees
2 Heap
In this part of the project, you need to implement an additional MaxHeapTree
Class; create the UML diagram. Calculate the running time of your functions
and include them in your report.
2.1 Description
A priority queue is like a dictionary in the sense that it stores entries (key,value).
However, a dictionary is used when you want to look up a particular key. A
priority queue is used when you want to prioritize entries. There is a total order
defined on the keys. The main operations that a priority key allows to do are:
• Identify or remove the entry that has the smallest (largest) key. It is the
only one that could be removed quickly.
• Insert anything you want in any time.
A binary heap is a particular implementation of the priority queue abstract
data type. ‘A heap data structure should not be confused with the
heap which is a common name for the pool of memory from which
dynamically allocated memory is allocated’. Its definition encompasses
several things:
• Identify or remove the entry that has the smallest (or largest) key. It is
the only one that can be removed quickly.
• Insert anything you want at a more specific location in the tree.
For this part of the project you will implement a max heap and all of its
operations. Entries are stored in a dynamic array. If an entry is being inserted,
and the array is already full, the capacity of the array is doubled. If, after
removing an entry from the heap, and the number of entries is one-quarter
(1/4) the capacity of the array, then the capacity of the array is halved. The
capacity of the array may not be reduced below the initially specified (by you)
capacity.
2.2 Data Members
Specify all the data members your implementation needs. You are required to
instantiate a TreeNode object for each of the nodes in the tree. Your nodes have
a key (integer) and a value (Type), and they are stored in a dynamic array.
2.3 Member Functions
Constructors
defines constructor.
4
2.3 Member Functions Trees, Trees, and more Trees
Destructor
defines destructor.
Accessors
getMax() returns the root of the tree.
getSize() returns number of elements in the tree.
getHeight() returns the height of the tree.
empty() returns true if the tree is empty, false otherwise.
leaves() returns the number of leaves in the tree.
print() prints the heap.
Mutators
clear() removes all the elements in the tree
insert(key,data) inserts data in the tree. This operation must satisfied
the heap property.
delMax() removes the entry specified by maximum key in the tree. This
operation must satisfied the heap property.
Friends
defines friends for this class.
5
Trees, Trees, and more Trees
3 AVL Tree
In this part of the project, you need to implement an additional AVL Class;
create the UML diagram. Calculate the running time of your functions and
include them in your report.
3.1 Description
A binary search tree (BST) is a powerful tool to quickly search values in a tree.
However, if the BST is not balanced its operations can degenerate to linear
behavior, which makes them no faster than lists.
An AVL tree is a BST that includes complicated updating rules to keep
the tree balanced. An AVL tree requires that the height of the left and right
children of every node to differ by at most ± 1. Simple and double rotation are
executed when inserting or deleting an entry to/from the tree.
3.2 Data Members
Specify all the data members your implementation needs. You are required to
instantiate a TreeNode object for each of the nodes in the tree. Each node has
a value (Type), and access to its parent, left and right child.
3.3 Member Functions
Constructors
defines constructor.
Destructor
defines destructor.
Accessors
getRoot() returns the root of the tree.
getSize() returns number of elements in the tree.
getHeight() returns the height of the tree.
getHeight(node) returns the height of the node in the argument (from
the root).
empty() returns true if the tree is empty, false otherwise.
leaves() returns the number of leaves in the tree.
6
3.3 Member Functions Trees, Trees, and more Trees
siblings(node) returns the number of siblings of the node in the argument.
find(data) returns a pointer to a node that holds the data in the argument.
preorder() performs preorder traversal.
postorder() performs postorder traversal.
inorder() performs inorder traversal.
inorder() performs inorder traversal.
Mutators
clear() removes all the elements in the tree
insert(data) inserts data in the tree. Tree must be kept balanced after
the insertion.
del(data) removes data from the tree. Tree must be kept balanced after
the deletion.
Friends
defines friends for this class.
7
Trees, Trees, and more Trees
4 The Menu Program
In order to test your program, you are required to implement a menu program
that provides the means to run each of the functions in your classes (name your
executable proj3). Please choose the string data type for the values (or ’data’)
of your entries. The TA will choose one group to demo the project.
Format for the Menu Program
First, take a character, ’g’, ’h’, or ’a’ (lowercase) that specifies whether we will
be working with a general tree, a heap, or an AVL tree, respectively, and creates
an instance of the tree. Next, give the options for each specific tree (please have
them in this EXACT order for grading purposes):
General Tree or AVL Tree
1. Return root
2. Return size
3. Return height
4. Return height (node)
5. Is tree empty?
6. Return number of leaves
7. Return number of siblings (node)
8. Find node (data)
9. Print preorder
10. Print postorder
11. Print inorder
12. Clear tree
13. Insert (data)
14. Delete (data)
15. Exit
Max Heap
1. Return root
2. Return size
3. Return height
4. Is tree empty?
5. Return number of leaves
6. Print
7. Clear tree
8. Insert (key, data)
9. Delete
10. Exit
8
Trees, Trees, and more Trees
Submit the following files to Canvas (named EXACTLY as shown below
without zipping for grading purposes: (you may also include implementation
files with the header files if you would like)
1. menu.cpp
2. treeNode.h
3. linkedTree.h
4. maxHeapTree.h
5. avlTree.h
6. makefile (name your executable ’proj3’)
7. project3.pdf
The rubric is as follows:
1. A program that does not compile will result in a zero
2. Runtime error and compilation warning 5%
3. Commenting and style 15%
4. Report 10%
5. Functionality 70% (functions were declared and implemented as required)
9
Introduction
You are required to implement three tree data structures: a general tree, a heap
tree, and an AVL tree. No tree should contain duplicate values. You are also
required to create UML diagrams for each of the classes that you implement.
Finally, you have to provide the means to test your system by developing a
menu program that allows the user to manipulate your structures.
It is strictly prohibited to use the structures and/or algorithms defined in
the C++ standard library (STL). So, if your design requires a list, queue, stack,
or a hash table, you can only use your own implementations.
Underflow exceptions might be generated in some of the functions you implement. Make sure exceptions are thrown and caught where appropriate.
Deliverables
• A 1 page report with your UML diagrams that explains the design of your
data structures. Please include what each teammate did and approximate
hours spent on the project.
• An implementation of a general tree.
• An implementation of a heap tree.
• An implementation of an AVL tree.
• A menu program to test the implemented data structures.
1 General Tree
In this part of the project, you need to implement two classes, a TreeNode Class
and a LinkedTree Class; create their respective UML diagrams. Your TreeNode
class can be used for all trees (not all trees will use all data members). If you
would like to include further data members you may although it is not necessary.
Some of the methods are the same but have different names, you may feel free
to rename them as you see fit as long as they are descriptive. Calculate the
running time of your functions and include them in your report.
1
1.1 Description Trees, Trees, and more Trees
1.1 Description
A tree is a structure that is formed by Nodes (vertices) and Edges (arcs). Edges
connect nodes together. Any two nodes in the tree are connected by one and
only one path.
1.2 Data Members
Specify all the data members your implementation needs. You are required to
instantiate a TreeNode object for each of the nodes in the tree. Each node has a
key(int) - for Heap tree only, value (Type), balanceFactor (short int: -1 for
right high, 0 for balanced, 1 for left high) - for AVL tree only, and a parent,
left and right child (pointers for General and AVL tree, unused for Heap tree
because it is an array implementation).
1.3 Member Functions
Constructors
defines constructor.
Destructor
defines destructor.
Accessors
getRoot() returns the root of the tree.
getSize() returns number of elements in the tree.
getHeight() returns the height of the three.
getHeight(node) returns the height of the node in the argument (from
the root).
empty() returns true if the tree is empty, false otherwise.
leaves() returns the number of leaves in the tree.
siblings(node) returns the number of siblings of the node in the argument.
findNode(data) returns a pointer to a node that holds the data in the
argument.
2
1.3 Member Functions Trees, Trees, and more Trees
preorder() performs preorder traversal.
postorder() performs postorder traversal.
inorder() performs in order traversal.
Mutators
clear() removes all the elements in the tree
insert(data) inserts data in the tree.
del(data) removes data from the tree.
Friends
no friends for this class.
3
Trees, Trees, and more Trees
2 Heap
In this part of the project, you need to implement an additional MaxHeapTree
Class; create the UML diagram. Calculate the running time of your functions
and include them in your report.
2.1 Description
A priority queue is like a dictionary in the sense that it stores entries (key,value).
However, a dictionary is used when you want to look up a particular key. A
priority queue is used when you want to prioritize entries. There is a total order
defined on the keys. The main operations that a priority key allows to do are:
• Identify or remove the entry that has the smallest (largest) key. It is the
only one that could be removed quickly.
• Insert anything you want in any time.
A binary heap is a particular implementation of the priority queue abstract
data type. ‘A heap data structure should not be confused with the
heap which is a common name for the pool of memory from which
dynamically allocated memory is allocated’. Its definition encompasses
several things:
• Identify or remove the entry that has the smallest (or largest) key. It is
the only one that can be removed quickly.
• Insert anything you want at a more specific location in the tree.
For this part of the project you will implement a max heap and all of its
operations. Entries are stored in a dynamic array. If an entry is being inserted,
and the array is already full, the capacity of the array is doubled. If, after
removing an entry from the heap, and the number of entries is one-quarter
(1/4) the capacity of the array, then the capacity of the array is halved. The
capacity of the array may not be reduced below the initially specified (by you)
capacity.
2.2 Data Members
Specify all the data members your implementation needs. You are required to
instantiate a TreeNode object for each of the nodes in the tree. Your nodes have
a key (integer) and a value (Type), and they are stored in a dynamic array.
2.3 Member Functions
Constructors
defines constructor.
4
2.3 Member Functions Trees, Trees, and more Trees
Destructor
defines destructor.
Accessors
getMax() returns the root of the tree.
getSize() returns number of elements in the tree.
getHeight() returns the height of the tree.
empty() returns true if the tree is empty, false otherwise.
leaves() returns the number of leaves in the tree.
print() prints the heap.
Mutators
clear() removes all the elements in the tree
insert(key,data) inserts data in the tree. This operation must satisfied
the heap property.
delMax() removes the entry specified by maximum key in the tree. This
operation must satisfied the heap property.
Friends
defines friends for this class.
5
Trees, Trees, and more Trees
3 AVL Tree
In this part of the project, you need to implement an additional AVL Class;
create the UML diagram. Calculate the running time of your functions and
include them in your report.
3.1 Description
A binary search tree (BST) is a powerful tool to quickly search values in a tree.
However, if the BST is not balanced its operations can degenerate to linear
behavior, which makes them no faster than lists.
An AVL tree is a BST that includes complicated updating rules to keep
the tree balanced. An AVL tree requires that the height of the left and right
children of every node to differ by at most ± 1. Simple and double rotation are
executed when inserting or deleting an entry to/from the tree.
3.2 Data Members
Specify all the data members your implementation needs. You are required to
instantiate a TreeNode object for each of the nodes in the tree. Each node has
a value (Type), and access to its parent, left and right child.
3.3 Member Functions
Constructors
defines constructor.
Destructor
defines destructor.
Accessors
getRoot() returns the root of the tree.
getSize() returns number of elements in the tree.
getHeight() returns the height of the tree.
getHeight(node) returns the height of the node in the argument (from
the root).
empty() returns true if the tree is empty, false otherwise.
leaves() returns the number of leaves in the tree.
6
3.3 Member Functions Trees, Trees, and more Trees
siblings(node) returns the number of siblings of the node in the argument.
find(data) returns a pointer to a node that holds the data in the argument.
preorder() performs preorder traversal.
postorder() performs postorder traversal.
inorder() performs inorder traversal.
inorder() performs inorder traversal.
Mutators
clear() removes all the elements in the tree
insert(data) inserts data in the tree. Tree must be kept balanced after
the insertion.
del(data) removes data from the tree. Tree must be kept balanced after
the deletion.
Friends
defines friends for this class.
7
Trees, Trees, and more Trees
4 The Menu Program
In order to test your program, you are required to implement a menu program
that provides the means to run each of the functions in your classes (name your
executable proj3). Please choose the string data type for the values (or ’data’)
of your entries. The TA will choose one group to demo the project.
Format for the Menu Program
First, take a character, ’g’, ’h’, or ’a’ (lowercase) that specifies whether we will
be working with a general tree, a heap, or an AVL tree, respectively, and creates
an instance of the tree. Next, give the options for each specific tree (please have
them in this EXACT order for grading purposes):
General Tree or AVL Tree
1. Return root
2. Return size
3. Return height
4. Return height (node)
5. Is tree empty?
6. Return number of leaves
7. Return number of siblings (node)
8. Find node (data)
9. Print preorder
10. Print postorder
11. Print inorder
12. Clear tree
13. Insert (data)
14. Delete (data)
15. Exit
Max Heap
1. Return root
2. Return size
3. Return height
4. Is tree empty?
5. Return number of leaves
6. Print
7. Clear tree
8. Insert (key, data)
9. Delete
10. Exit
8
Trees, Trees, and more Trees
Submit the following files to Canvas (named EXACTLY as shown below
without zipping for grading purposes: (you may also include implementation
files with the header files if you would like)
1. menu.cpp
2. treeNode.h
3. linkedTree.h
4. maxHeapTree.h
5. avlTree.h
6. makefile (name your executable ’proj3’)
7. project3.pdf
The rubric is as follows:
1. A program that does not compile will result in a zero
2. Runtime error and compilation warning 5%
3. Commenting and style 15%
4. Report 10%
5. Functionality 70% (functions were declared and implemented as required)
9
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