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  N-Queens 3D

A necklace of length `n' over an alphabet of `a' beads is invariant under rotation (but not reflection, that's bracelets apparently). We want to enumerate non-equivalent necklaces so we might as well enumerate the lexicographically least representative of each equivalence class.

Form, |alphabet|≥1

n=[] a=[]
op:[] total=[] necklaces

Note that `(p)' indicates a periodic solution, and `.' indicates a dead-end has been encountered.

CRSMS algorithm

function CRSMS(n, a, s, pos, p)
// s[1..pos-1] is the partial solution, NB. 1..
 { if( pos <= n )
    { s[pos] = s[pos-p];
      CRSMS(n, a, s, pos+1, p);
      for( s[pos]++; s[pos] < a; s[pos]++ )
      CRSMS(n, a, s, pos+1, pos);
   else // pos > n, done
    { if( n % p == 0 )
       { var j, ln = new Array();
         for(j=1; j < pos; j++) ln[j-1] = s[j];
	     //without the leading 0 of s[]
         document.theForm.opt.value += (Count > 0 ? '\n' : '') + ln + ' ';
         document.theForm.Count.value = Count;
      else document.theForm.opt.value += '.';

CRSMS(n, a, s, 1, 1);  //start


Search the [Bib] for
Cattell c2000
or for
-- 17/4/2006, L.A.
Coding Ockham's Razor, L. Allison, Springer

A Practical Introduction to Denotational Semantics, L. Allison, CUP

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© L. Allison   (or as otherwise indicated),
Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University,
was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.)
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