Subversion Repositories wimsdev

/*    Copyright (C) 1998-2003 XIAO, Gang of Universite de Nice - Sophia Antipolis

 *

 *  This program is free software; you can redistribute it and/or modify

 *  it under the terms of the GNU General Public License as published by

 *  the Free Software Foundation; either version 2 of the License, or

 *  (at your option) any later version.

 *

 *  This program is distributed in the hope that it will be useful,

 *  but WITHOUT ANY WARRANTY; without even the implied warranty of

 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

 *  GNU General Public License for more details.

 *

 *  You should have received a copy of the GNU General Public License

 *  along with this program; if not, write to the Free Software

 *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

 */

 /* Finds the shortest paths linking given points. */

/* fast algorithm is not ready. */

#define MAX_POINTS 32 /* cannot exceed number of bits in long */

#define MAX_DIM 10 /* dimension limit */

#define MAX_SHORT 20 /* limit of registered shortest paths */

#include "../config.h"

#include <stdio.h>

#include <stdlib.h>

#include <string.h>

#include <math.h>

#include <ctype.h>

int  pointcnt,dimension,first,last,count,shortcnt;

/* style = 0: loop to the start

 *    1: arbitrary open path

 *    2: open path with fixed start

 *    3: open path with fixed end

 *    4: open path with fixed start and end */

int style=0;

int fast=0; /* fast algo if 1, no rigor */

int optimize=0;

char *input;

double dist[MAX_POINTS][MAX_POINTS];

double ds[MAX_POINTS];

double coord[MAX_POINTS][MAX_DIM];

double shortest;

double tolerance; /* to compensate floating rounding error in comparison */

double distmin; /* minimum of distance between two points */

double firstlast; /* distance between first and last */

int shpath[MAX_SHORT][MAX_POINTS];

int chain[MAX_POINTS];

/* reverse a subchain */

void reverse(int i, int j)

{

    int k,t;

    for(k=0;k<(j-i+1)/2;k++) {

      t=chain[i+k]; chain[i+k]=chain[j-k];

      chain[j-k]=t;

    }

}

/* move point i to position j */

void reinsert(int i, int j)

{

    int t;

    t=chain[i];

    if(j>i) {

      j--;

      memmove(chain+i,chain+i+1,(j-i)*sizeof(chain[0]));

      chain[j]=t;

    }

    else {

      memmove(chain+j+1,chain+j,(i-j)*sizeof(chain[0]));

      chain[j]=t;

    }

}

int _fcalc(void)

{

    int modif;

    int i,j;

    modif=0;

/* four-configuration optimize */

    for(i=1;i<pointcnt-2;i++) {

      for(j=i+1;j<pointcnt-1;j++) {

          if(dist[chain[i-1]][chain[i]]+dist[chain[j]][chain[j+1]]

             >dist[chain[i-1]][chain[j]]+dist[chain[i]][chain[j+1]]

             +tolerance) {

            reverse(i,j); modif=1;

          }

      }

    }

/* Point relink */

    for(i=1;i<pointcnt-1;i++) {

      double dd;

      int th;

      th=chain[i];

      dd=dist[chain[i-1]][th]+dist[th][chain[i+1]]

        -dist[chain[i-1]][chain[i+1]];

      for(j=0;j<pointcnt-1;j++) {

          if(j==i || j==i-1) continue;

          if(dd>dist[chain[j]][th]+dist[chain[j+1]][th]

             -dist[chain[j]][chain[j+1]]+tolerance) {

            reinsert(i,j+1); modif=1;

          }

      }

    }

    for(i=0;i<pointcnt;i++) shpath[shortcnt][i]=chain[i];

    shortcnt+=modif; return modif;

}

void fastcalc(void)

{

    int i,j;

    for(i=0;i<pointcnt;i++) chain[i]=i;

    shortcnt=1;

    for(i=0,j=1;i<10 && j!=0;i++) j=_fcalc();

    for(shortest=0,i=0;i<pointcnt-1;i++) shortest+=dist[chain[i]][chain[i+1]];

    if(style==0) shortest+=dist[chain[0]][chain[pointcnt-1]];

    for(i=0;i<pointcnt;i++) shpath[0][i]=chain[i];

}

void _calc(int level, double dis, long used, int utab[])

{

    int current[MAX_POINTS];

    double dd,d1,d3,d2,dthis;

    int i;

    long l;

    dd=dis; d1=d2=d3=0;

    if(level<pointcnt-2) {

      int j,b,prec;

      double btab[MAX_POINTS];

      if(level>0) prec=utab[level-1]; else prec=0;

      if(level>2) {

          for(i=0;i<level-2;i++)

            btab[i]=dist[utab[i]][prec];

          if(level>3) {

            d1=ds[level-4]+ds[level-3]+ds[level-2];

            d3=dist[utab[level-4]][utab[level-2]]

              +ds[level-2]

              +dist[prec][utab[level-3]];

            d2=dist[utab[level-4]][prec]

              +dist[prec][utab[level-3]]

              +ds[level-3];

          }

      }

      if(level==0 || (level==1 && style==0)) b=last+1; else b=0;

      for(i=b,l=(long) 1<<b;i<pointcnt;i++,l<<=1) {

          if(used&l) continue;

          dthis=dist[prec][i];

          if(optimize) {

           if(style==0) {

            if(level>1 &&

               firstlast+dthis>dist[prec][last]+dist[first][i])

              continue;

           }

           else if(level>0) {

/* cut differently */

            if(style==1 && dthis>firstlast) continue;

/* switch with first */

            if((style&1) && level>1 && dist[first][i]<dthis) continue;

/* switch with last */

            if(style<3 && dist[prec][last]<dthis) continue;

          }

/* already too long */

          if(level>0 && shortcnt>0 &&

             dthis+dis+distmin*(pointcnt-level-1)>shortest)

            continue;

/* four-config optimize */

          for(j=0;j<=level-3;j++) {

              if(ds[j]+dthis>btab[j]+dist[utab[j+1]][i])

               goto next;

           }

/* five-config optimize */

          if(level>3 &&

             (d1+dthis>d2+dist[utab[level-2]][i] ||

            d1+dthis>d3+dist[utab[level-3]][i]))

            continue;

/* try prec elsewhere in the chain */

          if(level>3) {

            double dt;

            dt=dist[prec][i]+ds[level-2]-dist[utab[level-2]][i];

            for(j=0;j<level-3;j++) {

                if(dt>dist[prec][utab[j]]+dist[prec][utab[j+1]]-ds[j])

                  goto next;

            }

          }

  }

          memmove(current,utab,level*sizeof(utab[0]));

          current[level]=i;

          if(level>0) {dd=dis+dthis; ds[level-1]=dthis;}

          else {

            first=i; firstlast=dist[first][last];

          }

          _calc(level+1,dd,used|l,current);

          next: ;

      }

    }

    else {

      count++;

      for(i=0,l=(long) 1;i<pointcnt && used&l; i++,l<<=1);

      if(i>=pointcnt) {

          printf("ERROR: Internal error.\n"); exit(1);

      }

      utab[pointcnt-2]=i; utab[pointcnt-1]=last;

      dis+=dist[utab[pointcnt-3]][i]+dist[i][last];

      if(shortest==0 || dis<shortest-tolerance) {

          shortest=dis; shortcnt=0;

          memmove(shpath[shortcnt++],utab,MAX_POINTS*sizeof(utab[0]));

      }

      else if(dis<shortest+tolerance && shortcnt<MAX_SHORT)

          memmove(shpath[shortcnt++],utab,MAX_POINTS*sizeof(utab[0]));

    }

}

/* main calculation loops */

void calc(void)

{

    int i;

    long used;

    int utab[MAX_POINTS];

    if(fast) {

      fastcalc(); return;

    }

    count=0; shortest=0; shortcnt=0;

    memset(utab,0,sizeof(utab));

    switch(style) {

      case 0: { /* loop to the start */

          first=0; utab[0]=0;

          for(i=1;i<pointcnt;i++) {

            last=i; used=(long) 1<<i; used|=(long) 1;

            firstlast=dist[first][last];

            _calc(1,firstlast,used,utab);

          }

          break;

      }

      case 1: { /* arbitrary open path */

          for(i=0;i<pointcnt;i++) {

            last=i; used=(long) 1<<i;

            _calc(0,0,used,utab);

          }

          break;

      }

      case 2: { /* open path with fixed start */

          first=0; utab[0]=0;

          for(i=1;i<pointcnt;i++) {

            last=i; used=(long) 1|(1<<i);

            firstlast=dist[0][last];

            _calc(1,0,used,utab);

          }

          break;

      }

      case 3: { /* open path with fixed end */

          last=0; used=(long) 1;

          _calc(0,0,used,utab);

          break;

      }

      case 4: { /* open path with fixed start and end */

          first=0; utab[0]=0;

          last=pointcnt-1; used=(long) 1|(1<<last);

          firstlast=dist[first][last];

          _calc(1,0,used,utab);

          break;

      }

    }

}

/* Print the result */

void printresult(void)

{

    int i,j;

    printf("%f %d %d\n",shortest,shortcnt,count);

    for(j=0;j<shortcnt;j++) {

      for(i=0;i<pointcnt;i++) printf("%d ",shpath[j][i]+1);

      printf("\n");

    }

}

/* prepare distance table */

void makedist(void)

{

    int i,j,k;

    double d;

    distmin=-1;

    for(i=0;i<pointcnt-1;i++) {

      for(j=i+1;j<pointcnt;j++) {

          d=0;

          for(k=0;k<dimension;k++) {

            d+=pow(coord[i][k]-coord[j][k],2);

          }

          d=sqrt(d); dist[i][j]=dist[j][i]=d;

          if(distmin<0 || distmin>d) distmin=d;

      }

    }

    tolerance=distmin*0.000001;

}

int main(int argc, char *argv[])

{

    char *p,*p2,*p3;

    int dim;

    input=getenv("wims_exec_parm");

/* nothing to do if no problem */

    if(input==NULL || *input==0) return 0;

    for(p=input+strlen(input);p>input && isspace(*(p-1));p--);

    *p=0; dimension=0;

    for(pointcnt=0,p=input;*p!=0 && pointcnt<MAX_POINTS;p=p3) {

      p2=strchr(p,'\n');

      if(p2==NULL) p3=p+strlen(p);

      else {p3=p2+1; *p2=0;}

      dim=0;

      for(p2=strchr(p,','); p2!=NULL && dim<MAX_DIM;

          p=p2+1,dim++,p2=strchr(p,',')) {

          *p2=0; coord[pointcnt][dim]=strtod(p,NULL);

      }

      if(dim<MAX_DIM) coord[pointcnt][dim++]=strtod(p,NULL);

      if(dim<2) continue; /* bad line */

      if(dimension==0) dimension=dim;

      pointcnt++;

    }

    if(pointcnt<3) {

      printf("ERROR: Not enough points.\n"); exit(1);

    }

    p=getenv("w_shortpath_style");

    if(p!=NULL) style=atoi(p);

    if(style<0 || style>4) style=0;

    makedist();

    optimize=1; calc();printresult();

/*    optimize=0; calc();printresult();

*/    return 0;

}