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Revision: 191
          http://pure-lang.svn.sourceforge.net/pure-lang/?rev=191&view=rev
Author:   agraef
Date:     2008-06-06 23:36:38 -0700 (Fri, 06 Jun 2008)

Log Message:
-----------
Update examples.

Modified Paths:
--------------
    pure/trunk/examples/myutils.pure

Modified: pure/trunk/examples/myutils.pure
===================================================================

--- pure/trunk/examples/myutils.pure	2008-06-06 21:08:17 UTC (rev 190)
+++ pure/trunk/examples/myutils.pure	2008-06-07 06:36:38 UTC (rev 191)
@@ -1,13 +1,13 @@
 // Dr Libor Spacek, 21th May 2008
 
-//General mathematical iterators over one and two indices and examples of their use
+//General mathematical iterators over one and two indices
 MathIter1 op i1 i2 f = foldl1 op (map f (i1..i2));
-MathIter2 op i1 i2 j1 j2 f = foldl1 op (map (uncurry f) [x,y; x = i1..i2; y = j1..j2]);
-
+MathIter2 op i1 i2 j1 j2 f = 
+		foldl1 op (map (uncurry f) [x,y; x = i1..i2; y = j1..j2]);
+//Examples on how to use the mathematical iterators
 Sigma i1 i2 f = MathIter1 (+) i1 i2 f;
 Pi i1 i2 f = MathIter1 (*) i1 i2 f;
 Factorial n = Pi 1L n id;
-
 //Binomial using (k, n-k) symmetry and bignum division
 Binomial n k = (Pi (k+1L) n id) div (Pi 2L (n-k) id) if n-k < k;
 	     = (Pi (n-k+1L) n id) div (Pi 2L k id);
@@ -26,27 +26,28 @@
 
 // rotate n items, generalisation of "rotate the bits instruction"
 // example: head (nrotate (-33) (0..23)); 
-// what time is 33 hrs before midnight? 15 hrs. The clock was moved -9 = -33 mod 24
+// what time is 33 hrs before midnight? 15 hrs. 
+// The clock was moved -33 mod 24 = -9 hours from midnight (0)
 nrotate  n::int l = protate nm l when ll = #l; nm = ll + (n mod ll) end if n<0;
-	          = protate nm l when nm = n mod #l end;
+	               = protate nm l when nm = n mod #l end;
 
 // interpret any nonzero result as true: prevents errors in conditions
 nonzero 0 = 0;
 nonzero x = 1;
 
 // The Queens problem: 
-// the solution is only the rows permutation, without the ordered columns (1..n). 
+// the solution is only the rows permutation, without the ordered columns (1..n) 
 // full 2D board coordinates can be produced with: zip (1..n) (queens n); 
 safe _ _ [] = 1;
-safe id::int j::int (j2::int:l) = if (j==j2) || (id==j2-j) || (id==j-j2) then 0 
-				  else safe (id+1) j l;
+safe id::int j::int (j2::int:l) = 
+		if (j==j2) || (id==j2-j) || (id==j-j2) then 0 else safe (id+1) j l;
 
 queens n::int = list (search n n n [])
   with
-   search _ 0 _ _ = (); 	 	          // last i, solved
+   search _ 0 _ p = (); 	 	     // last i, solved
    search _ _ 0 _ = 0; 		  	 	  // fail, run out of alternative js
    search n::int i::int j::int p = 
-     if nonzero solution then j,solution          // new i led to a solution
+     if nonzero solution then j,solution   // new i led to a solution
      else search n i (j-1) p 		          // or it failed, try another j
      when solution = search n (i-1) n (j:p); end if safe 1 j p;     		          
      = search n i (j-1) p			  // also try another j when unsafe
@@ -55,34 +56,38 @@
 // this concise backtracking tailqueens throw a single solution
 tailqueens n::int = catch id (srch n n n []) 
   with srch _ 0 _ p = throw p; srch _ _ 0 _ = 0;
-       srch n::int i::int j::int p = () if safe 1 j p && nonzero (srch n (i-1) n (j:p));
-       	   			   = srch n i (j-1) p end;
+       srch n::int i::int j::int p = if safe 1 j p then 
+         ( if nonzero (srch n (i-1) n (j:p)) then 1 else srch n i (j-1) p ) 
+         else srch n i (j-1) p
+  end;
   
 // thequeens encodes my no search solution which is my original discovery, 
 // to my knowledge the simplest known algorithm for this kind of a problem.
 // there always exists one fundamental centre-symmetrical solution of this form, 
 // representing an orbit of just four solutions, instead of the usual eight.
 // these few lines of code are self-contained (not calling any square checking).
+// has been tested exhaustively from 0 to 5000 and individually for 50000.
 thequeens 1 = [0]; thequeens n::int = no solution if n<4;
-thequeens n::int = map (\x-> newsquare n x) (0..(n-1)) 
+thequeens n::int = map (newsquare n) (0..(n-1)) 
   with newsquare n::int x::int = (start+2*x) mod n if x < halfn;
          		       = (start2+2*(x-halfn)) mod n end //reflections
   when halfn = n div 2;
        start = if (n mod 3) then (halfn-1) else 1; // (n mod 3) == 0 is special
-       start2 = n-((start + 2*(halfn-1)) mod n)-1 end if (n mod 2)==0; // all even boards
-  = 0:(map (\x->1+x)(thequeens (n-1)));  // corner start solves odd size boards    
+       start2 = n-((start + 2*(halfn-1)) mod n)-1 end if (n mod 2)==0; // even
+  = 0:(map (\x->1+x)(thequeens (n-1))); // corner start solves odd size boards!    
 
 // row numbering in thequeens was changed to the "C style" e.g. 0..7. 
 // full board coordinates, e.g. (1..8) x (1..8) can be reconstructed with: 
 fullboard simple = zip (1..(#simple)) (map (\x->1+x) simple);
 
 // checks one queens solution either in 0..7 encoding or in 1..8 encoding.
-// returns 1 for a valid solution, 0 otherwise 
+// returns 1 for a correct result, including "no solution" for sizes 2 and 3. 
+// returns 0 if a queen attack exists anywhere in the presented solution
 checkqs [] = 1;
 checkqs (s::int:l) = if safe 1 s l then checkqs l else 0;
+checkqs (no solution) = 1;
 
-// conducts an exhaustive test of boards of all sizes from min to max, e.g. >queenstest (4..1000);
-// test _ min::int max::int = second argument must be greater than the first if min>=max;
+// conducts an exhaustive test of boards of all listed sizes. 
+// examples of use: >queenstest (1..1000); >queenstest (5000,4999..4990);
 queenstest [] = 1;
 queenstest (h:l) = if checkqs (thequeens h) then queenstest l else 0;
-


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