Sunday, 14 October 2012

Graph coloring problem with Backtracking in C

Today I am going to post a program in C that is used for solving the Graph Coloring problem.
What is Graph-Coloring : In this problem, for any given graph G we will have to color each of the vertices in G in such a way that no two adjacent vertices get the same color and the least number of colors are used.
How to solve the problem : First take input number of vertices and edges in graph G. Then input all the indexes of adjacency matrix of G whose value is 1. Now we will try to color each of the vertex. A next_color(k) function takes in index of the kth vertex which is to be colored. First we assign color1 to the kth vertex.Then we check whether it is connected to any of previous (k-1) vertices using backtracking. If connected then assign a color x[i]+1 where x[i] is the color of ith vertex that is connected with kth vertex.
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SOURCE CODE
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#include<stdio.h>
int G[50][50],x[50]; 
//G:adjacency matrix,x:colors
void next_color(int k){
   int i,j;
   x[k]=1; 
//coloring vertex with color1
   for(i=0;i<k;i++){
//checking all k-1 vertices-backtracking
     if(G[i][k]!=0 && x[k]==x[i])  /
/if connected and has same color
       x[k]=x[i]+1; 
//assign higher color than x[i]
   }
}

int main(){
  int n,e,i,j,k,l;
  printf("Enter no. of vertices : ");
  scanf("%d",&n); 
//total vertices
  printf("Enter no. of edges : ");
  scanf("%d",&e); 
//total edges
 
  for(i=0;i<n;i++)
    for(j=0;j<n;j++)
      G[i][j]=0; 
//assign 0 to all index of adjacency matrix
     
  printf("Enter indexes where value is 1-->\n");
  for(i=0;i<e;i++){
    scanf("%d %d",&k,&l);
    G[k][l]=1;
    G[l][k]=1;
  }
 
  for(i=0;i<n;i++)
    next_color(i); 
//coloring each vertex

  printf("Colors of vertices -->\n");
  for(i=0;i<n;i++) 
//displaying color of each vertex
    printf("Vertex[%d] : %d\n",i+1,x[i]);

  return 0;
}

NOTE : This code is written,compiled and run with GCC compiler under Linux environment Ubuntu12.04LTS Precise Pangolin.
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OUTPUT
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Enter no. of vertices : 4
Colored vertices of Graph G
Enter no. of edges : 5
Enter indexes where value is 1-->
0 1
1 2
1 3
2 3
3 0
Colors of vertices -->
Vertex[1] : 1
Vertex[2] : 2
Vertex[3] : 1
Vertex[4] : 3
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RELATED POSTS
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 To understand m-coloring i.e. to color a graph with all possible m colors (hence known as M-Way Coloring or m-coloring) visit :

7 comments:

  1. thnx for sharing...
    plz post n-queens problem

    ReplyDelete
  2. hello, welch coloring algorithm with the exam schedule will do Powel How can I watch the way, can you help?

    ReplyDelete
  3. I think this is greedy coloring, not backtracking.

    ReplyDelete
    Replies
    1. this is backtracking because of the checking of all previous adjacent nodes for a current node under processing;

      Delete
  4. thank you very very much :)

    ReplyDelete