Description
This assignment covers learning objective 1: An understanding of basic data structures, including stacks, queues, and trees; learning objective 3: An ability to apply appropriate sorting and
search algorithms for a given application.
This assignment is to be completed on your own. You will implement Shell sort on an array
and Shell sort on a linked list. In both cases, you will use the following sequence for Shell sort:
{h(1) = 1,h(2) = 4,h(3) = 13,…,h(i),h(i+1) = 3×h(i) +1,…,h(p)
where h(p) is the largest number in the sequence that is smaller than the size of the array to be
sorted.
You are not allowed to pre-compute the sequence and store them in your program. The sequence has to be generated (but not stored) as part of your Shell sort functions.
Functions to be written
We provide you three .h files: shell array.h, shell list.h, and list of list.h. You
will develop the functions declared in these shell array.h and shell list.h files in the corresponding .c files: shell array.c and shell list.c. These .c files and pa1.c are the only
files you will submit for this assignment.
If you need additional helper functions, you should define them in the corresponding .c files.
It is best that these helper functions be declared as static. Do not name these help functions with a
prefix of two underscores ” ”.
You are allowed to use only structures defined in shell list.h and list of list.h in
this assignment. You are not allowed to define new structures.
Do not modify the provided .h files because you are not submitting them. Any modifications
you have made to the provided .h will not be reflected in the .h files that we use to evaluate your
submission.
Functions you will write for shell array.c:
There are three functions that deal with performing Shell sort on an array. The first two functions Array Load From File and Array Save To File, are not for sorting, but are needed to
transfer the long integers to be sorted from and to a file in binary form to and from an array,
respectively.
long *Array Load From File(char *filename, int *size)
The size of the binary file whose name is stored in the char array pointed to by filename
should determine the number of long integers in the file. The size of the binary file should be a
multiple of sizeof(long). You should allocate sufficient memory to store all long integers in the
file into an array and assign to *size the number of integers you have in the array. The function
should return the address of the memory allocated for the long integers.
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You may assume that all input files that we will use to evaluate your code will be of the correct
format.
Note that we will not give you an input file that stores more than INT MAX long integers (see
limits.h for INT MAX). If the input file is empty, an array of size 0 should still be created and
*size be assigned 0. You should return a NULL address and assign 0 to *size if you could not
open the file or fail to allocate sufficient memory.
It is important that the caller function, e.g., the main function, has an int variable to store the
size of the array, and pass the address of this variable into long *Array Load From File(char
*filename, int *size) using the size parameter.
int Array Save To File(char *filename, long *array, int size)
The function saves array to an external file specified by filename in binary format. The
output file and the input file have the same format. The integer returned should be the number of
long integers in the array that have been successfully saved into the file.
If array is NULL or size is 0, an empty output file should be created.
void Array Shellsort(long *array, int size, long *n comp)
The function takes in an array of long integers and sort them (using the Shell sorting algorithm). size specifies the number of integers to be sorted, and *n comp should store the number
of comparisons involving items in array throughout the entire process of sorting. This function
will have to use the sequence {h(1) = 1,h(2) = 4,h(3) = 13,…,h(i),h(i+1) = 3×h(i) +1,…}
for sorting. You may choose to use insertion sort or bubble sort to sort each sub-array. (If you use
selection sort to sort each sub-array, your program will most likely have high run-time complexity.
Why?)
A comparison that involves an item in array, e.g., temp < array[i] or array[i] < temp,
corresponds to one comparison. A comparison that involves two items in array, e.g., array[i]
< array[i-1], also corresponds to one comparison. Comparisons such as i < j where i or j
are indices are not considered as comparisons for this programming assignment.
It is important that the caller function, e.g., the main function, has a long integer variable to
store the number of comparisons, and pass the address of this variable into void Array Shellsort(long
*array, int size, long *n comp) using the n comp parameter.
Any support functions for these three functions, if any, must reside in shell array.c. It is
best that these helper functions be declared as static. Do not name these help functions with a
prefix of two underscores ” ”.
Functions you will have to write for shell list.c:
There are also three functions that deal with performing Shell sort on a linked list. In this
assignment, you will use the following user-defined type to store integers in a linked list:
typedef struct Node {
long value;
struct Node *next;
} Node;
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This structure has been defined in shell list.h. Given the definition of the structure Node,
these are the three functions you have to write to deal with performing Shell sort on a linked list:
Node *List Load From File(char *filename)
The load function should read all (long) integers in the input file into a linked-list and return
the address pointing to the first node in the linked-list. The linked-list must contain as many nodes
as the number of long integers in the file. You should not have additional nodes in the linked list.
Moreover, the long integers should be stored in the same order in the linked-list as they are
stored in the file. In other words, the first (last) long integer in the input file is the long integer
stored in the first (last) node of the list.
int List Save To File(char *filename, Node *list)
The save function should write all (long) integers in a linked-list into the output file in the order
in which they are stored in the linked list. This function returns the number of integers successfully
written into the file.
Node *List Shellsort(Node *list, long *n comp)
The Shell sort function takes in a list of long integers and sort them. To correctly apply Shell
sort, you would have to know the number of elements in the list and compute the sequence used
for sorting accordingly. The address pointing to the first node of the sorted list is returned by the
function. Similar to the case of an array, a comparison here is defined to be any comparison that
involves the field value in the structure Node. Note that if you are given a list of n Nodes, you
should return a sorted list of n Nodes.
100
addr: 30
104
addr: 40
12
addr: 50
99
addr: 20
9
addr: 10
NULL
(a) Original list
(b) Sorting by manipulating addresses of Nodes
100
addr: 30
104
addr: 40
12
addr: 50
99
addr: 20
9
addr: 10
NULL
40
value next
50 20 10 0
40 0 20 30 50
The List Shellsort function must perform sorting by manipulating the next fields of the
Nodes. Figure (a) shows an original list that is unsorted. Figure (b) shows how the list is sorted
by storing the correct addresses in the next fields. The long integers stored in the value fields
remain in the original Nodes. For example, the integer 99 is stored in a Node with an address 20
in the original list. The field of the same Node stores the address 10, allowing it to point to the
Node storing the value 9.
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After sorting, 99 is still stored in the value field of the Node with address 20. However, the
next field of the Node now stores 30, allowing it to point to the Node storing the value 100.
In other words, each long integer must reside in the same Node in the original list before and
after sorting.
You are not allowed to have arrays (of any types) in this file. Therefore, you cannot divide
a list into sub-lists and use an array to store these sub-lists. This restriction also applies to all
helper functions of List Shellsort.
If you want to divide a list into sub-lists, you must use a list of linked-lists to maintain these
sub-lists. You may use the following user-defined type to store a linked-list of linked-lists. To be
exact, the following structure can be used to implement a linked-list of addresses pointing to the
Node structure.
typedef struct List {
Node *node;
struct List *next;
} List;
This structure is probably useful for you to maintain k linked-lists, where k is a number in your
sequence. However, it is not necessary that you use this structure in your implementation. My
implementation uses only the structure Node. You may have a faster run-time if you use a list of
linked-lists. Using only the structure Node may slow down the sorting.
If you want to use the List structure in shell list.c, you must include the file list of list.h
in the shell list.c.
Any additional helper functions should be defined in shell list.c file. It is best that these
helper functions be declared as static. Do not name these helper functions with a prefix of two
underscores ” ”.
It is important that the linked list returned from and/or passed into these three functions in
shell list.c contain only nodes that store valid values.
main function you will write in pa1.c:
You have to write another file called pa1.c that would contain the main function to invoke the
functions in shell array.c and shell list.c.
You should be able to obtain the executable pa1 with the following command:
gcc -O3 -std=c99 -Wall -Wshadow -Wvla -pedantic shell_array.c shell_list.c pa1.c -o pa1
The flags used are very similar to the flags used in ECE264, except that the -Werror flag has
been taken out. Also, the optimization flag -O3 is used. It is recommended that while you are
developing your program, you use the “-g” flag instead of the “-O3” flag for compilation so that
you can use a debugger if necessary. It is your responsibility to make sure that your submission
can be complied successfully on ecegrid. Just to be sure, you should type in alias gcc at the
command line and check whether your gcc uses the correct set of flags.
When the following command is issued,
./pa1 -a input.b output.b
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the program should load from input.b the long integers to be sorted and store them in an array,
run Shell sort on the array, and save the sorted long integers in output.b. The program should
also print the number of comparisons performed to the standard output with the format ”%ld\n”.
When the following command is issued,
./pa1 -l input.b output.b
the program should load from input.b the long integers to be sorted and store them in a linkedlist, run Shell sort on the linked-list, and save the sorted long integers in output.b. The program
should also print the number of comparisons performed to the standard output with the format
”%ld\n”.
What should the main function do when an empty file or an invalid file is given?
For the “-a” option, the load function (Array Load From File) returns a NULL address if you
could not open the file or fail to allocate sufficient memory. The main function should exit with
EXIT FAILURE when the returned address of the load function is NULL.
For an empty file, the load function should return a valid array of size 0. Therefore, an empty
output file should be created.
For the “-l” option, the current setup does not allow you to distinguish between an empty file
or an invalid input filename (they both will result in an empty linked list from the load function
(List Load From File) for linked-lists). Therefore, you should continue to perform sorting and
writing (an empty output file).
You may declare and define other (static) helper functions in pa1.c.
Submission and Grading:
The assignment requires the submission (electronically) of a zip file called pa1.zip through
Brightspace. The zip file should contain shell array.c, shell list.c, and pa1.c. We do not
expect you to turn in a Makefile because we are going to evaluate your functions individually.
Any other files in the zip file will be discarded. Your zip file should not contain a folder (that
contains the source files). Assuming that your folder contains shell array.c, shell list.c,
and pa1.c, you can create pa1.zip as follows:
zip pa1.zip shell_array.c shell_list.c pa1.c
It is important that if the instructor has a working version of pa1.c, it should be compilable with your shell array.c and shell list.c to produce an executable. Similarly, if the
instructor has a working version of shell array.c, it should be compilable with your pa1.c and
shell list.c to produce an executable. For evaluation purpose, we will use different combinations of your submitted .c files and our .h and .c files to generate different executables. If a
particular combination does not allow an executable to be generated, you do not get any credit for
the function(s) that the executable is supposed to evaluate.
The loading and saving functions will account for 20 points. The Shellsort function for arrays
will account for 30 points. The Shellsort function for lists will account for 50 points. The main
function does not account for any points. However, if your main function does not work properly,
we will deduct up to 5 points.
Be aware that we set a time-limit for each test case based on the size of the test case. If your
program does not complete its execution before the time limit for a test case, it is deemed to have
failed the test case. We will not announce the time-limits that we will use. You should instead
analyze whether your implementation has the expected time complexity through the numbers of
comparisons or the runtimes for various test cases. You can obtain the runtime using the command
time, e.g., time ./pa1 -l input.b output.b.
It is important all the files that have been opened are closed and all the memory that have
been allocated are freed before the program exits. A caller function that receives heap memory should be responsible for freeing it. For example, if the instructor’s main function calls
the Array Load From File function, it is the responsibility of the main function to free the
returned array. It is not the responsibility of the Array Shellsort or Array Save To File
to free the array. Memory issues will result in 50-point penalty.
Given:
We provide the .h files and sample input files in pa1 examples.zip. All “.b” files are binary
files. The number in the name refers to the number of long integers the file is associated with. For
example, 15.b contains 15 long integers, 15sa.b contains 15 sorted long integers from 15.b. In
particular, 15sa.b is created by pa1 by the following command:
./pa1 -a 15.b 15sa.b
My implementation of pa1 prints the following output to the screen when the above command
is issued:
60
My implementation of pa1 prints the following output to the screen when the following command is issued:
./pa1 -l 15.b 15sl.b
121
My implementation of pa1 also created 1Ksa.b and 1Ksl.b. Of course, 15sa.b and 15sl.b
are identical and 1Ksa.b and 1Ksl.b are also identical. For the input files 10K.b, 100K.b, and
1M.b, the output files of my implementation of pa1 are not included.
Your implementation should not try to match the number of comparisons that my implementation reported. That is not the purpose of the assignment.
Getting started:
Copy over the files from the Brightspace website. Any updates to these instructions will be
announced through Brightspace.
Given that the input files are in binary format, you probably want to write some helper functions
to print the array of long integers before and after sorting in text (instead of binary) for debugging
purpose. Keep in mind that fread and fwrite for binary files are analogous to fscanf and
fprintf for text files.
If you want to perform Shell sort on a linked list without dividing the list into several sub-lists,
it is easier to implement bubble sort in your Shell sort routine. (This is a rare example when bubble
sort is more useful than insertion sort.)
To perform insertion sort on a linked list, ask yourself whether it is easier to form a complete
list and then perform insertion sort, or it is easier to insert an item into a sorted list in the right
order.
If you want to divide a linked list into several sub-lists, you should ask yourself the question of
how the “sortedness” of a linked list affect the time complexity of insertion sort.
You also have to ask the question of whether you have performed (Shell) sorting correctly. If
the array of long integers is in ascending order after sorting, have you sorted correctly?
As you have to generate the sequence for Shell sort in shell array.c and shell list.c,
there will be similar lines of code in both .c files. While we do not encourage that in general, for
the purpose of this assignment, we will reluctantly allow you to copy-and-paste these lines of code.
This assignment is about performing Shell sort. If you implement other sorting algorithms,
your submission does not meet the specifications of the assignment. Your program will not earn
the relevant credits if it does not meet the specifications.
Other than the required output to stdout as specified, do not print other messages to stdout.
If you want to print error messages for debugging purposes, use fprint to print the messages to
stderr. If your program produces messages that are not expected, your submission does not meet
the specifications of the assignment and it will not earn the relevant credits.
We will use valgrind to check for memory issues. While you are most familar with memory
leaks, valgrind can be useful in helping you find the cause of a segmentation fault and identify
allocated memory locations that have not been initialized properly. The tool is useful only when
you pay attention to all messages that valgrind reports. One useful programming habit is to keep
your code valgrind-clean at any stage of programming. In other words, do not leave any memory
issues unresolved at any stage of programming.
Another good habit to cultivate is to pay attention to the number of memory allocations made
by your program. Does the number of memory allocations reported by valgrind match your
expectation? For example, I expect my pa1 to make 3 allocations for Shell sorting an array, and
18 allocations for Shell sorting a list of 15 integers (without splitting the linked list into sublists).
Why do we need 3 and 17 allocations, respectively?
