### Spring 2019 :: ECE 264 :: Purdue University

⚠ This is for Spring 2019, not the current semester.
Due 2/28

# Sorting

## Goals

The goals of this assignment are as follows:
1. Practice writing code using linked lists and binary search trees (dynamic structures).
2. Practice writing code using recursion.
3. Learn to use function addresses (function pointers).
4. Learn to use the `qsort(…)` function.
5. Gain some perspective on different sorting algorithms.

## Overview

In this assignment, you will implement the merge sort algorithm for linked lists. To add some perspective, you will also implement a tree sort (based on binary search trees) and write a wrapper function for the standard `qsort(…)` function, an implementation of the quicksort algorithm. However, the main focus on merge sort and linked lists.

There are no starter files.

// Credit: Wikipedia user 'Swfung8', License: CC BY-SA

Recursion is an elegant method for solving many problems. At first it can seem unnatural; however, it is actually very simple once you are used to it. The key thing to understand is that recursive programming has two steps:

1. A base case which is trivial.
2. A recursive case where you write the solution for the larger case in terms of the solution to smaller cases.

What makes (2) easy is that you simply assume that you have the solution of a smaller case. Life does not generally let you assume you have a solution that you have not yet found; however, if you think about it, it should be obvious (by induction) that recursion works this way.

In this assignment, we will use (1) and (2) above to sort linked-lists of integers using the "merge-sort" algorithm. Merge-sort is a beautiful algorithm that sorts extremely quickly with large inputs. It is also the best possible algorithm to use for sorting linked-lists.

Merge sort works as follows:

1. Base case:
You never need to sort a list of length 0 or 1; it is already "sorted", so-to-speak. To implement the base case, simply return the input list if its length is 0 or 1. (In general, base cases are trivial like this.)
2. Recursive case:
Lets wave our hand, and assume that we know how to sort smaller lists already. (See, recursion is easy.) For the recursive case, we do the following:
1. Divide the list into two smaller lists of equal size, +/- one node.
2. Recursively sort each of the two smaller lists. (Wow: easy.)
3. You now have two small lists that are sorted. To produce the final large sorted list, you "merge" the two smaller lists together.
1. Create a brand new empty list, which will be the result-list.
2. While both small lists are non-empty, look at the head node of each. Take the smaller head node off of the front of its list, and append it to the result-list.
3. Eventually one (or perhaps both) of the smaller lists will be empty. At this stage, append the non-empty list (if there is one) onto the end of the result-list.

// Credit: Aaron Michaux, Prof. Yung-Hsiang Lu … This description adapted from a previous ECE 264 assignment

## Requirements

1. Your submission must contain each of the following files, as specified:
2. file contents
sorts.h type definitions
List
struct type with 3 fields: `head` (ListNode*), `tail` (ListNode*) and `size` (int)
• Whenever `size`==0, `head` and `tail` must be NULL.
ListNode
struct type with 2 fields: `value`(int), `next` (ListNode*)
BST
struct type with 2 fields: `root` (BSTNode*) and `size` (int).
• Whenever `size`==0, `root` must be NULL.
BSTNode
struct type with 3 fields: `value`(int), `left`, and `right` (BSTNode*)
function declarations one for each required function in your sorts.c
• Do not include helpers (if any) here.
sorts.c function definitions
`merge sort array(int✶ array, size t size)`
return type: void
Sort `array` using `merge_sort_list(…)`.
• Do not merge sort the array directly. This must use your `merge_sort_list(…)`.
• Store the result in the same array that was passed in.
• Steps: ① call `create_list(…)`, ② call `merge_sort_list(…)`, ③ store the sorted values in `array` (same memory), ④ call `empty_list(…)`.
• The purpose is to make `merge_sort_list(…)` comparable with the other sort functions.
• This may not result in any heap allocation (i.e., calls to `malloc(…)`), except for the list nodes allocated as a result of calling `create_list(…)`; those must be freed before this function returns.
`tree sort array(int✶ array, size t size)`
return type: void
Sort `array` by creating a BST and then traversing it.
• Steps: ① call `create_bst(…)`, ② use in-order traversal to store sorted values in `array` (same memory), ③ call `empty_bst(…)`.
• Store the result in the same array that was passed in.
• This may not result in any heap allocation (i.e., calls to `malloc(…)`), except for the BST nodes allocated as a result of calling `create_bst(…)`; those must be freed before this function returns.
`quick sort array(int✶ array, size t size)`
return type: void
Sort `array` using the `qsort(…)` standard library function.
• This should simply call the `qsort(…)` library function.
• The `qsort(…)` function requires the use of function addresses (function pointers).
• This may not result in any heap allocation (i.e., calls to `malloc(…)`) by your code.
• Yes, this is easy, but make sure you understand how it works!
`create list(const int✶ array, int size)`
return type: List
Create a new `List`.
• `size` is the number of elements in `array`.
• When size==0 array must be NULL and vice versa.
• If size==0 then return a list with the head and tail set to NULL.
• `malloc(…)` may be called from a total of one place in this function and any it depends on.
`merge sort list(List✶ a list)`
return type: void
Merge sort `list`.
• This may not result in any heap allocation (i.e., calls to `malloc(…)`).
`empty list(List✶ a list)`
return type: void
Free all the nodes in the list.
• Set `head` and `tail` to NULL, and `size` to 0.
• `free(…)` may be called from a total of one place in this function and any it depends on.
`create bst(const int✶ array, int size)`
return type: BST
Create a new `BST`.
• `size` is the number of elements in `array`.
• When size==0 array must be NULL and vice versa.
• If size==0 then return a BST with the root set to NULL.
• `malloc(…)` may be called from a total of one place in this function and any it depends on.
`empty bst(BST✶ bst)`
return type: void
Free all the nodes in the BST.
• Set `root` to NULL, and `size` to 0.
• `free(…)` may be called from a total of one place in this function and any it depends on.
test_sorts.c function definitions
`main(int argc, char✶ argv[])`
return type: int
• This must cause every line of code in your sorts.c to be executed.
• Every public function in sorts.c must be called directly from `main(…)` and/or from a helper within test_sorts.c.
expected.txt functions Expected output from running your test_sorts.c
3. Use the `typedef` syntax to declare all struct types.
4. Only the following externally defined functions and constants are allowed in your .c files. (You may put the corresponding #include <…> statements in the .c file or in your sorts.h, at your option.)
stdbool.h `bool`, `true`, `false` `sorts.c`, `sorts.h`, `test_sorts.c`
stdio.h `printf`, `fprintf`, `stdout`, `FILE` `test_sorts.c`
stdlib.h `malloc`, `free`, `NULL`, `EXIT_SUCCESS`, `EXIT_FAILURE` `sorts.c`, `test_sorts.c`, `sorts.h`
assert.h `assert` `sorts.c`, `test_sorts.c`
Feel free to suggest additional header files or functions that you would like to use.
5. Submissions must meet the code quality standards and the policies on homework and academic integrity.

## Submit

To submit HW07, type `264submit HW07 sorts.h sorts.c test_sorts.c expected.txt` from inside your hw07 directory.

## Pre-tester ●

The pre-tester for HW07 has been released and is ready to use.

## Q&A

1. Where's the starter code? How am I supposed to start?
Learning to program in C entails learning to set up your files and code your project to meet a specification—without being given step-by-step instructions. That said, here is a general process you can use for doing that.
How to do any coding homework in ECE 264
1. First, identify the files you are responsible for producing. In this case, there are four files: sorts.c, sorts.h, test_sorts.c, and expected.txt. Create an (almost) empty file for each.
2. In the .c and .h files, add a Vim modeline. (Tip: In Vim on ecegrid, type `newc` and press Tab to get a skeleton file, including the modeline. Remove any `#include` statements or anything else that isn't needed or allowed.)
3. In the .h file (sorts.h), add an include guard.
4. Create your makefile. This is optional, but recommended. You do not need to use miniunit.h or clog.c in order to use make (but you may if you wish).
5. Submit. Your code is nearly empty, but this gives you a backup.
`make submit` (or `264submit sorts.h sorts.c test_sorts.c expected.txt` for Luddites).
6. Decide on a general order in which to implement the various parts of the assignment. For HW07, you could do the three parts in any order. If you have no opinion, we lightly suggest doing in this order: ① `merge_sort_array(…)`, ②`tree_sort_array(…)`, ③ `quick_sort_array(…)`. But again, it's up to you.
8. Write one very simple test (e.g., sort empty array). At this point, your sorts.c should have no useful code in it.
9. Write just enough code in sorts.c to pass your easy test.
10. Run your test (e.g., `make test` (or `./test_sorts` for Luddites). Hopefully, your simple test passes. This step is to test the mechanics of your testing, and verify that you have the correct function signatures and such.
11. Add a slightly harder test (e.g., sort array of size one).
13. Run your tests. Make any fixes so that both of your tests do pass.
14. Gradually add tests, extend implementation, run tests, and fix, until one section of your project is complete (e.g., until `merge_sort_array(…)` is working).
15. Follow the above steps to complete the rest of HW07.
16. Re-read the specification—especially the Requirements table—and make sure you have done everything, and your types/fields/functions all match the specification.
17. Check for gaps in your tests. Make sure you get 100% line coverage from `make coverage`. This is no guarantee of perfection, but if you don't have 100% coverage, you need to fix that. Make sure your tests cause every part of your implementation code to be executed.
18. Think through your tests carefully. Make sure you have covered all:
• “edge cases” – extreme values
• “corner cases” – values that cause your code to behave differently
• “special cases” – exceptions to normal functionality described in the specification
• "easy cases" – easy for you to understand
(Note: These are not standard terms.)
2. Can I add helper functions to sorts.c?
Yes. Make sure the names begin with "_".
3. Is there a warm-up?
No.
4. Is it a violation of the spec if `qsort(…)` calls `malloc(…)`?
No. The only requirement is that your code not call `malloc(…)` as a result of calling `quick_sort_array(…)`.
5. Should I use recursion for the BST operations (`create_bst(…)`, `tree_sort_array(…)`, and `empty_bst(…)`)?
Long answer: All of these things can be accomplished without recursion, using only `while` loops. However, those methods are messier.
The methods demonstrated in class (see snippets) use recursion, and that is what we recommend.
6. How do I create a BST? … delete a BST?
To create a BST, start with an empty BST (`root = NULL`) and then insert each element you wish to add.
To delete a BST, delete the left and right subtree (recursively). Then, free the root.
The bst.c snippet from 2/21/2019 illustrates everything you need to do. You may not copy that snippet, but once you understand it, you should have no trouble doing what you need to do with BSTs for HW07.
7. What is “in-order traversal”?
That is just a fancy name for the method of printing a BST shown in the snippet from 2/21/2019.
With in-order traversal means you “visit” (i.e., do something with) the left subtree, then the root, and finally the right subtree. In that example, “visit” meant printing the value of a node. For a BST, this results in printing the values in order.
You will learn a bit more about tree traversals later, but for HW07, this is all you need to know.
Example:
In the `print_bst(Node* root)` function in the snippet:
1. Print the left subtree by calling `print_bst(root -> left)`recursively.
2. Print the root by calling `printf("%d\n", root -> value)`.
3. Print the right subtree by calling `print_bst(root -> right)`recursively.
If the tree has zero nodes (i.e., empty), we do nothing.
If the tree has one node (i.e., root has no children):
1. `print_bst(root -> left)` has no effect.
2. `printf("%d ", root -> value)` prints 4 .
3. `print_bst(root -> right)` has no effect.
If the tree has three nodes (i.e., root has children but no grandchildren):
1. `print_bst(root -> left)` prints 2 .
2. `printf("%d ", root -> value)` prints 4 .
3. `print_bst(root -> right)` prints 6 .
Altogether, it prints 2 4 6 .
If the tree has seven nodes (i.e., root has children but no grandchildren):
1. `print_bst(root -> left)` prints 1 2 3 .
2. `printf("%d ", root -> value)` prints 4 .
3. `print_bst(root -> right)` prints 5 6 7 .
Altogether, it prints 1 2 3 4 5 6 7 .
For `tree_sort_array(…)`, you are following the same process, except instead of printing a value with `printf(…)`, you store it in the array.