The 3-Coloring Problem Iterative Algorithm Input:An undirected graph G=,E). Output:A 3-coloring d1...]of the vertices of G where each di]is 1,2,or 3. 1.for k1 to n 2.d←-0； 3.end for; 4.fag-false; 5.k-1; 6.while 1 7. while d2 8. ①←+1； 9. if cis a legal coloring then set fag-true and exit from the two while loops; 10. else if cis partial then+1; 11. end while; 12. ←-0； 13. k-k1; 14.end while; 15.if fag then output c 16.else output "no solution";The 3-Coloring Problem Iterative Algorithm Input: An undirected graph G=(V, E). Output: A 3-coloring c[1…n] of the vertices of G, where each c[j] is 1, 2, or 3. 1. for k1 to n 2. c[k]0; 3. end for; 4. flagfalse; 5. k1; 6. while k1 7. while c[k]2 8. c[k]c[k]+1; 9. if c is a legal coloring then set flagtrue and exit from the two while loops; 10. else if c is partial then kk+1; 11. end while; 12. c[k]0; 13. kk-1; 14. end while; 15. if flag then output c; 16. else output “no solution”;