re: Article "Optimal Queens" by Timothy Rolfe, Dr. Dobb's Journal May,
2005
Seems like a good time for a food fight. I made a few mods to Rolfe's
Queens.c code to adapt it for a Mac CodeWarrior C console program that
automates testing using each of the four optimizations listed below for
4-18 queens. Rolfe must enjoy sitting around waiting for each test to
finish so he can enter the next set of n-queens and optimization parms
[24 times for n-queens 12-18], then wait again. I globalized a few
vars, paired allocs with frees inside nested for loops, and let the
program handle the permutations.
Since times start exceeding one second at about 14 queens, my times can
be directly compared with Rolfe's without too much picking of nits or
other amusements.
Rolfe's times followed by mine
-------------------------------------------------------
Rolfe's Dell desktop computer with a 2-GHz Pentium 4, OS not specified
No Optimization 20:59:51
Wirth's Validity Check 08:51:50
Permutation Vector 03:52:36
Both Optimizations 01:54:54
Total Time 35:39:11 [128351 secs]
-------------------------------------------------------
Macintosh 2003 MDD Dual 1.25-GHz G4, OS-X 10.3.9
No Optimization 22:34:59
Wirth's Validity Check 08:06:42
Permutation Vector 03:49:08
Both Optimizations 01:53:54
Total Time 36:24:45 [131085 secs]
-------------------------------------------------------
Mac at ~63% MHz gets ~98% of the performance.
-------------------------------------------------------
My modified Queens.c
/*
Derived from Queens.c from the article "Optimal Queens - A classical
problem
solved by backtracking" by Timothy Rolfe [Eastern Wa****ngton
University]
in Dr Dobb's Journal May 2005.
Adapted for Macintosh CodeWarrior 8.3 carbon console under OS-X
10.3.9
by F.C. Kuechmann, 1-3 May 2005. Memory variables *Col, *Diag,
*AntiD
made global in order to allow continuous operation for all queens
numbers
4-18 and all optimizations 0-3.
*/
#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
#include <ctype.h>
#include <string.h>
#include <DateTimeUtils.h>
#define kSecsInHr 3600
#define kSecsInMin 60
#define kMaxQueens 18
#define kMinQueens 4
long int Nunique, Ntotal;
short Opt1, Opt2;
short int *Col, *Diag, *AntiD;
/* Check two vectors for equality; return first inequality
(a la strncmp) */
int intncmp (int L[], int R[], int N)
{
int Idx;
for (Idx = 0; Idx < N; Idx++)
{
if ( L[Idx] - R[Idx] )
{
return L[Idx]-R[Idx];
} /*if*/
} /*for*/
return 0;
}
/* Rotate +90 or -90: */
void Rotate(int R[], int C[], int N, int Neg)
{
int Idx, Jdx;
Jdx = Neg ? 0 : N-1;
for (Idx = 0; Idx < N; Neg ? Jdx++ : Jdx--)
{
C[Idx++] = R[Jdx];
} /*for*/
Jdx = Neg ? N-1 : 0;
for (Idx = 0; Idx < N; Neg ? Jdx-- : Jdx++)
{
R[C[Idx++]] = Jdx;
} /*for*/
}
void Vmirror(int R[], int N)
{
int Idx;
for (Idx = 0; Idx < N; Idx++)
{
R[Idx] = (N-1) - R[Idx];
} /*for*/
return;
}
int SymmetryOps(
int Board[], /* The fully-populated board */
int Trial[], /* Used for symmetry checks */
/* Holds its own scratch space too! */
int Nqueenz) /* Number of cells in a row/column
*/
{
int Idx; /* Loop variable, array difference */
int Nequiv; /* Number equivalent boards */
/* Copy over; now Trial will be subjected to
the transformations */
for (Idx = 0; Idx < Nqueenz; Idx++)
{
Trial[Idx] = Board[Idx];
} /*for*/
/* 90 degrees --- clockwise */
Rotate (Trial, &Trial[Nqueenz], Nqueenz, 0);
Idx = intncmp (Board, Trial, Nqueenz);
if (Idx > 0)
{
return 0;
} /*if*/
if (Idx == 0)
{
Nequiv = 1;
}
else
{
/* 180 degrees */
Rotate (Trial, &Trial[Nqueenz], Nqueenz, 0);
Idx = intncmp (Board, Trial, Nqueenz);
if (Idx > 0)
{
return 0;
} /*if*/
if (Idx == 0)
{
Nequiv = 2;
}
else
{
/* 270 degrees */
Rotate (Trial, &Trial[Nqueenz], Nqueenz, 0);
Idx = intncmp (Board, Trial, Nqueenz);
if (Idx > 0)
{
return 0;
} /*if*/
Nequiv = 4;
} /*if*/
} /*if*/
/* Reflect -- vertical mirror */
for (Idx = 0; Idx < Nqueenz; Idx++)
{
Trial[Idx] = Board[Idx];
} /*for*/
Vmirror (Trial, Nqueenz);
Idx = intncmp (Board, Trial, Nqueenz);
if (Idx > 0)
{
return 0;
} /*if*/
/* -90 degrees --- equiv. to diagonal mirror */
Rotate (Trial, &Trial[Nqueenz], Nqueenz, -1);
Idx = intncmp (Board, Trial, Nqueenz);
if (Idx > 0)
{
return 0;
} /*if*/
if (Idx < 0)
{
/* -180 degrees --- equiv. to horizontal mirror */
Rotate (Trial, &Trial[Nqueenz], Nqueenz, -1);
Idx = intncmp (Board, Trial, Nqueenz);
if (Idx > 0)
{
return 0;
} /*if*/
if (Idx < 0)
{
/* -270 degrees --- equiv. to anti-diagonal
mirror */
Rotate (Trial, &Trial[Nqueenz], Nqueenz, -1);
Idx = intncmp (Board, Trial, Nqueenz);
if (Idx > 0)
{
return 0;
} /*if*/
} /*if*/
} /*if*/
/* WE HAVE A GOOD ONE! */
return Nequiv * 2;
}
void Mark (int R, int C, int Nqueenz, short Flag)
{
int Idx;
Col[C] = Flag;
/* Diagonal: Row-Col == constant */
Idx = R - C + Nqueenz-1;
Diag[Idx] = Flag;
/* AntiDiagonal: Row+Col == constant */
Idx = R + C;
AntiD[Idx] = Flag;
}
int Valid (int Board[], int Nqueenz, int Row)
{
int Idx; /* Index into Diag[] / AntiD[] */
short Chk; /* Occupied flag */
int p;
if (Opt1)
{
Chk = Col[Board[Row]];
/* Diagonal: Row-Col == constant */
Idx = Row - Board[Row] + Nqueenz-1;
Chk = Chk || Diag[Idx];
/* AntiDiagonal: Row+Col == constant */
Idx = Row + Board[Row];
Chk = Chk || AntiD[Idx];
return !Chk; /* Valid if NOT any occupied */
}
else
{
for (Idx = 0; Idx < Row; Idx++)
{
p = abs(Board[Row]-Board[Idx]);
if ( Board[Idx] == Board[Row] || p == (Row-Idx) )
{
return 0;
} /*if*/
} /*for*/
return 1;
} /*if*/
}
void Nqueens (int Board[], int Trial[], int Nqueenz, int Row)
{
int Idx, Lim, Vtemp;
if (Row < Nqueenz-1)
{
if (Valid (Board, Nqueenz, Row))
{
if (Opt1)
{
Mark (Row, Board[Row], Nqueenz, 1);
} /*if*/
Nqueens (Board, Trial, Nqueenz, Row+1);
if (Opt1)
{
Mark (Row, Board[Row], Nqueenz, 0);
} /*if*/
} /*if*/
Lim = Row ? Nqueenz : (Nqueenz+1)/2 ;
for (Idx = Row+1; Idx < Lim; Idx++)
{
Vtemp = Board[Idx];
Board[Idx] = Board[Row];
Board[Row] = Vtemp;
if (Valid (Board, Nqueenz, Row))
{
Mark (Row, Board[Row], Nqueenz, 1);
Nqueens (Board, Trial, Nqueenz, Row+1);
Mark (Row, Board[Row], Nqueenz, 0);
} /*if*/
} /*for*/
/* Regenerate original vector from Row to
Nqueenz-1: */
Vtemp = Board[Row];
for (Idx = Row+1; Idx < Nqueenz; Idx++)
{
Board[Idx-1] = Board[Idx];
} /*for*/
Board[Idx-1] = Vtemp;
}
else
{
if ( !Valid (Board, Nqueenz, Row) )
{
return;
} /*if*/
Idx = SymmetryOps (Board, Trial, Nqueenz);
if (Idx)
{
Nunique++;
Ntotal += Idx;
} /*if*/
} /*if*/
return;
}
void Nqueens1 (int Board[], int Trial[], int Nqueenz, int Row)
{
int Colum;
int Tst;
if (Row == Nqueenz)
{
Tst = SymmetryOps (Board, Trial, Nqueenz);
if (Tst)
{
Nunique++;
Ntotal += Tst;
} /*if*/
}
else
{
for (Colum = 0; Colum < Nqueenz; Colum++)
{
Board[Row] = Colum;
if (Valid (Board, Nqueenz, Row))
{
if (Opt1)
{
Mark (Row, Board[Row], Nqueenz, 1);
} /*if*/
Nqueens1 (Board, Trial, Nqueenz, Row+1);
if (Opt1)
{
Mark (Row, Board[Row], Nqueenz, 0);
} /*if*/
} /*if*/
} /*for*/
} /*if*/
}
void DoIt(int Idx, int Nqueenz)
{
int *Board, *Trial;
Opt1 = Idx & 1;
Opt2 = (Idx>>1) & 1;
printf ("Opt1 = %2d\n", Opt1);
printf ("Opt2 = %2d\n", Opt2);
Board = (int *) calloc (Nqueenz, sizeof *Board);
Trial = (int *) calloc (Nqueenz*2, sizeof *Board);
/* Initial permutation generated. */
for (Idx = 0; Idx < Nqueenz; Idx++)
{
Board[Idx] = Idx;
}/*for*/
AntiD = NULL;
Col = (short *) calloc (Nqueenz, sizeof *Col);
Diag = (short *) calloc ( 2*Nqueenz-1, sizeof *Diag );
AntiD = (short *) calloc ( 2*Nqueenz-1, sizeof *AntiD );
if ( !AntiD )
{
printf ("calloc failed --- out of memory!");
exit (6);
} /*if*/
if (Opt2)
{
Nqueens (Board, Trial, Nqueenz, 0);
}
else
{
Nqueens1(Board, Trial, Nqueenz, 0);
} /*if*/
free(Col);
free(Diag);
free(AntiD);
free(Board);
free(Trial);
}
void PrintLapsed(unsigned long Lapsed)
{
int quot;
quot = Lapsed/kSecsInHr;
printf (" %02d", quot);
Lapsed = Lapsed - (quot * kSecsInHr);
quot = Lapsed/kSecsInMin;
printf (" : %02d", quot);
Lapsed = Lapsed - (quot * kSecsInMin);
printf (" : %02d\n\n", Lapsed);
}
void PrintDateTime(DateTimeRec theTime)
{
printf ("%02d", theTime.day);
switch (theTime.month)
{
case 1:
printf (" Jan ");
break;
case 2:
printf (" Feb ");
break;
case 3:
printf (" Mar ");
break;
case 4:
printf (" Apr ");
break;
case 5:
printf (" May ");
break;
case 6:
printf (" Jun ");
break;
case 7:
printf (" Jul ");
break;
case 8:
printf (" Aug ");
break;
case 9:
printf (" Sep ");
break;
case 10:
printf (" Oct ");
break;
case 11:
printf (" Nov ");
break;
case 12:
printf (" Dec ");
break;
} /*switch*/
printf ("%04d", theTime.year);
printf (" %02d", theTime.hour);
printf (" : %02d", theTime.minute);
printf (" : %02d\n", theTime.second);
}
int main(void)
{
int Idx, Nqueenz, min, max, p;
unsigned long begsecs, finsecs, bgsecs, fnsecs,
opt0secs, opt1secs, opt2secs, opt3secs, Lapsed;
DateTimeRec begTime, finTime;
Nqueenz = 0;
p = 0;
Idx = 0;
opt0secs = 0;
opt1secs = 0;
opt2secs = 0;
opt3secs = 0;
min = kMinQueens;
max = kMaxQueens + 1;
printf ("N-Queens");
printf ("\n\n\n");
GetDateTime(&begsecs);
GetTime(&finTime); /*do this just to init*/
GetDateTime(&finsecs); /* init */
GetTime(&begTime);
for(Nqueenz=min; Nqueenz<max; Nqueenz++)
{
printf ("\n\n");
for(Idx=0; Idx<4; Idx++)
{
Nunique = 0;
Ntotal = 0;
GetTime(&finTime);
PrintDateTime(finTime);
printf ("N-Queens = %2d\n", Nqueenz);
printf ("Optimization: %1d\n", Idx);
GetDateTime(&bgsecs);
DoIt(Idx, Nqueenz);
GetDateTime(&fnsecs);
Lapsed = fnsecs - bgsecs;
printf ("Solutions: %10ld\n", Ntotal);
printf ("Unique: %10ld\n", Nunique);
printf ("Time [sec]: %10ld\n", Lapsed);
switch (Idx)
{
case 0:
opt0secs += Lapsed;
break;
case 1:
opt1secs += Lapsed;
break;
case 2:
opt2secs += Lapsed;
break;
case 3:
opt3secs += Lapsed;
break;
} /*switch*/
printf ("Time : ");
PrintLapsed(Lapsed);
} /*for*/
} /*for*/
GetDateTime(&finsecs);
Lapsed = finsecs - begsecs;
printf ("\n\nTime [sec]: %10ld\n", Lapsed);
printf ("Total Time : ");
PrintLapsed(Lapsed);
for(p=0; p<4; p++)
{
switch (p)
{
case 0:
Lapsed = opt0secs;
printf ("\nOptimization 0 Time [sec]: %10ld\n", Lapsed);
break;
case 1:
Lapsed = opt1secs;
printf ("\nOptimization 1 Time [sec]: %10ld\n", Lapsed);
break;
case 2:
Lapsed = opt2secs;
printf ("\nOptimization 2 Time [sec]: %10ld\n", Lapsed);
break;
case 3:
Lapsed = opt3secs;
printf ("\nOptimization 3 Time [sec]: %10ld\n", Lapsed);
break;
} /*switch*/
PrintLapsed(Lapsed);
} /*for*/
GetTime(&finTime);
printf ("\n\nStarted : ");
PrintDateTime(begTime);
printf ("Finished : ");
PrintDateTime(finTime);
printf ("\n\nWhere ignorance is bliss, 'tis folly to be wise.\n");
return 0;
} /* That's all, folks! */
---------------------------------------------
Saved console output for a run
N-Queens
23 May 2005 22 : 14 : 26
N-Queens = 4
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 2
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 4
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 2
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 4
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 2
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 4
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 2
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 5
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 10
Unique: 2
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 5
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 10
Unique: 2
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 5
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 10
Unique: 2
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 5
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 10
Unique: 2
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 6
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 4
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 6
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 4
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 6
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 4
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 6
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 4
Unique: 1
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 7
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 40
Unique: 6
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 7
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 40
Unique: 6
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 7
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 40
Unique: 6
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 7
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 40
Unique: 6
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 8
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 92
Unique: 12
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 8
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 92
Unique: 12
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 8
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 92
Unique: 12
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 8
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 92
Unique: 12
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 9
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 352
Unique: 46
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 9
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 352
Unique: 46
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 9
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 352
Unique: 46
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 9
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 352
Unique: 46
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 10
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 724
Unique: 92
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 10
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 724
Unique: 92
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 10
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 724
Unique: 92
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 10
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 724
Unique: 92
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 11
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 2680
Unique: 341
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 11
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 2680
Unique: 341
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 11
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 2680
Unique: 341
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 11
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 2680
Unique: 341
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 27
N-Queens = 12
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 14200
Unique: 1787
Time [sec]: 1
Time : 00 : 00 : 01
23 May 2005 22 : 14 : 28
N-Queens = 12
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 14200
Unique: 1787
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 28
N-Queens = 12
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 14200
Unique: 1787
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 28
N-Queens = 12
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 14200
Unique: 1787
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 28
N-Queens = 13
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 73712
Unique: 9233
Time [sec]: 4
Time : 00 : 00 : 04
23 May 2005 22 : 14 : 32
N-Queens = 13
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 73712
Unique: 9233
Time [sec]: 1
Time : 00 : 00 : 01
23 May 2005 22 : 14 : 33
N-Queens = 13
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 73712
Unique: 9233
Time [sec]: 1
Time : 00 : 00 : 01
23 May 2005 22 : 14 : 34
N-Queens = 13
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 73712
Unique: 9233
Time [sec]: 0
Time : 00 : 00 : 00
23 May 2005 22 : 14 : 34
N-Queens = 14
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 365596
Unique: 45752
Time [sec]: 22
Time : 00 : 00 : 22
23 May 2005 22 : 14 : 56
N-Queens = 14
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 365596
Unique: 45752
Time [sec]: 9
Time : 00 : 00 : 09
23 May 2005 22 : 15 : 05
N-Queens = 14
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 365596
Unique: 45752
Time [sec]: 5
Time : 00 : 00 : 05
23 May 2005 22 : 15 : 10
N-Queens = 14
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 365596
Unique: 45752
Time [sec]: 2
Time : 00 : 00 : 02
23 May 2005 22 : 15 : 12
N-Queens = 15
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 2279184
Unique: 285053
Time [sec]: 150
Time : 00 : 02 : 30
23 May 2005 22 : 17 : 42
N-Queens = 15
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 2279184
Unique: 285053
Time [sec]: 64
Time : 00 : 01 : 04
23 May 2005 22 : 18 : 46
N-Queens = 15
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 2279184
Unique: 285053
Time [sec]: 31
Time : 00 : 00 : 31
23 May 2005 22 : 19 : 17
N-Queens = 15
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 2279184
Unique: 285053
Time [sec]: 17
Time : 00 : 00 : 17
23 May 2005 22 : 19 : 34
N-Queens = 16
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 14772512
Unique: 1846955
Time [sec]: 1110
Time : 00 : 18 : 30
23 May 2005 22 : 38 : 05
N-Queens = 16
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 14772512
Unique: 1846955
Time [sec]: 446
Time : 00 : 07 : 26
23 May 2005 22 : 45 : 31
N-Queens = 16
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 14772512
Unique: 1846955
Time [sec]: 202
Time : 00 : 03 : 22
23 May 2005 22 : 48 : 53
N-Queens = 16
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 14772512
Unique: 1846955
Time [sec]: 110
Time : 00 : 01 : 50
23 May 2005 22 : 50 : 43
N-Queens = 17
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 95815104
Unique: 11977939
Time [sec]: 8703
Time : 02 : 25 : 03
24 May 2005 01 : 15 : 46
N-Queens = 17
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 95815104
Unique: 11977939
Time [sec]: 3308
Time : 00 : 55 : 08
24 May 2005 02 : 10 : 54
N-Queens = 17
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 95815104
Unique: 11977939
Time [sec]: 1619
Time : 00 : 26 : 59
24 May 2005 02 : 37 : 53
N-Queens = 17
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 95815104
Unique: 11977939
Time [sec]: 841
Time : 00 : 14 : 01
24 May 2005 02 : 51 : 54
N-Queens = 18
Optimization: 0
Opt1 = 0
Opt2 = 0
Solutions: 666090624
Unique: 83263591
Time [sec]: 71309
Time : 19 : 48 : 29
24 May 2005 22 : 40 : 23
N-Queens = 18
Optimization: 1
Opt1 = 1
Opt2 = 0
Solutions: 666090624
Unique: 83263591
Time [sec]: 25374
Time : 07 : 02 : 54
25 May 2005 05 : 43 : 17
N-Queens = 18
Optimization: 2
Opt1 = 0
Opt2 = 1
Solutions: 666090624
Unique: 83263591
Time [sec]: 11890
Time : 03 : 18 : 10
25 May 2005 09 : 01 : 27
N-Queens = 18
Optimization: 3
Opt1 = 1
Opt2 = 1
Solutions: 666090624
Unique: 83263591
Time [sec]: 5864
Time : 01 : 37 : 44
Time [sec]: 131085
Total Time : 36 : 24 : 45
Optimization 0 Time [sec]: 81299
22 : 34 : 59
Optimization 1 Time [sec]: 29202
08 : 06 : 42
Optimization 2 Time [sec]: 13748
03 : 49 : 08
Optimization 3 Time [sec]: 6834
01 : 53 : 54
Started : 23 May 2005 22 : 14 : 26
Finished : 25 May 2005 10 : 39 : 11
Where ignorance is bliss, 'tis folly to be wise.
--
³Granted I am a babbler, a harmless vexacious babbler, but what is to be
done
if the sole vocation of every intelligent man is babble -- that is, the
deliberate pouring of water through a sieve?" -- Fyodor Dostoyevsky,
*Notes
from Underground*
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