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hb.c
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hb.c
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/* ************************************************************************
** hb.c Hilbert bases package version 0.1 (experimental)
**
** Copyright (C) 1995 Dmitrii V. Pasechnik
** RIACA, Amsterdam, The Netherlands
**
** construct the Hilbert basis for the solutions of an inhomogeneous
** diophantine equation
** (Clausen - Fortenbacher algorithm)
* *********************************************************************** */
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include "hb.h"
struct step {int node; int edge;};
int hb(eq *e, int **sols, int savesols) /* return number elts in the basis; */
{ /* or -1 if out of memory */
int nvert,amon,bmon,i,j,n,m,lsol,nnodes,
*sol,*mark,amax,bmax,bcmax,nsol,lp;
struct step *p, *p_t;
int *mark_t, *sol_t, ntests;
int w,*x,*pb,sign,nx,offset;
int ismsol(eq *,int *,int *,struct step *,int *);
void saves(int, int *, int, int, int *, int **), oomem(char *);
int solmax;
lsol=e->n + e->m; /* length of the vectors */
amax=getmax(e->n, e->a);
bmax=getmax(e->m, e->b);
if (e->c>bmax) bcmax=e->c;
else bcmax=bmax;
/* vertices of the graph are labelled by [-bcmax..amax] */
nvert=amax+bcmax+1; /* number of vertices in the graph */
if (savesols) /* allocate inital chunk for solutions */
{
solmax=SOLCHUNK;
if ((*sols=(int *)malloc(lsol*solmax*sizeof(int)))==NULL)
oomem("hb(sols)");
}
if ((sol=(int *)calloc(lsol, sizeof(int)))==NULL)
oomem("hb"); /* to store (partial) solution */
if ((p=(struct step *)calloc(nvert+1, sizeof(struct step)))==NULL)
oomem("hb"); /* the path */
if ((mark=(int *)calloc(nvert, sizeof(int)))==NULL)
oomem("hb"); /* mark visited vertices */
if ((sol_t=(int *)calloc(lsol, sizeof(int)))==NULL)
oomem("hb"); /* to store (partial) solution */
if ((p_t=(struct step *)calloc(nvert+1, sizeof(struct step)))==NULL)
oomem("hb"); /* the path */
if ((mark_t=(int *)calloc(nvert, sizeof(int)))==NULL)
oomem("hb"); /* mark visited vertices */
ntests=0;
mark+=bcmax; /* adjust to use the original node names */
if (e->c) mark[-e->c]=1; /* mark the visited node (don't mark if 0) */
lp=0; /* length of the path (# of edges) */
nsol=0; /* number of elts in the basis */
amon=0; bmon=0; /* to mantain monotonousness */
p[0].node=-e->c; /* 1st vertex of the path is -c,trying to reach 0 */
do
{
if (!p[lp].node && lp) /* found a solution */
{
ntests++;
if (e->m==0 || ismsol(e,sol,sol_t,p_t,mark_t))
saves(savesols, &solmax, lsol, ++nsol, sol, sols);
goto getnext;
}
else /* forward ! */
{
if (p[lp].node<=0)
{ offset=0; nx=e->n; x=e->a; pb=&amon; sign=1;}
else { offset=e->n; nx=e->m; x=e->b; pb=&bmon; sign=-1;}
for (w=*pb; w<nx && mark[p[lp].node+sign*x[w]]; w++);
if (w<nx) /* success */
{
p[lp].edge=w;
sol[offset+w]++;
*pb=w;
p[lp+1].node=p[lp].node+sign*x[w];
mark[p[++lp].node]=1;
ntests++;
if (e->m>0 && !ismsol(e,sol,sol_t,p_t,mark_t)) goto getnext;
}
else
getnext:
{
while (lp>=1)
{
mark[p[lp].node]=0;
if (p[lp-1].node<=0)
{ offset=0; nx=e->n; x=e->a; pb=&amon; sign=1;}
else { offset=e->n; nx=e->m; x=e->b; pb=&bmon; sign=-1;}
sol[offset+p[lp-1].edge]--;
for (w=p[lp-1].edge+1;
w<nx && mark[p[lp-1].node+sign*x[w]]; w++);
if (w<nx) /* success */
{
p[lp-1].edge=w;
sol[offset+w]++;
*pb=w;
p[lp].node=p[lp-1].node+sign*x[w];
mark[p[lp].node]=1;
ntests++;
if (e->m>0 && !ismsol(e,sol,sol_t,p_t,mark_t)) goto getnext;
goto cont;
}
else
{
lp--;
/* reset *pb */
for (w=lp-1; w>=0 && (sig(p[w].node) != sign); w--);
if (w<0) *pb=0;
else *pb=p[w].edge;
}
}
cont:
;
}
}
}
while(lp);
free(sol);
free(p);
free(mark-bcmax);
free(sol_t);
free(p_t);
free(mark_t);
if (prtlev>1) printf("\n number of nonmin. (partial) solutions found %d\n",
ntests - nsol);
/* getting rid of extra space */
if (nsol)
{
if ((*sols=(int *)realloc(*sols,lsol*nsol*sizeof(int)))==NULL)
oomem("hb(realloc)");
}
else free(*sols); /* no solutions found */
return nsol;
}
/* ***************************************************************
find maximum of an array of ints
*/
int getmax(int n, int a[])
{
int i, maxa;
for(maxa=0,i=0; i<n; i++)
if (maxa<a[i]) maxa=a[i];
return maxa;
}
/* ***************************************************************
check minimality of a solution (1-minimal, 0-not minimal)
*/
int ismsol(eq *e, int bound[], int sol[], struct step p[], int mark[])
{
int nvert,amon,bmon,i,j,n,m,lsol,nnodes,
amax,bmax,bcmax,nsol,lp;
int w,*x,*pb,sign,nx,offset;
lsol=e->n + e->m; /* length of the vectors */
amax=getmax(e->n, e->a);
bmax=getmax(e->m, e->b);
if (e->c>bmax) bcmax=e->c;
else bcmax=bmax;
/* vertices of the graph are labelled by [-bcmax..amax] */
nvert=amax+bcmax+1; /* number of vertces in the graph */
bzero(sol,lsol*sizeof(int));
bzero(p,(nvert+1)*sizeof(struct step));
bzero(mark,nvert*sizeof(int));
mark+=bcmax; /* adjust to use the original node names */
if (e->c) mark[-e->c]=1; /* mark the visited node (don't mark if 0) */
lp=0; /* length of the path (# of edges) */
nsol=0; /* number of elts in the basis */
amon=0; bmon=0; /* to mantain monotonousness */
p[0].node=-e->c; /* 1st vertex of the path is -c,trying to reach 0 */
do
{
if (!p[lp].node && lp) /* found a solution */
{
/* if (nsol++) return 0; */
nsol++;
if (memcmp(bound,sol,lsol*sizeof(int))) return 0;
goto getnext;
}
else /* forward ! */
{
if (p[lp].node<=0)
{ offset=0; nx=e->n; x=e->a; pb=&amon; sign=1;}
else { offset=e->n; nx=e->m; x=e->b; pb=&bmon; sign=-1;}
for (w=*pb; w<nx &&
(mark[p[lp].node+sign*x[w]] ||
sol[offset+w]>=bound[offset+w]); w++);
if (w<nx) /* success */
{
p[lp].edge=w;
sol[offset+w]++;
*pb=w;
p[lp+1].node=p[lp].node+sign*x[w];
mark[p[++lp].node]=1;
}
else
getnext:
{
while (lp>=1)
{
mark[p[lp].node]=0;
if (p[lp-1].node<=0)
{ offset=0; nx=e->n; x=e->a; pb=&amon; sign=1;}
else { offset=e->n; nx=e->m; x=e->b; pb=&bmon; sign=-1;}
sol[offset+p[lp-1].edge]--;
for (w=p[lp-1].edge+1;
w<nx && (mark[p[lp-1].node+sign*x[w]] ||
sol[offset+w]>=bound[offset+w]); w++);
if (w<nx) /* success */
{
p[lp-1].edge=w;
sol[offset+w]++;
*pb=w;
p[lp].node=p[lp-1].node+sign*x[w];
mark[p[lp].node]=1;
goto cont;
}
else
{
lp--;
/* reset *pb */
for (w=lp-1; w>=0 && (sig(p[w].node) != sign); w--);
if (w<0) *pb=0;
else *pb=p[w].edge;
}
}
cont:
;
}
}
}
while(lp);
return 1;
}
/* ***************************************************************
*/
void saves(int savesol, int *solmax, int l, int num, int s[], int **sols)
{
void oomem(char *);
if (!(num%1000)) printf("\n %8d",num);
if (savesol) /* storing the solution */
{
if (*solmax<num) /* get another chunk */
{
*solmax+=SOLCHUNK;
if ((*sols=(int *)realloc(*sols, l*(*solmax)*sizeof(int)))==NULL)
oomem("savesol");
}
memcpy(*sols+l*(num-1),s,sizeof(int)*l);
}
}
/* ***************************************************************
*/
inline int sig(int z)
{
if (z<=0) return 1;
return -1;
}