Description
This assignment covers learning objective 4: An ability to apply graph theoretic techniques, data structures, and algorithms for problem solving; learning objective 5: An ability to design and implement appropriate data structures and algorithms for engineering applications.
Grid traversal
This programming assignment is to be completed on your own. You will implement a program that
involves finding a fastest way to travel from a location at the top of a grid and exit at a location at the bottom
of the grid. Consider the following 4×5 (or 4-rows-by-5-rows) grid:
4 2 1 0 5
2 0 4 1 0
4 2 2 2 7
1 7 2 9 2
We label the rows from top to bottom 0 to 3 and the columns from left to right 0 to 4. Let the coordinates
of location i be (ri
, ci), where ri
is the index of the row that i is in, and ci
is the index of the column that i is
in. The highlighted (2,1)-location of the grid, for example, stores the a non-negative value of 2 (stored as
short).
The value at a location corresponds to the amount of time a visitor has to spend there once the visitor
enters that location. After spending that amount of time at that location, the visitor moves to one of its
adjacent locations. If a visitor enters the (2,1)-location at time t, the earliest the visitor can leave that
location and enter a location adjacent to (2,1) is at time t +2.
If a visitor enters the (1,1)-location, which stores the value 0, at time t, the visitor can immediately exit
that location and enter a location adjacent to (1,1) at time t.
Two locations, i of coordinates (ri
, ci) and j of coordinates (rj
, cj), are adjacent if rj = ri −1 (j is above
i), rj = ri + 1 (j is below i), cj = ci + 1 (j is to the right of i), or cj = ci − 1 (j is to the left of i). For the
(2,1)-location, the adjacent neighbor above it is the (1,1)-location, the adjacent neighbor below it is the
(3,1)-location, the adjacent neighbor to its right is the (2,2)-location, and the adjacent neighbor to its left is
the (2,0)-location. For the boundary locations in the grid, they do not have four adjacent neighbors. They
have only two adjacent neighbors (for the corner entries) or three adjacent neighbors (for the non-corner
boundary entries).
For the given 4 × 5 grid, A visitor must enter the grid at one of the (0,i)-locations, 0 ≤ i ≤ 4. It must
exit the grid at one of the (3, j)-locations, 0 ≤ j ≤ 4.
Suppose a visitor enters the grid at the (0,0)-location at time 0, the values stored in the following table
show the respective earliest times when the visitor could enter the corresponding locations in the given grid:
0 4 6 7 7
4 6 6 7 8
6 6 8 8 8
10 8 10 10 15
For the entrance at the (0,0)-location at time 0, the highlighted path of (0,0) → (1,0) → (2,0) → (3,0)
allows the visitor to exit the grid at the (3,0)-location the earliest in 11 time units. The visitor arrives at
the (3,0)-location the earliest in 10 time units, as shown in the preceding table, spends 1 unit of time there
before exiting. This path contains 4 locations in the grid.
ECE36800 Purdue University 1
c Cheng-Kok Koh
Suppose a visitor enters the grid at the (0,1)-location at time 0, the values stored in the following table
show the respective earliest times when the visitor could enter the corresponding locations in the given grid:
2 0 2 3 3
2 2 2 3 4
4 2 4 4 4
8 4 6 6 11
For the entrance at the (0,1)-location at time 0, the highlighted path of (0,1) → (1,1) → (2,1) →
(2,2) → (3,2) allows the visitor to exit the grid at the (3,2)-location the earliest in 8 time units.
Suppose a visitor enters the grid at the (0,2)-location at time 0, the values stored in the following table
show the respective earliest times when the visitor could enter the corresponding locations in the given grid:
3 1 0 1 1
3 3 1 1 2
5 3 4 2 2
9 5 6 4 9
For the entrance at the (0,2)-location at time 0, the highlighted path of (0,2) → (0,3) → (1,3) →
(2,3) → (2,2) → (3,2) allows the visitor to exit the grid at the (3,2) location the earliest in 8 time units.
The following table is obtained using the (0,3)-location as the entry point. The visitor could exit the
grid in 7 time units at the (3,2)-location.
3 1 0 0 0
3 3 1 0 1
5 3 3 1 1
9 5 5 3 8
The following table is obtained using the (0,4)-location as the entry point. The visitor could exit the
grid in 12 time units at the (3,2)-location.
8 6 5 5 0
8 8 6 5 5
10 8 8 6 5
14 10 10 8 12
There is another fastest path when the entry point is the (0,4)-location, as highlighted below:
8 6 5 5 0
8 8 6 5 5
10 8 8 6 5
14 10 10 8 12
Among all these entry points, the entry point at the (0,3)-location allows a visitor to enter the grid at the
top and exit the grid at the bottom at the (3,2)-location the earliest in 7 time units. The corresponding path
is (0,3) → (1,3) → (2,3) → (2,2) → (3,2), which contains 5 locations in the grid.
Deliverables
In this assignment, you are required to develop include file(s) and source file(s) that can be compiled
with the following command:
gcc -std=c99 -pedantic -Wvla -Wall -Wshadow -O3 *.c -o pa6
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.
The executable pa6 should be run as follows:
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./pa6 binary grid file text grid file fastest times file fastest path file
Given a 2-dimensional grid stored in the (binary) input file binary grid file, the program produces
three output files: text grid file stores the input grid in text form, fastest times file stores the
fastest time to exit the grid at the bottom for each entry location at the top of the grid, and fastest path file
stores the fastest path that allows a visitor to enter a location in the top row of the grid and exit at a location
in the bottom row of the grid the earliest possible. Both fastest times file and fastest path file
should be binary.
Binary grid file format
The binary grid file argv[1] is an input file in binary format. Given a grid of m rows and n
columns, 0 < m,n ≤ SHRT MAX, the first two short’s stored in binary grid file are m and n, respectively.
Here, SHRT MAX is the largest short integer (see limits.h).
After those two short’s, the file is followed by a total of m×n short’s. All m×n short’s are within
the range of [0,SHRT MAX].
Out of these m×n short’s, the first n short’s are in row 0. Out of these n short’s, the first short is
at column 0 and the last short is at column n − 1. The next n short’s are in row 1. The last group of n
short’s are in row m−1.
The total size of the file is (2+mn)×sizeof(short) bytes. You may assume that all input files are all
correct.
In general, the sample files given to you are named as m n.b where m is the number of rows and n is the
number of columns. However, you should always determine the true dimensions of a given grid from the
first two short’s of the input file. The file 4 5.b provided to you for this assignment contains the example
given earlier.
Suppose we run pa6 with the following command
./pa6 4_5.b 4_5.t 4_5.f 4_5.p
The file 4 5.t should store the 2-dimensional grid in text form. The file 4 5.f should store the fastest
times to exit the grid for all entry locations in binary form. The file 4 5.p should store the fastest path in
binary form. These files are also provided to you for this assignment.
Text grid file format
The first output file argv[2] is simply a conversion of the binary grid file to a text form. Again, we
assume that there are m rows and n columns in the binary file. The first line is printed with the format
“%hd %hd\n”, where the first short is the number of rows, m, and the second short is the number of
columns, n.
After that, there should be m lines. Each line should print n short’s, where each short is printed with
the format “%hd”. There should be a space (’ ’) character between a pair of consecutive short’s. There
should be a newline character (’\n’) immediately after the last short in each line (row). There should not
be a space character after the last short in a line.
Fastest times file format
The second output file argv[3] stores the fastest time to exit the grid for each entry location in the top
row in binary form.
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The file first stores the number of entry locations in the top row of the input grid. This should correspond
to the number of columns in the given input grid. The number of columns should be stored as an short.
Let n be the number of columns in the given grid. The file next stores n int. Assuming that we label
the int from 0 to n−1. The ith int, 0 ≤ i ≤ n−1, is the fastest time to exit at the bottom of the grid when
the entry point is the (0,i)-location.
The total size of the path file is (sizeof(short)+n×sizeof(int)) bytes.
Fastest path file format
The third output file argv[4] stores the fastest path information in binary form.
The file first stores the fastest time it would take for a visitor to enter at a location in the top row of the
input grid and exit at a location in the bottom row of the input grid. The fastest time should be stored as an
int.
Then, we store in the file an int for the number of locations that constitute the path. Let l be the number
of locations that constitute the path, the output file next contains coordinates of the l entries that form the
path. Each location is stored as a pair of shorts, the (row, column) coordinates of the location, with the
row coordinate followed by the column coordinate. The order in which the coordinates appear in the output
file should follow the order in which the corresponding locations appear in the path. The path should start
with a location in the top row of the grid and end with a location in the bottom row of the grid.
The total size of the path file is (2×sizeof(int)+2l ×sizeof(short)) bytes.
Return value of main function
The main function should simply return EXIT FAILURE if the argument count is incorrect.
If the given input file cannot be opened, your program should terminate and return EXIT FAILURE.
Now, assume that the given input file can be opened. If in the process of determining the fastest path,
your program encounters a failure in memory allocation or a failure in writing to the output files, your
program should gracefully exit and return EXIT FAILURE. We will test your program with valid input files
of reasonable sizes. Therefore, it is unlikely that you will have to return EXIT FAILURE when you could
open an input file.
Of course, your program should return EXIT SUCCESS otherwise.
Electronic Submission
The project requires the submission (electronically) of the C-code (source and include files) through
Brightspace. You should create and submit a zip file called pa6.zip, which contains the .h and .c files.
Your zip file should not contain a folder.
zip pa6.zip *.c *.h
You should submit pa6.zip to Brightspace.
If you want to use a Makefile for your assignment, please include the Makefile in the zip file. In that
case, you can create the zip file as follows:
zip pa6.zip *.c *.h Makefile
If the zip file that you submit contains a Makefile, we use that file to make your executable (by typing
“make pa6” at the command line to create the executable called pa6).
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Grading
The assignment will be graded based on the two tasks performed by your program. The first output file
accounts for 10%, the second output file accounts for 60%, and the third output file accounts for 30%.
It is important that all the files that have been opened are closed and all the memory that have been
allocated are freed before the program exits. Memory leaks or memory errors reported by valgrind will
result in a 50-point penalty.
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.
What you are given
You are given 4 sample binary grid files (4 5.b, 5 4.b, 5 5.b, 7 7.b) and the corresponding text grid
files (4 5.t, 5 4.t, 5 5.t, 7 7.t), fastest times files (4 5.f, 5 4.f, 5 5.f, and 7 7.f), and path files
(4 5.p, 5 4.p, 5 5.p, and 7 7.p). It is possible that a binary grid file may contain multiple paths that allow
a visitor to enter and exit a grid in the shortest time possible. Your program should not try to match the path
exactly. However, the shortest time that it took to enter and exit a grid should match.
To help you to understand the fastest times files and path files, we also provide the text version of these
files (5 4.ft and 5 4.pt, 4 5.ft and 4 5.pt, 5 5.ft and 5 5.pt, and 7 7.ft and 7 7.pt).
In each .ft file, the first line stores the number of columns in the given grid file (printed with the
format “%hd\n”). Let n be the number of columns. The second line has n int, where each int is printed
with the format “%d”. There is a space (’ ’) character between a pair of consecutive int’s. There is a
newline character (’\n’) immediately after the last int. Assuming that we label the int from 0 to n−1.
The ith int, 0 ≤ i ≤ n − 1, is the fastest time to exit at the bottom of the grid when the entry point is the
(0,i)-location.
In each .pt file, the first line stores the (fastest) time (printed with the format “%d\n”). The second line
stores the number of locations in the path (printed with the format “%d\n”). Each subsequent line stores the
(row, column) coordinates of an entry (printed with the format “%hd %hd\n”).
Additional information
You may want to write a program that allows you to convert from a text grid file into a binary grid file.
This allows you to easily create other examples to test your programs. Similarly, you may want to create
programs to convert from a binary fastest times file (or binary path file) to a text fastest times file (or text
path file) for testing.
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