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Assignment #2 Bit manipulation

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COMP2401 – Assignment #2

In this assignment, you will practice using bit manipulation.
Consider a 32×32 maze as shown here.
This maze can easily be represented as a
2D array (i.e., char maze[32][32]) where
each char is a 1 for a wall or 0 otherwise.
This would require 1024 bytes to store.
Instead, we will consider encoding a maze
by making use of each bit in the byte. We
will take each row of the maze, and encode it
into a single 32-bit integer (i.e., an int in c).
Therefore, the encoded representation of the
maze will only require 32 ints of storage
(i.e., one per row) … which is just 128 bytes
in total.
Looking, for example, at the third row of the
maze … we can convert it to a 32-bit
sequence of bits where a 1 indicates a wall
and 0 indicates an open spot. Then, if
stored in an int, when printed, it would show
the two’s compliment representation, which
in this case is -1109928277 … as shown here:
Write a program called decodeMaze.c which does the following:
1) The main function should define an array of 32 int values that represent the above maze.
You should hard-code the values for this maze. The value for the third row has been given to
you above. There are some on-line binary to two’s compliment converters that can do this.
You MUST NOT hard-code this maze anywhere in your code as a 2D array. It MUST be
hard-coded as a single 32 int array.
2) Write a function that has this signature:
void printEncodedMaze(int [], unsigned char)
It should take in the above 32 int maze array and the dimension (which is 32) and then display
the maze as shown on the next page as figure (a). Note that the character representing a wall
is the @ symbol. The function must not create any other arrays, nor attempt to convert the
maze to another format. You may not use helper functions. It must simply process the
encoded maze and display it as shown. Call this function from your main function to make
sure that it works.
3) Consider now a particular encoded path in the maze. The path is encoded as 32 integers as well,
but this time a bit is set to 1 if the path is on that maze cell and 0 otherwise. Obviously, the path
will have a zero for each bit that corresponds to a wall. In your main function, define the following
array that represents the path:
{0, 0, 0, 0, 12, 8, 56, 32, 8032, 4416, 134115648, 67354944, 67109184,
67109312, 133169152, 1048576, 1835008, 262144, 262144, 262144, 458752,
65536, 65536, 65536, 65536, 983040, 67633152, 67633152, 201850880,
164102144, 259522560, 0};
Write a function that has this signature:
void printEncodedMazeWithPath(int [], int [], unsigned char)
Here, the first parameter is the maze, the second is the encoded path, the third is dimension
again. The function should display the maze and the path together as shown in (b) below. The
code must be as efficient as possible. The highlighted yellow is just to make it clear where the
path is … you will not be highlighting anything in your code. Make sure to call this function from
your main function to ensure that it works properly.
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@ @ @ @ @ @ @
@ @@@@ @@@ @ @@@@@ @ @@ @ @ @ @@
@ @ @ @ @ @ @ @ @ @@
@ @ @@@@ @@@@ @@ @@@ @ @@
@ @ @@@@ @@@@ @ @ @@@
@ @ @ @ @@@@ @@@ @@@ @
@ @@ @ @ @ @ @@ @@@ @@@@@
@ @ @@@@ @@@ @@@ @ @
@ @ @@@@ @@@@ @ @ @@@ @ @@@@ @
@ @ @ @@ @@ @ @ @ @
@ @@@ @@@@ @@ @ @ @ @ @@
@ @@@ @ @ @ @ @ @ @@ @ @@
@ @ @ @@@ @ @ @@ @@@ @@ @@@
@ @@ @ @ @ @ @@@@ @ @
@ @ @@@@ @ @@@ @@@@ @ @ @ @
@ @@ @ @ @ @ @@@@@@ @@ @
@ @ @ @@ @ @ @ @@@@ @ @ @ @
@ @@@ @@@ @ @ @ @ @ @ @@@ @
@ @ @@ @@ @ @@@@ @ @ @ @ @ @
@ @@@ @ @ @ @ @@ @ @
@ @ @@ @@ @ @ @@@@ @@@@ @@ @
@ @@@@@ @@ @ @ @@@ @ @
@ @ @@ @ @ @@@@@@ @@@ @ @
@@ @@ @ @ @@@@ @ @@ @ @@@@@
@ @@@@@@ @ @@ @@ @ @ @
@ @@@ @ @ @@ @ @ @ @@ @@@ @
@ @ @ @@@@ @ @ @ @ @ @ @
@ @ @ @ @ @@@@@ @ @@ @@@@ @ @
@@@@ @@ @@ @ @ @ @ @@@@ @
@ @ @ @ @ @@ @
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@ @ @ @ @ @ @
@ @@@@ @@@ @ @@@@@ @ @@ @ @ @ @@
@ @ @ @ @ @ @ @ @ @@
@ @ @@@@ @@@@ @@ @@@ @..@@
@ @ @@@@ @@@@ @ @.@@@
@ @ @ @ @@@@ @@@ @@@ … @
@ @@ @ @ @ @ @@ @@@.@@@@@
@ @ @@@@ @@@ @@@…..@.. @
@ @ @@@@ @@@@ @ @.@@@.@.@@@@ @
@ @ @……….@@… @@.@.@ @ @
@ .@@@ @@@@….@@ @.@.@ @ @@
@ @@@.@ @ @ @ @ @ @@.@. @@
@ @.@ @@@ @ @ @@ @@@ …@@ @@@
@ @@ …….@ @ @ @ @@@@ @ @
@ @ @@@@ @.@@@ @@@@ @ @ @ @
@ @@ @ @ @…@ @@@@@@ @@ @
@ @ @ @@ @ @.@ @@@@ @ @ @ @
@ @@@ @@@.@ @ @ @ @ @ @@@ @
@ @ @@ @@ @.@@@@ @ @ @ @ @ @
@ @@@ @ @… @ @ @@ @ @
@ @ @@ @@ @ @.@@@@ @@@@ @@ @
@ @@@@@ @@ @.@ @@@ @ @
@ @ @@ @ @.@@@@@@ @@@ @ @
@@ @@ @ @ @@@@. @ @@ @ @@@@@
@ @@@@@@ @….@@ @@ @ @ @
@ @@@.@ @.@@ @ @ @ @@ @@@ @
@ @ @.@@@@ @. @ @ @ @ @ @
@ @ ..@ @ @.@@@@@ @ @@ @@@@ @ @
@@@@.@@…@@.@ @ @ @ @@@@ @
@ ….@….@ @ @ @@ @
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
(a) (b)
4) Consider the following four 8×8 mazes:
In your main function, hardcode these mazes as char arrays of 1’s and 0’s
{{1,1,1,1,1,1,1,1},
{1,0,0,0,1,0,0,1},
{1,0,1,0,1,1,0,1},
{1,0,1,0,0,0,0,1},
{1,0,1,1,1,1,0,1},
{1,0,0,0,0,0,0,1},
{1,0,1,0,1,0,1,1},
{1,1,1,1,1,1,1,1}}
{{1,1,1,1,1,1,1,1},
{1,0,0,0,0,1,0,1},
{1,1,1,1,0,1,0,1},
{1,0,0,1,0,1,1,1},
{1,1,0,0,0,0,0,1},
{1,1,1,1,0,1,1,1},
{1,0,0,0,0,1,0,1},
{1,1,1,1,1,1,1,1}}
{{1,1,1,1,1,1,1,1},
{1,0,1,0,0,0,1,1},
{1,0,1,0,1,0,0,1},
{1,0,1,0,1,0,1,1},
{1,0,1,0,1,0,1,1},
{1,0,1,0,1,0,1,1},
{1,0,0,0,1,0,0,1},
{1,1,1,1,1,1,1,1}}
{{1,1,1,1,1,1,1,1},
{1,0,1,0,1,0,1,1},
{1,0,1,0,0,0,0,1},
{1,0,0,0,1,1,1,1},
{1,1,1,0,1,0,0,1},
{1,0,0,0,0,0,1,1},
{1,1,0,1,1,0,0,1},
{1,1,1,1,1,1,1,1}}
Write a function that has this signature:
void encode8by8Maze(char inputMaze[8][8], int encodedMaze[8]) {
The function should encode the given 8×8 maze into an array of 8 ints. Normally we would store
it as an array of 8 unsigned chars to save more space, but we will be passing these encoded
mazes into our print function, which requires an int. The structure of your code must be efficient.
Make sure to call this function for each of the 8×8 mazes and then display each maze by calling
the print function from step 2). You should be able to verify the output from the images of the
mazes that I gave you in this step.
5) We will now merge mazes together. Write a function with this signature:
void merge8by8Mazes(int topLeft[8], int topRight[8],
int bottomLeft[8], int bottomRight[8],
int finalMaze[14]) {
It should take in four encoded 8×8 mazes and output a final encoded 14×14 maze. You MUST
NOT convert the mazes into any other format and you cannot create any other arrays within
the function. You may not use helper functions. Your code must be concise and efficient.
The function should combine the first 7 rows of the topLeft and topRight mazes such that the
last column of the topLeft maze and the first column of the topRight maze is discarded. The
result is that there will be 14 columns. Similarly, the last 7 rows of the bottomLeft and
bottomRight mazes are combined. The result is a 14×14 maze as shown below. Essentially,
the inside border cells have been removed. You must write this function as efficiently as
possible.
6) In your main function, write some test code that will generate all 256 combinations of 14×14
mazes by combining all possible combinations of the given four 8×8 mazes. Your code should
be efficient (i.e., with minimal duplication of code) and it must make use of your function in step
5) as well as the print function in step 2 to display the 14×14 maze each time. Also, just
before printing the 14×14 maze, indicate which maze combination you used. For example, in
the above example, it was mazes 1, 2, 3 and 4. Whereas if maze 1 (i.e., the red one) was
used in all 4 corners, you would print out 1, 1, 1, 1 before the 14×14 maze.
7) Write a function with this signature:
char isPathInMaze(int[], int[], unsigned char)
Here, the first parameter is an encoded maze, the second is an encoded path and the third is
the maze dimension. The code should return 1 if the given path fits properly in the maze and
0 otherwise. A path fits properly if it lies completely in the open areas of the maze. That is,
the path should not cross onto a wall of the maze. You must write this code efficiently without
creating any additional arrays nor helper functions and you must not try to convert the arrays
into any other format.
In your main function, after displaying the large maze and the maze with the path, call this
function to determine whether or not the path fits in the maze. It should. Display the result of
the function call to be sure.
In your main function … when you display the 256 maze combinations … for each one … you
should call this isPathInMaze() function with the following path (for a 14×14 maze):
{0, 4096, 4096, 4096, 4096, 7936, 256, 256, 448, 112, 16, 28, 6, 0}
You can hardcode this path in your main function. When you run the 256 combinations, you
should notice that exactly 8 mazes will return a result of 1 (or true) for the function call. As
you are printing the 256 mazes, make sure to only display (with a sentence of some sort)
which mazes can fit the path. If a maze does not fit the path, do not print a sentence. You
should be able to easily spot the 8 mazes that fit the path as you scroll through the results.
________________________________________________________________________________
IMPORTANT SUBMISSION INSTRUCTIONS:
Submit all of your c source code files (in this case there is just one) as a single tar file containing:
1. A Readme text file containing
• your name and studentNumber
• a list of source files submitted
• any specific instructions for compiling and/or running your code
2. All of your .c source files and all other files needed for testing/running your programs.
3. Any output files required, if there are any.
The code MUST compile and run on the course VM.
• If your internet connection at home is down or does not work, we will not accept this as a reason for
handing in an assignment late … so make sure to submit the assignment WELL BEFORE it is due !
• You WILL lose marks on this assignment if any of your files are missing. So, make sure that you hand
in the correct files and version of your assignment. You will also lose marks if your code is not written
neatly with proper indentation and containing a reasonable number of comments. See course
notes for examples of what is proper indentation, writing style and reasonable commenting).

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