#!/usr/bin/perl # # NOTES: This code will not solve a 1 x 1 matrix as all numbers are "reused" # use strict; use warnings; use constant TRUE => 1; use constant FALSE => 0; use constant MATRIX_DIM => 3; # Set your matrix size here use constant MAX_NUM => (10 ** MATRIX_DIM) - 1; use constant DEBUG => 0; # 0=Nothing, 1=Summary, 2=Detail use constant SEPARATOR => '-'; # Since you need to find 2 times the matrix width distinct numbers, you cannot # have a divisor greater than the maximum number divided by that product. # # For example, a 3 x 3 matrix has a maximum number of 999. You need 6 distinct # numbers to "solve" the matrix, so the maximum possible divisor would be 166. # 166 would result in 166, 332, 498, 664, 830, and 996. # my \$Divisor = int(MAX_NUM / (MATRIX_DIM * 2)); my @Num; my @PermPtrs; # Saves the position of the pointers between GetNextPerm() calls my @Sol=(); # GetNextPerm generates purmutations from the passed array (one at a time) # and uses a global array of pointers (@PermPtrs). This method seems to be # fast and uses less memory than computing all the permutations at once. # # NOTE: The first time this sub is called, @PermPtrs should be an empty array. # sub GetNextPerm { my \$pNum=shift; my \$Perm=''; my @PtrStack; if (\$#PermPtrs > -1) { my \$Ptr=MATRIX_DIM-1; while (TRUE) { \$PermPtrs[\$Ptr]++; if (\$PermPtrs[\$Ptr] > \$#\$pNum) { push @PtrStack,\$Ptr; \$Ptr--; return undef if (\$Ptr == -1); next; } else { my \$OkInc=TRUE; foreach (0..MATRIX_DIM-1) { next if (\$_ == \$Ptr); \$OkInc=FALSE if (\$PermPtrs[\$_] == \$PermPtrs[\$Ptr]); } next unless(\$OkInc) } last unless (\$#PtrStack > -1); \$Ptr=pop(@PtrStack); \$PermPtrs[\$Ptr]=-1; } } else { @PermPtrs=(0..MATRIX_DIM-1); } foreach (@PermPtrs) { \$Perm.=SEPARATOR if (length(\$Perm)); \$Perm.=\$\$pNum[\$_]; } return \$Perm; } sub CheckSolution { my \$pNum=shift; my \$CheckNum; my \$PossSol; my \$Ptr; my @Sol=(); my %Check; my %Num; # # This code checks every permutation of possible numbers (from the passed # numberarray) as rows and checks if there are MATRIX_DIM other numbers # (also in the passed array) which can act as columns. # # For example, with a 3 x 3 matrix, this code should go through each # permutation of three number (for rows) from the passed array and see if # there are three other numbers which would work with the selected rows as # their columns. # # WISH LIST: Verify members of each permutation for "fitness" in their # assigned spot. "Fitness" means you do not put a number in the # top row whose first digit is not the first digit of at least # one other number... whose second digit is not the first digit # of at least one other number... etc... This may speed up this # section of the code. # # Benchmark the code which checks the columns (foreach \$Ptr block) # That code gets executed a lot, and *may* benefit from recoding. # @PermPtrs=(); while(\$PossSol=GetNextPerm(\$pNum)) { print "\t",'Checking ',\$PossSol,'... ' if (DEBUG >= 2); %Num=map { \$_ => TRUE } @\$pNum; @Sol=split(SEPARATOR,\$PossSol); delete \$Num{\$_} foreach (@Sol); foreach \$Ptr (0..length(\$Sol[0])-1) { \$CheckNum=''; \$CheckNum.=substr(\$_,\$Ptr,1) foreach (@Sol); if (defined(\$Num{\$CheckNum})) { delete \$Num{\$CheckNum}; } else { print 'nope',"\n" if (DEBUG >= 2); @Sol=(); last; } } last if (\$#Sol > -1); } return @Sol; } while (\$Divisor >= 1) { @Num=(); foreach (1..int(MAX_NUM / \$Divisor)) { next if ((\$Divisor * \$_) < (MAX_NUM / 10)); # Numbers which begin with zero push @Num, (\$Divisor * \$_); } print 'Checking solution for divisor ',\$Divisor,': ',join('-',@Num),"\n" if (DEBUG >= 1); @Sol=CheckSolution(\@Num); last if (\$#Sol > -1); \$Divisor--; } print "\n"; if (\$#Sol > -1) { print 'Maximum divisor is ',\$Divisor,', solution is ',join('-',@Sol),"\n"; } else { print 'No solution found...',"\n"; } # End of Script