/* This program demonstrates how an isomorphism is found between
   two graphs, using the Moebius graph as an example.
   This version uses Traces.
*/

#include "traces.h"

int
main(int argc, char *argv[])
{
    DYNALLSTAT(int,lab1,lab1_sz);
    DYNALLSTAT(int,lab2,lab2_sz);
    DYNALLSTAT(int,ptn,ptn_sz);
    DYNALLSTAT(int,orbits,orbits_sz);
    DYNALLSTAT(int,map,map_sz);
    static DEFAULTOPTIONS_TRACES(options);
    TracesStats stats;
 /* Declare and initialize sparse graph structures */
    SG_DECL(sg1); SG_DECL(sg2);
    SG_DECL(cg1); SG_DECL(cg2);

    int n,m,i;

 /* Select option for canonical labelling */

    options.getcanon = TRUE;
 
 /* Read a number of vertices and process */

    while (1)
    {
        printf("\nenter n : ");
        if (scanf("%d",&n) == 1 && n > 0)
        {
            if (n%2 != 0)
            {
                fprintf(stderr,"Sorry, n must be even\n");
                continue;
            }

            m = SETWORDSNEEDED(n);
            nauty_check(WORDSIZE,m,n,NAUTYVERSIONID);

            DYNALLOC1(int,lab1,lab1_sz,n,"malloc");
            DYNALLOC1(int,lab2,lab2_sz,n,"malloc");
            DYNALLOC1(int,ptn,ptn_sz,n,"malloc");
            DYNALLOC1(int,orbits,orbits_sz,n,"malloc");
            DYNALLOC1(int,map,map_sz,n,"malloc");

         /* Now make the first graph */

            SG_ALLOC(sg1,n,3LU*n,"malloc");
            sg1.nv = n;              /* Number of vertices */
            sg1.nde = 3LU*n;           /* Number of directed edges */

            for (i = 0; i < n; ++i)
            {
                sg1.v[i] = 3LU*i;     /* Position of vertex i in v array */
                sg1.d[i] = 3;       /* Degree of vertex i */
            }
             
            for (i = 0; i < n; i += 2)   /* Spokes */
            {
                sg1.e[sg1.v[i]] = i+1;
                sg1.e[sg1.v[i+1]] = i;
            }

            for (i = 0; i < n-2; ++i)  /* Clockwise edges */
                sg1.e[sg1.v[i]+1] = i+2;
            sg1.e[sg1.v[n-2]+1] = 1;
            sg1.e[sg1.v[n-1]+1] = 0;

            for (i = 2; i < n; ++i)  /* Anticlockwise edges */
                sg1.e[sg1.v[i]+2] = i-2;
            sg1.e[sg1.v[1]+2] = n-2;
            sg1.e[sg1.v[0]+2] = n-1;
                
         /* Now make the second graph */

            SG_ALLOC(sg2,n,3LU*n,"malloc");
            sg2.nv = n;              /* Number of vertices */
            sg2.nde = 3LU*n;           /* Number of directed edges */

            for (i = 0; i < n; ++i)
            {
                sg2.v[i] = 3LU*i;
                sg2.d[i] = 3;
            }

            for (i = 0; i < n; ++i)
            {
                sg2.v[i] = 3LU*i;
                sg2.d[i] = 3;
                sg2.e[sg2.v[i]] = (i+1) % n;      /* Clockwise */
                sg2.e[sg2.v[i]+1] = (i+n-1) % n;  /* Anti-clockwise */
                sg2.e[sg2.v[i]+2] = (i+n/2) % n;  /* Diagonals */
            }

         /* Label sg1, result in cg1 and labelling in lab1; similarly sg2.
            It is not necessary to pre-allocate space in cg1 and cg2, but
            they have to be initialised as we did above.  */
            
            Traces(&sg1,lab1,ptn,orbits,&options,&stats,&cg1);
            Traces(&sg2,lab2,ptn,orbits,&options,&stats,&cg2);

         /* Compare canonically labelled graphs */

            if (aresame_sg(&cg1,&cg2))
            {
                printf("Isomorphic.\n");
                if (n <= 1000)
                {
                 /* Write the isomorphism.  For each i, vertex lab1[i]
                    of sg1 maps onto vertex lab2[i] of sg2.  We compute
                    the map in order of labelling because it looks better. */

                    for (i = 0; i < n; ++i) map[lab1[i]] = lab2[i];
                    for (i = 0; i < n; ++i) printf(" %d-%d",i,map[i]);
                    printf("\n");
                }
            }
            else
                printf("Not isomorphic.\n");
        }
        else
            break;
    }

    exit(0);
}
