## Sunday, July 15, 2012

### ANSI C: Coloring Problem

Introduction

The Coloring Problem is coloring the vertices of a graph such that no two adjacent vertices share the same color, in this post, we will try to implement it in ANSI C.

The Program

Coloring_Problem.c

``````#include <stdbool.h>
#include <stdlib.h>
#include <stdio.h>

/**
* Graph coloring
* Coloring the vertices of a graph such that
* no two adjacent vertices share the same color;
* Wiki: http://en.wikipedia.org/wiki/Graph_coloring
*/

FILE *res;

// The 2-D array denotes a graph adjacent status,
// For example, [a, b] are adjacent vertices,
// [a, d] are also adjacent vertices.
// the index starts from 1,
// [x] and [x] are not considered
// #,a,b,c,d,e,f
int _adjacentMatrix  = {0,0,0,0,0,0,0, // not use
0,0,1,0,1,0,0, // a
0,1,0,1,0,1,0, // b
0,0,1,0,0,0,1, // c
0,1,0,0,0,1,0, // d
0,0,1,0,1,0,1, // e
0,0,0,1,0,1,0  // f
};

int _verticeAmount = 6;  // six points

// three colors
char _colors = { "NULL",
"RED",
"GREEN",
"WHITE"
};

// temp store the result
int _result = {0};

void m_coloring( int i );
bool promising( int i );

int main()
{
res = fopen("result.txt", "w");
printf("there are %d vertices, the color combinations are as below: \n\n", _verticeAmount);
fprintf(res, "there are %d vertices, the color combinations are as below: \n\n", _verticeAmount);
m_coloring( 0 );
fclose( res );

system("PAUSE");
return 0;
}

/**
* The coloring function that will recursively create different combinations
* then call promising function to test whether the combination is valid.
*
* Three actions:
*         Output the result if
*         the current combination is valid and reach the latest vertice.
*
*         Continue add color - vertice to extend combination if
*         the current combination is valid but not reach the latest vertice.
*
*         Terminate the recursive to skip any combination
*         that starts with the current combination if
*         the current combination is not valid.
*
*/
void m_coloring ( int i )
{
int color; // color index for test
int j; // index for output result

if( promising(i) )  // coloring success
{
if( i == _verticeAmount ) // is latest vertice
{
for( j = 1;j <= _verticeAmount;j ++ )  // output the result
{
if (j > 1) {
printf(",");
fprintf(res, ", ");
}
printf("%s", _colors[_result[j]]);
fprintf(res, "%s", _colors[_result[j]]);
}
printf("\n\n");
fprintf(res, "\n\n");

}

else  // not latest vertice
{
for( color = 1;color <= 3;color ++ )  // test each color
{
_result[i+1] = color;  // set color to next vertice
m_coloring(i+1); // recursive to continue combination
}
}
}
}

/**
* check whether has adjacent virtice share color with current virtice
* return bool
* true: no adjacent vertice share the same color, can
* continue this combination
* false: has adjacent vertice share the same color,
* this combination should be terminated
*/
bool promising( int currentVerticeIndex )
{
int j = 1; // start from first virtice
bool sw = true;  // default to success (no two adjacent vertices share the same color)

while( (j < currentVerticeIndex) && sw)  // scan all previous vertices
{
// if found an adjacent vertice share the same color
if( _adjacentMatrix[currentVerticeIndex][j] && (_result[currentVerticeIndex] == _result[j])) {
sw = false;  // set to fail (has two adjacent vertices share the same color)
break;
}
j++;
}

return sw;  // return the result (success or fail)
}
``````

The promising function will return whether current combination is valid.

The m_coloring function that will recursively create different combinations then call promising function to test whether the combination is valid. It will do three different actions with respect to the different status and the result of promising function:

1. Output the result if the current combination is valid and reach the latest vertice.

2. Continue add color - vertice to extend combination if the current combination is valid but not reach the latest vertice.

3. Terminate the recursive to skip any combination that starts with the current combination if the current combination is not valid.

The Result

Reference
Wiki
http://en.wikipedia.org/wiki/Graph_coloring