#!/usr/bin/perl

use strict;
use warnings;

# set to 1 for elapsed time calculations
my ($TIME)=1;

# declare the grid array as global
my (@grid);

# precalculated search space for each cell
my %search = (
(0=>[0,1,2,3,4,5,6,7,8,9,10,11,18,19,20,27,36,45,54,63,72]),
(1=>[0,1,2,3,4,5,6,7,8,9,10,11,18,19,20,28,37,46,55,64,73]),
(2=>[0,1,2,3,4,5,6,7,8,9,10,11,18,19,20,29,38,47,56,65,74]),
(3=>[0,1,2,3,4,5,6,7,8,12,13,14,21,22,23,30,39,48,57,66,75]),
(4=>[0,1,2,3,4,5,6,7,8,12,13,14,21,22,23,31,40,49,58,67,76]),
(5=>[0,1,2,3,4,5,6,7,8,12,13,14,21,22,23,32,41,50,59,68,77]),
(6=>[0,1,2,3,4,5,6,7,8,15,16,17,24,25,26,33,42,51,60,69,78]),
(7=>[0,1,2,3,4,5,6,7,8,15,16,17,24,25,26,34,43,52,61,70,79]),
(8=>[0,1,2,3,4,5,6,7,8,15,16,17,24,25,26,35,44,53,62,71,80]),
(9=>[0,1,2,9,10,11,12,13,14,15,16,17,18,19,20,27,36,45,54,63,72]),
(10=>[0,1,2,9,10,11,12,13,14,15,16,17,18,19,20,28,37,46,55,64,73]),
(11=>[0,1,2,9,10,11,12,13,14,15,16,17,18,19,20,29,38,47,56,65,74]),
(12=>[3,4,5,9,10,11,12,13,14,15,16,17,21,22,23,30,39,48,57,66,75]),
(13=>[3,4,5,9,10,11,12,13,14,15,16,17,21,22,23,31,40,49,58,67,76]),
(14=>[3,4,5,9,10,11,12,13,14,15,16,17,21,22,23,32,41,50,59,68,77]),
(15=>[6,7,8,9,10,11,12,13,14,15,16,17,24,25,26,33,42,51,60,69,78]),
(16=>[6,7,8,9,10,11,12,13,14,15,16,17,24,25,26,34,43,52,61,70,79]),
(17=>[6,7,8,9,10,11,12,13,14,15,16,17,24,25,26,35,44,53,62,71,80]),
(18=>[0,1,2,9,10,11,18,19,20,21,22,23,24,25,26,27,36,45,54,63,72]),
(19=>[0,1,2,9,10,11,18,19,20,21,22,23,24,25,26,28,37,46,55,64,73]),
(20=>[0,1,2,9,10,11,18,19,20,21,22,23,24,25,26,29,38,47,56,65,74]),
(21=>[3,4,5,12,13,14,18,19,20,21,22,23,24,25,26,30,39,48,57,66,75]),
(22=>[3,4,5,12,13,14,18,19,20,21,22,23,24,25,26,31,40,49,58,67,76]),
(23=>[3,4,5,12,13,14,18,19,20,21,22,23,24,25,26,32,41,50,59,68,77]),
(24=>[6,7,8,15,16,17,18,19,20,21,22,23,24,25,26,33,42,51,60,69,78]),
(25=>[6,7,8,15,16,17,18,19,20,21,22,23,24,25,26,34,43,52,61,70,79]),
(26=>[6,7,8,15,16,17,18,19,20,21,22,23,24,25,26,35,44,53,62,71,80]),
(27=>[0,9,18,27,28,29,30,31,32,33,34,35,36,37,38,45,46,47,54,63,72]),
(28=>[1,10,19,27,28,29,30,31,32,33,34,35,36,37,38,45,46,47,55,64,73]),
(29=>[2,11,20,27,28,29,30,31,32,33,34,35,36,37,38,45,46,47,56,65,74]),
(30=>[3,12,21,27,28,29,30,31,32,33,34,35,39,40,41,48,49,50,57,66,75]),
(31=>[4,13,22,27,28,29,30,31,32,33,34,35,39,40,41,48,49,50,58,67,76]),
(32=>[5,14,23,27,28,29,30,31,32,33,34,35,39,40,41,48,49,50,59,68,77]),
(33=>[6,15,24,27,28,29,30,31,32,33,34,35,42,43,44,51,52,53,60,69,78]),
(34=>[7,16,25,27,28,29,30,31,32,33,34,35,42,43,44,51,52,53,61,70,79]),
(35=>[8,17,26,27,28,29,30,31,32,33,34,35,42,43,44,51,52,53,62,71,80]),
(36=>[0,9,18,27,28,29,36,37,38,39,40,41,42,43,44,45,46,47,54,63,72]),
(37=>[1,10,19,27,28,29,36,37,38,39,40,41,42,43,44,45,46,47,55,64,73]),
(38=>[2,11,20,27,28,29,36,37,38,39,40,41,42,43,44,45,46,47,56,65,74]),
(39=>[3,12,21,30,31,32,36,37,38,39,40,41,42,43,44,48,49,50,57,66,75]),
(40=>[4,13,22,30,31,32,36,37,38,39,40,41,42,43,44,48,49,50,58,67,76]),
(41=>[5,14,23,30,31,32,36,37,38,39,40,41,42,43,44,48,49,50,59,68,77]),
(42=>[6,15,24,33,34,35,36,37,38,39,40,41,42,43,44,51,52,53,60,69,78]),
(43=>[7,16,25,33,34,35,36,37,38,39,40,41,42,43,44,51,52,53,61,70,79]),
(44=>[8,17,26,33,34,35,36,37,38,39,40,41,42,43,44,51,52,53,62,71,80]),
(45=>[0,9,18,27,28,29,36,37,38,45,46,47,48,49,50,51,52,53,54,63,72]),
(46=>[1,10,19,27,28,29,36,37,38,45,46,47,48,49,50,51,52,53,55,64,73]),
(47=>[2,11,20,27,28,29,36,37,38,45,46,47,48,49,50,51,52,53,56,65,74]),
(48=>[3,12,21,30,31,32,39,40,41,45,46,47,48,49,50,51,52,53,57,66,75]),
(49=>[4,13,22,30,31,32,39,40,41,45,46,47,48,49,50,51,52,53,58,67,76]),
(50=>[5,14,23,30,31,32,39,40,41,45,46,47,48,49,50,51,52,53,59,68,77]),
(51=>[6,15,24,33,34,35,42,43,44,45,46,47,48,49,50,51,52,53,60,69,78]),
(52=>[7,16,25,33,34,35,42,43,44,45,46,47,48,49,50,51,52,53,61,70,79]),
(53=>[8,17,26,33,34,35,42,43,44,45,46,47,48,49,50,51,52,53,62,71,80]),
(54=>[0,9,18,27,36,45,54,55,56,57,58,59,60,61,62,63,64,65,72,73,74]),
(55=>[1,10,19,28,37,46,54,55,56,57,58,59,60,61,62,63,64,65,72,73,74]),
(56=>[2,11,20,29,38,47,54,55,56,57,58,59,60,61,62,63,64,65,72,73,74]),
(57=>[3,12,21,30,39,48,54,55,56,57,58,59,60,61,62,66,67,68,75,76,77]),
(58=>[4,13,22,31,40,49,54,55,56,57,58,59,60,61,62,66,67,68,75,76,77]),
(59=>[5,14,23,32,41,50,54,55,56,57,58,59,60,61,62,66,67,68,75,76,77]),
(60=>[6,15,24,33,42,51,54,55,56,57,58,59,60,61,62,69,70,71,78,79,80]),
(61=>[7,16,25,34,43,52,54,55,56,57,58,59,60,61,62,69,70,71,78,79,80]),
(62=>[8,17,26,35,44,53,54,55,56,57,58,59,60,61,62,69,70,71,78,79,80]),
(63=>[0,9,18,27,36,45,54,55,56,63,64,65,66,67,68,69,70,71,72,73,74]),
(64=>[1,10,19,28,37,46,54,55,56,63,64,65,66,67,68,69,70,71,72,73,74]),
(65=>[2,11,20,29,38,47,54,55,56,63,64,65,66,67,68,69,70,71,72,73,74]),
(66=>[3,12,21,30,39,48,57,58,59,63,64,65,66,67,68,69,70,71,75,76,77]),
(67=>[4,13,22,31,40,49,57,58,59,63,64,65,66,67,68,69,70,71,75,76,77]),
(68=>[5,14,23,32,41,50,57,58,59,63,64,65,66,67,68,69,70,71,75,76,77]),
(69=>[6,15,24,33,42,51,60,61,62,63,64,65,66,67,68,69,70,71,78,79,80]),
(70=>[7,16,25,34,43,52,60,61,62,63,64,65,66,67,68,69,70,71,78,79,80]),
(71=>[8,17,26,35,44,53,60,61,62,63,64,65,66,67,68,69,70,71,78,79,80]),
(72=>[0,9,18,27,36,45,54,55,56,63,64,65,72,73,74,75,76,77,78,79,80]),
(73=>[1,10,19,28,37,46,54,55,56,63,64,65,72,73,74,75,76,77,78,79,80]),
(74=>[2,11,20,29,38,47,54,55,56,63,64,65,72,73,74,75,76,77,78,79,80]),
(75=>[3,12,21,30,39,48,57,58,59,66,67,68,72,73,74,75,76,77,78,79,80]),
(76=>[4,13,22,31,40,49,57,58,59,66,67,68,72,73,74,75,76,77,78,79,80]),
(77=>[5,14,23,32,41,50,57,58,59,66,67,68,72,73,74,75,76,77,78,79,80]),
(78=>[6,15,24,33,42,51,60,61,62,69,70,71,72,73,74,75,76,77,78,79,80]),
(79=>[7,16,25,34,43,52,60,61,62,69,70,71,72,73,74,75,76,77,78,79,80]),
(80=>[8,17,26,35,44,53,60,61,62,69,70,71,72,73,74,75,76,77,78,79,80])
);

sub main {
  my ($line,$aa);

  # load the array
  $aa = "";
  foreach $line (<>) {
    chomp ($line);
    # want 0 instead of '-'
    $line =~ s/\-/0/g;
    $aa .= $line . ",";
  } 
  # convert grid to one dimensional array
  chomp $aa;
  @grid = split /,/,$aa;
  
  sudoku_print();
  
  # start the clock
  if ($TIME) {
    start_clock();
  }
  
  # go to it!
  grid_check();
}

# 
sub grid_check {
  my ($cntr,$val,$et,$cell,$sudoku);
  my (@list,@range);
  my (%solve);
  
  # first find cells with fewest possibiles
  for $cntr (0..80) {
    # if cell is allready set skip it
    next if($grid[$cntr]);
    
    # create a list of impossible values
    # target cell is at $cntr
    # test cell is at $cell
    # check each cell in the precalculated search space
    @list = (1,0,0,0,0,0,0,0,0,0);
    foreach $cell (@{$search{$cntr}}) {
      $list[$grid[$cell]] = 1;
    }
    # count the number of possible values
    # remember @list is the illegal values so invert the sense of the 
+search
    $solve{$cntr} = (grep{!$list[$_]}1..9);
  }
  # now sort by the number of possiblities
  @range = (sort {$solve{$a}<=>$solve{$b}} keys %solve);

  # run thru the sorted list. 
  # This loop looks at undeterined cells in ascending order of possibi
+litie
  # with a recursve call to this function.  It will not finish until e
+very
  # cell is non-zero.
  foreach $cntr (@range) {
    # skip the cell if it already has a value.  T
    next if($grid[$cntr]);
    @list = (1,0,0,0,0,0,0,0,0,0);
    foreach $cell (@{$search{$cntr}}) {
      $list[$grid[$cell]] = 1;
    }
    # For each possible value of the target -- 
    # remember to invert the sense of the search
    foreach $val (grep{!$list[$_]}1..9) {
      $grid[$cntr] = $val;
      grid_check();
    }
    # return and try next value
    return $grid[$cntr] = 0;
  }
  # if we ever get this far then print the results
  # silly to restart the clock for subsequent solutions since the firs
+t was
  # the costly one.
  sudoku_print();
  
  return;
}

{ 
my ($solution) = 0;
  sub sudoku_print {
    my($cntr,$cell,$sudoku,$et);
    
    $et = ($TIME ? ": ".time_format(elapsed_time()) : "");
    $cntr = 0;
    if($solution) {
      $sudoku = "Solution $solution" . $et;
    } else {
      $sudoku = "Original Puzzle"
    }
    
    $sudoku .= "\n\n";
    while ($cntr < 80) {
      # print a row
      for $cell($cntr..($cntr+8)) {
        $sudoku .= $grid[$cell];
        $sudoku .= ((($cell+1)%3) ? " " : "  ");
      }
      $cntr += 9;
      $sudoku .= (($cntr%27) ? "\n" : "\n\n");
    }
    $sudoku .= "\n";
    print $sudoku;
    $solution++;
  }
}

sub time_format {
  my ($et) = @_;
  my ($hours,$min,$sec,$rtn);
  
  $hours = int($et/3600);
  $et -= (3600*$hours);
  $min = int($et/60);
  $et -= (60*$min);
  
  $rtn .= sprintf "%dh",$hours if $hours;
  $rtn .= sprintf "%02dm",$min if $min;
  $rtn .= sprintf "%05.3fs",$et;
  
  return $rtn;
}

# time fucntions
use Time::HiRes qw();
{
my ($start);
  sub start_clock {
      $start = [Time::HiRes::gettimeofday()]; 
  }
  sub elapsed_time {
    return Time::HiRes::tv_interval($start);
  }
}

main();
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