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- 首页 >> Matlab编程 Assignment Two
Objectives
• Understand how AVL tree works
• Understand how to design an efficient algorithm
• Give you further practice with time complexity analysis of algorithms
• Give you further practice with C and data structures
Admin
Marks 12 marks. Marking is based on the correctness and efficiency of your code. Your
code must be well commented.
Group? This assignment is completed individually.
Due Time 09:59:59pm on Sunday 4 April 2021.
Late Submissions Late submissions will not be accepted!
In this assignment, you will implement AVL tree and a set of functions associated with AVL
tree. For simplicity, we make the following assumptions:
1. Each item of an AVL tree contains an integer key and an integer value.
2. No AVL tree contains duplicate items. Two items (k1, v1) and (k2, v2) are duplicates
iff k1=k2 and v1=v2 hold.
3. An AVL tree may contain multiple items with the same key.
A template file named MyAVLTree.c is provided. MyAVLTree.c contains the type definitions of
AVL tree and AVL tree node as well as some basic functions. You can add your own helper
functions and auxiliary data structures for better performance in terms of time complexity.
You need to implement the following functions:
1. AVLTree *CreateAVLTree(const char *filename). This function creates an AVL tree by
reading all the items from a text file or from the standard input (keyboard)
depending on the argument filename. If filename is “stdin”, this function will read all
the items from the standard input. Otherwise, it will read all the items from a text
file with filename as its full path name. (2 marks)
An input text file contains zero or more items where each item is of the form (key,
value). Any characters such as white space between two adjacent items are ignored.
For example, the following sample file contains 10 items:
(2, 50) (4, 30) (9, 30) (10, 400) (-5, -40)
(7, 20) (19, 200) (20, 50) (-18, -200) (-2, 29)
Similarly, when reading from the standard input, each input line may have zero or
more items, separated by one or more white space characters. An empty line
indicates the end of input.
In case of an error in the input, this function will print the error and your program
terminates.
You may assume that the input does not contain duplicate items and thus this
function does not need to check for duplicate items.
The time complexity of this function cannot be higher than O(n logn), where n is the
size of the resulting AVL tree. If your time complexity is higher, you will get 0 mark
for this function. You may assume that each call to a C built-in function takes O(1)
time.
2. AVLTree *CloneAVLTree(AVLTree *T). This function creates an identical copy (clone)
of the input AVL tree T, and returns a pointer to the clone tree. (1 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get at most 0.5 mark depending on
your time complexity.
3. AVLTree *AVLTreesUnion(AVLTree *T1, AVLTree *T2). This function computes the
union tree of two AVL trees T1 and T2 and returns a pointer to the union tree. The
union tree of two AVL trees T1 and T2 is an AVL tree that contains all the items of
both T1 and T2 without duplicate items. Assume that neither T1 nor T2 contains
duplicate items. (3 marks)
The time complexity of this function cannot be higher than O(m+n), where m and n
are the sizes of T1 and T2, respectively. If your time complexity is higher, you will get
at most 1.5 marks depending on your time complexity.
An example: consider the following two AVL trees T1 and T2:
The union tree of T1 and T2 is shown as follows:
Note that in general the union tree may not be unique with respect to shape
(structure) depending on how it is constructed.
4. AVLTree *AVLTreesIntersection(AVLTree *T1, AVLTree *T2). This function computes
the intersection tree of two AVL trees T1 and T2 and returns a pointer to the
intersection tree. The intersection tree of two AVL trees T1 and T2 is an AVL tree
that contains all the items that appear in both T1 and T2. Assume that neither T1 nor
T2 contains duplicate items. (3 marks)
The time complexity of this function cannot be higher than O(m+n), where m and n
are the sizes of T1 and T2, respectively, and k the size of the intersection tree. If your
time complexity is higher, you will get t most 1.5 marks depending on your time
complexity.
An example: consider the previous two AVL trees T1 and T2. The intersection tree is
shown as follows:
Note that in general the intersection tree may not be unique with respect to shape
(structure) depending on how it is constructed.
5. int InsertNode(AVLTree *T, int k, int v). If the item (k, v) exists in the tree, this
function simply returns 0 without adding the new item (k, v) to the tree. Otherwise,
it inserts the new item (k, v) into the AVL tree T, increases the tree size by one and
returns 1. (0.5 mark)
The time complexity of this function cannot be higher than O(log n), where n is the
size of T. If your time complexity is higher, you will get 0 mark for this function.
6. int DeleteNode(AVLTree *T, int k, int v). If the item (k, v) exists in the AVL tree T, this
function deletes the node containing this item, decreases the tree size by one and
returns 1. Otherwise, it returns 0 only. (1 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function.
7. AVLTreeNode *Search(AVLTree *T, int k, int v). This function search for the item (k,
v) in the AVL tree T. If the item is found, it returns a pointer to the node containing
the item. Otherwise, it returns NULL. (0.5 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function.
8. void FreeAVLTree(AVLTree *T). This function frees up the heap space occupied by
the AVL tree T. (0.5 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function. You may
assume that each call to free() takes O(1) time.
9. void PrintAVLTree(AVLTree *T). This function prints all the items stored in the AVL
tree T sorted in non-decreasing order of keys on the standard output (screen). Each
item is denoted by (key, value) with one item per line. (0.5 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function. You may
assume that each call to a built-in C function takes O(1) time.
For each function, analyze its time complexity, and put the time complexity analysis as
comments before the function. For the time complexity of each function, you just need to give
the time complexity of major components (loops) and the total time complexity. You may
assume that each call to a built-in C function takes constant (O(1)) time.
How to submit your code?
a. Go to the assignment page
b. Click on Assignment Specifications for Assignment 2
c. Click on Make Submission
d. Submit your MyAVLTree.c file that contains all the code.
Plagiarism
This is an individual assignment. Each student will have to develop their own solution without
help from other people. In particular, it is not permitted to exchange code or pseudocode.
You are not allowed to use code developed by persons other than yourself. All work
submitted for assessment must be entirely your own work. We regard unacknowledged
copying of material, in whole or part, as an extremely serious offence. For further information,
see the Course Information.
Objectives
• Understand how AVL tree works
• Understand how to design an efficient algorithm
• Give you further practice with time complexity analysis of algorithms
• Give you further practice with C and data structures
Admin
Marks 12 marks. Marking is based on the correctness and efficiency of your code. Your
code must be well commented.
Group? This assignment is completed individually.
Due Time 09:59:59pm on Sunday 4 April 2021.
Late Submissions Late submissions will not be accepted!
In this assignment, you will implement AVL tree and a set of functions associated with AVL
tree. For simplicity, we make the following assumptions:
1. Each item of an AVL tree contains an integer key and an integer value.
2. No AVL tree contains duplicate items. Two items (k1, v1) and (k2, v2) are duplicates
iff k1=k2 and v1=v2 hold.
3. An AVL tree may contain multiple items with the same key.
A template file named MyAVLTree.c is provided. MyAVLTree.c contains the type definitions of
AVL tree and AVL tree node as well as some basic functions. You can add your own helper
functions and auxiliary data structures for better performance in terms of time complexity.
You need to implement the following functions:
1. AVLTree *CreateAVLTree(const char *filename). This function creates an AVL tree by
reading all the items from a text file or from the standard input (keyboard)
depending on the argument filename. If filename is “stdin”, this function will read all
the items from the standard input. Otherwise, it will read all the items from a text
file with filename as its full path name. (2 marks)
An input text file contains zero or more items where each item is of the form (key,
value). Any characters such as white space between two adjacent items are ignored.
For example, the following sample file contains 10 items:
(2, 50) (4, 30) (9, 30) (10, 400) (-5, -40)
(7, 20) (19, 200) (20, 50) (-18, -200) (-2, 29)
Similarly, when reading from the standard input, each input line may have zero or
more items, separated by one or more white space characters. An empty line
indicates the end of input.
In case of an error in the input, this function will print the error and your program
terminates.
You may assume that the input does not contain duplicate items and thus this
function does not need to check for duplicate items.
The time complexity of this function cannot be higher than O(n logn), where n is the
size of the resulting AVL tree. If your time complexity is higher, you will get 0 mark
for this function. You may assume that each call to a C built-in function takes O(1)
time.
2. AVLTree *CloneAVLTree(AVLTree *T). This function creates an identical copy (clone)
of the input AVL tree T, and returns a pointer to the clone tree. (1 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get at most 0.5 mark depending on
your time complexity.
3. AVLTree *AVLTreesUnion(AVLTree *T1, AVLTree *T2). This function computes the
union tree of two AVL trees T1 and T2 and returns a pointer to the union tree. The
union tree of two AVL trees T1 and T2 is an AVL tree that contains all the items of
both T1 and T2 without duplicate items. Assume that neither T1 nor T2 contains
duplicate items. (3 marks)
The time complexity of this function cannot be higher than O(m+n), where m and n
are the sizes of T1 and T2, respectively. If your time complexity is higher, you will get
at most 1.5 marks depending on your time complexity.
An example: consider the following two AVL trees T1 and T2:
The union tree of T1 and T2 is shown as follows:
Note that in general the union tree may not be unique with respect to shape
(structure) depending on how it is constructed.
4. AVLTree *AVLTreesIntersection(AVLTree *T1, AVLTree *T2). This function computes
the intersection tree of two AVL trees T1 and T2 and returns a pointer to the
intersection tree. The intersection tree of two AVL trees T1 and T2 is an AVL tree
that contains all the items that appear in both T1 and T2. Assume that neither T1 nor
T2 contains duplicate items. (3 marks)
The time complexity of this function cannot be higher than O(m+n), where m and n
are the sizes of T1 and T2, respectively, and k the size of the intersection tree. If your
time complexity is higher, you will get t most 1.5 marks depending on your time
complexity.
An example: consider the previous two AVL trees T1 and T2. The intersection tree is
shown as follows:
Note that in general the intersection tree may not be unique with respect to shape
(structure) depending on how it is constructed.
5. int InsertNode(AVLTree *T, int k, int v). If the item (k, v) exists in the tree, this
function simply returns 0 without adding the new item (k, v) to the tree. Otherwise,
it inserts the new item (k, v) into the AVL tree T, increases the tree size by one and
returns 1. (0.5 mark)
The time complexity of this function cannot be higher than O(log n), where n is the
size of T. If your time complexity is higher, you will get 0 mark for this function.
6. int DeleteNode(AVLTree *T, int k, int v). If the item (k, v) exists in the AVL tree T, this
function deletes the node containing this item, decreases the tree size by one and
returns 1. Otherwise, it returns 0 only. (1 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function.
7. AVLTreeNode *Search(AVLTree *T, int k, int v). This function search for the item (k,
v) in the AVL tree T. If the item is found, it returns a pointer to the node containing
the item. Otherwise, it returns NULL. (0.5 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function.
8. void FreeAVLTree(AVLTree *T). This function frees up the heap space occupied by
the AVL tree T. (0.5 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function. You may
assume that each call to free() takes O(1) time.
9. void PrintAVLTree(AVLTree *T). This function prints all the items stored in the AVL
tree T sorted in non-decreasing order of keys on the standard output (screen). Each
item is denoted by (key, value) with one item per line. (0.5 mark)
The time complexity of this function cannot be higher than O(n), where n is the size
of T. If your time complexity is higher, you will get 0 mark for this function. You may
assume that each call to a built-in C function takes O(1) time.
For each function, analyze its time complexity, and put the time complexity analysis as
comments before the function. For the time complexity of each function, you just need to give
the time complexity of major components (loops) and the total time complexity. You may
assume that each call to a built-in C function takes constant (O(1)) time.
How to submit your code?
a. Go to the assignment page
b. Click on Assignment Specifications for Assignment 2
c. Click on Make Submission
d. Submit your MyAVLTree.c file that contains all the code.
Plagiarism
This is an individual assignment. Each student will have to develop their own solution without
help from other people. In particular, it is not permitted to exchange code or pseudocode.
You are not allowed to use code developed by persons other than yourself. All work
submitted for assessment must be entirely your own work. We regard unacknowledged
copying of material, in whole or part, as an extremely serious offence. For further information,
see the Course Information.