GRAPH COLORING PROBLEM USING BACKTRACKING METHOD

#include<stdio.h>
#include<conio.h>
#define MAX 10
int G[MAX][MAX],edges;
int color_tab[MAX];
void main()
{
int i,j,n;
void Gen_col_value(int,int);
void Gr_coloring(int,int);
int get_data();
void display(int);
clrscr();
printf("\n\n\t Graph coloring \n");
for(i=0;i<MAX;i++)/*intialilisation of the graph and color table*/
{
for(j=0;j<MAX;j++)
{
G[i][j]=0;
color_tab[i]=0;
}
}
n=get_data();
Gr_coloring(1,n);
display(n);
getch();
}
void Gen_col_value(int k,int n)
{
int j,m;
int a,b;
while(1)
{
a=color_tab[k]+1;
b=m+1;
color_tab[k]=a%b;//next highest color
if(color_tab[k]==0)return;//all colors have been used
for(j=1;j<=n;j++)
{
//check if this color is distinct from adjacent colors
if(G[k][j]&&color_tab[k]==color_tab[j])
break;
}
if(j==n+1)return;//next new color found
}
}
//such that adjacent vertices are assigned distinct integers
//k is the index of next vertex color.
void Gr_coloring(int k,int n)
{
Gen_col_value(k,n);
if(color_tab[k]==0)return;//No new color available
if(k==n)return;//atmost m colors have been
else Gr_coloring(k+1,n);//used to color the n vertices
}
int get_data()
{
int m,v1,v2,i,n;
printf("\n Enter the number of nodes");
scanf("%d",&n);
printf("\n Enter the number of edges");
scanf("%d",&edges);
m=n-1;
printf("\n Enter the edges of the graph");
printf("By giving values of V1 and V2\n");
for(i=1;i<edges;i++)
{
scanf("%d%d",&v1,&v2);
G[v1][v2]=G[v2][v1]=1;//if na edge is present then set it
}
return n;
}
void display(int n)
{
int i;
printf("\n the vertices to be colored as....\n");
for(i=1;i<=n;i++)
printf("\nV%d:=%d",i,color_tab[i]);
}

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