Description

Reflections and Kindred Spirits

Overview, Part 1 of 2: Reflections

Given two binary trees, we say that one is a reflection of the other if they are symmetric in terms of
both their structure and their node values. For example, the following trees are reflections of one
another:

Figure 1: Two trees that are reflections of one another.
The following trees are not reflections of one another, because although they are symmetric images of
one another structurally, they are not symmetric in terms of their values:

Figure 2: Two structurally symmetric trees that are not reflections of one another
because they are lack symmetry with respect to their node values.
Because the following binary trees are not structurally symmetric (and therefore they also cannot be
symmetric in terms of the values contained in each node), they are not reflections of one another:

Figure 3: Structurally asymmetric trees cannot be reflections of one another.
10
20 30
40 1
10
30 20
1 40
10
30 20
40 1
10
30 20
1 40
18
16 51
33 19
18
16 51
33
19
The following binary trees are reflections of one another:

Figure. 4: Two trees that are reflections of one another. They are
perfect binary trees. They are also large and in charge.
Recall that the tree above is a perfect binary tree. You might ask yourself, “Is it always the case that a
perfect binary tree is a reflection of itself?” The answer is, “No!” Here’s a counterexample that shows
that a perfect binary tree is not always a reflection of itself:

Figure 5: This perfect binary tree is not a reflection of itself. Despite its
structural symmetry, it is not symmetric to itself with respect to its node values.
Any binary tree with a single node is a reflection of itself. For example:

Figure 6: Two trees that are reflections of one another.
However, it is not the case that all binary trees with a single node are reflections of one another. For
example:

Figure 7: Two trees that are not reflections of one another, because
they are not symmetric with respect to their values.
2
14 14
34
62 62 62 62
34 34 34 34 34 34 34
2
14 14
34
62 62 62 62
34 34 34 34 34 34 34
38
1
70 47
3 5 9
38
1
70 47
3 5 9
33 33
15 21
Finally, note that the empty tree is a reflection of itself:
Figure 8: Two trees (both empty) that are reflections of one another.
This example is serene and beautiful, and brings with it an overwhelming
sense that everything is going to be okay.

2. Overview, Part 2 of 2: Kindred Spirits

We say that two binary trees are kindred spirits if the preorder traversal of one of the trees corresponds
to the postorder traversal of the other tree. For example, the following trees are kindred spirits:

Figure 9: These trees are kindred spirits. The preorder traversal of the
tree on the left is 23, 12, 5, 18, 71, 56, which corresponds to the postorder
traversal of the tree on the right.
Note that the trees above are still kindred spirits even if we swap their order:

Figure 10: These trees from Figure 9 are still kindred spirits, despite the fact
that the preorder traversal of the tree on the right now matches the postorder
traversal of the tree on the left, instead of the other way around.
23
12 71
5 18 56
56
23 71
5 18
12
23
12 71
5 18 56
56
23 71
5 18
12

3. Binary Tree Node Struct (KindredSpirits.h)

You must use the node struct we have specified in KindredSpirits.h without any modifications. You
will have to #include the header file in your KindredSpirits.c source file like so:
#include “KindredSpirits.h”
Note that the capitalization of KindredSpirits.c matters! Filenames are case sensitive in Linux, and
that is of course the operating system we’ll be using to test your code. If you’re using Code::Blocks,
you will need to add the KindredSpirits.h header file to your project. See the instructions in Section
8, “Compilation and Testing (Code::Blocks).”
The node struct is defined in KindredSpirits.h as follows:
typedef struct node
{
int data;
struct node *left, *right;
} node;

4. Test Cases and the test-all.sh Script

As always, I’ve included several test cases, which show some ways in which I might test your code.
These test cases are not comprehensive. You should also create your own test cases if you want to test
your code comprehensively.
I’ve also included a script, test-all.sh, that will compile and run all test cases for you. Using the
test-all.sh script on Eustis is the safest, most sure-fire way to make sure your code is working
properly before submitting. To run the script on Eustis, type the following:
bash test-all.sh

5. Output

The functions you write for this assignment should not produce any output. If your functions cause
anything to print to the screen, it might interfere with our test case evaluation. Be sure to disable or
remove any printf() statements you have in your code before submitting this assignment.

6. Function Requirements

You have a lot of leeway with how to approach this assignment. There are only five required functions,
and you may write helper functions as you see fit. For the kindredSpirits() function, you will likely
need quite a few helper functions, and a good measure of creative thinking and/or cleverness.
Function descriptions for this assignment are included on the following page. Please do not include a
main() function in your submission.
int isReflection(node *a, node *b);
Description: A function to determine whether the trees rooted at a and b are reflections of one
another, according to the definition of “reflection” given above. This must be implemented
recursively.

Returns: 1 if the trees are reflections of one another, 0 otherwise.
node *makeReflection(node *root);
Description: A function that creates a new tree, which is a reflection of the tree rooted at root.
This function must create an entirely new tree in memory. As your function creates a new tree,
it must not destroy or alter the structure or values in the tree that was passed to it as a parameter.
Tampering with the tree rooted at root will cause test case failure.
Returns: A pointer to the root of the new tree. (This implies, of course, that all the nodes in the
new tree must be dynamically allocated.)
int kindredSpirits(node *a, node *b);

Description: A function that determines whether the trees rooted at a and b are kindred spirits.
(See definition of “kindred spirits” above.) The function must not destroy or alter the trees in
any way. Tampering with these trees will cause test case failure.
Special Restrictions: To be eligible for credit, the worst-case runtime of this function cannot
exceed O(n), where n is the number of nodes in the larger of the two trees being compared. This
function must also be able to handle arbitrarily large trees. (So, do not write a function that has
a limit as to how many nodes it can handle.) You may write helper functions as needed.

Returns: 1 if the trees are kindred spirits, 0 otherwise.
double difficultyRating(void);
Returns: A double indicating how difficult you found this assignment on a scale of 1.0
(ridiculously easy) through 5.0 (insanely difficult).
double hoursSpent(void);

Returns: A reasonable estimate (greater than zero) of the number of hours you spent on this
assignment.
The remaining pages of this document contain compilation instructions for Linux/Mac
(pg. 7) and Windows (pg. 8), further restrictions and guidelines for your program (see
pgs. 8 and 9), and grading criteria (pg. 9).

7. Compilation and Testing (Linux/Mac Command Line)

To compile multiple source files (.c files) at the command line:
gcc KindredSpirits.c testcase01.c
By default, this will produce an executable file called a.out, which you can run by typing:
./a.out
If you want to name the executable file something else, use:
gcc KindredSpirits.c testcase01.c -o KindredSpirits.exe
…and then run the program using:
./KindredSpirits.exe

Running the program could potentially dump a lot of output to the screen. If you want to redirect your
output to a text file in Linux, it’s easy. Just run the program using the following command, which will
create a file called whatever.txt that contains the output from your program:
./KindredSpirits.exe > whatever.txt

Linux has a helpful command called diff for comparing the contents of two files, which is really
helpful here since we’ve provided several sample output files. You can see whether your output
matches ours exactly by typing, e.g.:
diff whatever.txt output01.txt

If the contents of whatever.txt and output01.txt are exactly the same, diff won’t have any output.
It will just look like this:
seansz@eustis:~$ diff whatever.txt output01.txt
seansz@eustis:~$ _
If the files differ, it will spit out some information about the lines that aren’t the same. For example:
seansz@eustis:~$ diff whatever.txt output01.txt
1c1
< fail whale 🙁
—
> Success!
seansz@eustis:~$ _

8. Compilation and Testing (Code::Blocks)

The key to getting your program to include a custom header file in Code::Blocks (or any IDE) is to
create a project. Here are the step-by-step instructions for creating a project in Code::Blocks, importing
KindredSpirits.h and the KindredSpirits.c file you’ve created (even if it’s just an empty file so far).
1. Start Code::Blocks.
2. Create a New Project (File → New → Project).
3. Choose “Empty Project” and click “Go.”
4. In the Project Wizard that opens, click “Next.”
5. Input a title for your project (e.g., “KindredSpirits”).
6. Pause to reflect on life a bit. Isn’t this amazing?
7. Choose a folder (e.g., Desktop) where Code::Blocks can create a subdirectory for the project.
8. Click “Finish.”

Now you need to import your files. You have two options:
1. Drag your source and header files into Code::Blocks. Then right click the tab for each file and
choose “Add file to active project.”
– or –
2. Go to Project → Add Files…. Then browse to the directory with the source and header files you
want to import. Select the files from the list (using CTRL-click to select multiple files). Click
“Open.” In the dialog box that pops up, click “OK.”

You should now be good to go. Try to build and run the project (F9). As a friendly reminder: Even if
you develop your code with Code::Blocks on Windows, you ultimately have to transfer it to the Eustis
server to compile and test it there. See the following page (Section 7, “Compilation and Testing
(Linux/Mac Command Line)”) for instructions on command line compilation in Linux.

9. Deliverables

Submit a single source file, named KindredSpirits.c, via Webcourses. The source file should contain
definitions for all the required functions (listed above), as well as any auxiliary functions you need to
make them work. Don’t forget to #include “KindredSpirits.h” in your source code. Your program
must compile on Eustis with both of the following:
gcc -c KindredSpirits.c
gcc KindredSpirits.c testcase01.c

10.Special Restrictions

1. As always, you must avoid the use of global variables, mid-function variable declarations, and
system calls (such as system(“pause”)).
2. Do not read from or write to any files. File I/O is forbidden in this assignment.
3. Be sure you don’t write anything in KindredSpirits.c that conflicts with what’s given in
KindredSpirits.h. Namely, do not try to define a node struct in KindredSpirits.c, since
your source file will already be importing the definition of a node struct from
KindredSpirits.h.
4. No shenanigans. For example, if you write a kindredSpirits() function that always returns 1,
you might not receive any credit for the test cases that it happens to pass.
5. Your KindredSpirits.c file must not include a main() function. If it does, your code will fail
to compile during testing, and you will not receive credit for this assignment.
6. Be sure to include your name and NID as a comment at the top of your source file.

11.Grading

The tentative scoring breakdown (not set in stone) for this programming assignment is:
80% Correct output for test cases used in grading
10% Appropriate use of functional decomposition
10% Comments and whitespace
Note! Your program must be submitted via Webcourses, and it must compile and run on Eustis to
receive credit. Programs that do not compile will receive an automatic zero.

Your grade will be based primarily on your program’s ability to compile and produce the exact results
expected. Even minor deviations will cause your program’s output to be marked as incorrect, resulting
in severe point deductions. The same is true of how you name your functions and their parameters.
Please be sure to follow all requirements carefully and test your program thoroughly.

Note also that your functions should not print anything to the screen. If they do, it will interfere with
the output we generate while testing, resulting in incorrect test case results and an unfortunate loss of
points.

Additional points will be awarded for style (commenting and whitespace practices) and functional
decomposition (i.e., don’t write a 300-line kindredSpirits() function; break it up into meaningful
functions!). The graders will inspect your isReflection() and kindredSpirits() functions to
ensure they aren’t just bogus functions that always returns

1. Shenanigans like that might result in
severe point deductions. Also, don’t forget that the runtime of kindredSpirits() should not exceed
O(n), where n is the number of nodes in the larger of the two trees being compared.