Project 1 (30 points)  Assigned: Thursday, January 21, 2010 Due: Thursday 28, 2010, 11:59 PM

Programming Assignment #2  Game of Life

### Abstract

Write a C program that plays the Game of Life. Accept as inputs the size of the board, the initial configuration, and the number of generations to play. Play that number of generations and display the final configuration of the board.

### Outcomes

After successfully completing this assignment, you should be able to:

·         Develop a C program that uses two-dimensional arrays

·         Allocate memory for the arrays at run time

·         Pass arrays as arguments to functions

### Before Starting

Read Chapters 5 K&R or Chapter 6 of D&D, both pertaining to arrays.

### John Conways Game of Life

The Game of Life was invented by the mathematician John Conway and was originally described in the April 1970 issue of Scientific American (page 120). The Game of Life has since become an interesting object of mathematical study and amusement, and it is the subject of many websites.

The game is played on a rectangular grid of cells, so that each cell has eight neighbors (adjacent cells). Each cell is either occupied by an organism or not. A pattern of occupied and unoccupied cells in the grid is called a generation. The rules for deriving a new generation from the previous generation are these:

1.      Death. If an occupied cell has 0, 1, 4, 5, 6, 7, or 8 occupied neighbors, the organism dies (0 or 1 of loneliness; 4 thru 8 of overcrowding).

2.      Survival. If an occupied cell has two or three neighbors, the organism survives to the next generation.

3.      Birth. If an unoccupied cell has precisely three occupied neighbors, it becomes occupied by a new organism.

Examples can be found at http://www.math.com/students/wonders/life/life.html.

Once started with an initial configuration of organisms (Generation 0), the game continues from one generation to the next until one of three conditions is met for termination:

1.      all organisms die, or

2.      the pattern of organisms repeats itself from a previous generation, or

3.      a predefined number of generations is reached.

Note that for some patterns, a new generation is identical to the previous one  i.e., a steady state. When this occurs, termination under condition #2 occurs. In some other common cases, a new generation is identical to the second previous generation; that is, the board oscillates back and forth between to configurations. In rare cases, a pattern repeats after an interval of two or more generations. In this assignment, you will be responsible for terminating after a steady state is reached or an oscillation of two alternating patterns is reached.

In theory, the Game of Life is played on an infinite grid. In this assignment, your program will play on a finite grid. The same rules apply, but squares beyond the edge of the grid are assumed to be always unoccupied.

Your program should be called life. It needs to do several things:

·         Prompt for input to configure the program. (For extra credit, you may get the input from the command line; see below.)

·         Allocate at least three arrays, each large enough to hold one generation of the game. Initialize one generation with the initial configuration in the approximate center of the board.

·         Play the game for as many generations as needed until one of the three termination conditions above is met.

·         Print out the final configuration, along with a message saying how many generations were played and under what condition the game terminated.

#### Input

The first line of input should include 3-5 numerical values to be interpreted as:

X Y gens print pause

where

·         X and Y are unsigned integers indicating the number of elements in the x and y directions if the grid, respectively.

·         gens is the number of generations to play. This value must be greater than zero. The program should halt prior to this number of generations if it determines that the game has reached a termination condition.

·         print is an optional argument with value of y or n indicating whether each generation (including generation 0) should be printed or displayed before proceeding to the next generation. If this item is missing, it defaults to n.

·         pause is an optional argument with value of y or n indicating whether keyboard input should be required between generations. If this item is missing (or the print item is missing), it defaults to n.

Following the first line of input should be a sequence of lines consists of a series of x and o characters, indicating the occupied and unoccupied cells of the initial configuration. This sequence of lines is terminated by an end-of-file indication or by an empty line. You must place this initial configuration in the approximate center of your board.

For example, here is a simple pattern that happens to be a still life or steady state:

xx
xx

That is, the next generation starting from this pattern produces exactly the same pattern. Here is another still life pattern:

oxo
xox
xox
oxo

The following pattern produces an oscillation between a vertical line of three occupied cells and a horizontal line of three occupied cells

x
x
x

Likewise, the following pattern is a well-studied one called the R-Pentomino.

oxx
xxo
oxo

This creates an interesting sequence of generations, including many sub-patterns that come and go, until it finally reaches a steady state after 1176 generations.

There are two ways in C to create an array dynamically at run-time:

·         Use the malloc() function to allocate memory from The Heap and return a pointer to that memory. Although this is the most common practice in C, we will not yet have studied pointers at a suitable depth before this project is due. Therefore, you should not use this approach unless you already know what you are doing.

·         Inside a function or compound statement, declare an array whose size is specified by a variable with a value determined at run time. For example, the following is legal in C

void Life(unsigned int x, unsigned int y, ) {
int A[x][y], B[x][y], C[x][y];

/* use arrays A, B, and C to play the game */

}  //   Life

When the function Life is entered, it allocates the three arrays on the stack based on the integer parameters x and y.

#### Playing the Game

To play the game, you should set up a function such as

void PlayOne (unsigned int x, unsigned int y, int Old[][], int New[][]) {
/* loop through array New, setting each array element to zero or
one depending up its neighbors in Old.*/

}  // PlayOne

This can be called by the function Life using:

PlayOne(x, y, A, B);

The result is that PlayOneGen reads the contents of the first array argument and updates the array of the second argument. Subsequent generation might be called by

PlayOne(x, y, B, C);

PlayOne(x, y, C, A);

so that the generations cycle among the three arrays you allocated.

To test for termination conditions, you could adapt PlayOneGen to return values of zero or non-zero to indicate whether anything has changed. You could also construct another function to compare two arrays, returning zero if they are the same and non-zero if they are different, for example.

### Testing

You should test your Game of Life with several initial conditions, including patterns that you find on the web. When the graders test your program, they will use one or more standard input files comprising one initial line followed by several pattern lines.

### Deliverables

You must provide the following:

·         Two or more .c files and one or more .h file to implement your game.

·         A makefile to build your assignment. The executable program must be called life.

·         At least one test case that demonstrates that your program works on a non-trivial pattern.

·         A document called README.txt, README.pdf, or README.doc summarizing your program, how to run it, and detailing any problems that you had. Also, if you borrowed all or part of the algorithm for this assignment, be sure to cite your sources and explain in detail how it works.

From your CCC Linux shell, submit your C source code file using the following turnin command:

Programs submitted after 11:59 pm on due date (January 28) will be tagged as late, and will be subject to the late homework policy.

This assignment is worth thirty (30) points. Your program must compile without errors in order to receive any credit. It is suggested that before your submit your program, compile it again on a CCC system to be sure that it does not blow up or contain surprising warnings.

·         Correct compilation without warnings  2 points

·         Correct makefile to build program and individual components and to clean up  3 points

·         Correct allocation of arrays at run time  4 points

·         Correct implementation of game function  4 points

·         Correct test for termination  3 points

·         Satisfactory test cases  4 points

·         Correct execution with graders test cases  5 points

·         Satisfactory README file, including loop invariants  5 points

### Extra Credit

For five points of extra credit, read the first line of input from the command line. In this case, the command line for executing your program would be

life X Y gens print pause

Command line arguments are described in §14.4 of D&D and in §5.10 of K&R. To parse a particular command line argument, you should use the library function atoi(). This is described in §8.4 of D&D, at several places in K&R, and in the man pages of Linux.