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It's probably a bit late to post this but since the code is now written I might as well. Corion's mention of a binary counter made me think of this thread in which I ventured this solution. I can use this to generate all strings of, say, three ones and two zeros and then use a regex and pos to generate an array of elements to sum. Because the iterator returns strings in this order for the above example

00111 01011 01101 01110 10011 10101 10110 11001 11010 11100

I use unshift rather than push to build the array of sums so that they are in the same order as in the OP. The routine returns a ref. to an AoAoH where elements 0 and 1 are empty, element 2 contains an array of hashes of all possible 2-element sums where the key is the string representing the sum and the value is the result, element 3 an array of hashes of 3-element sums etc. The code:-

use 5.026; use warnings; use List::Util qw{ sum }; use Data::Dumper; my @tests = ( 5, [ 1 ], [ 1, 2 ], [ 1, 2, 3 ], [ 1, 2, 3, 4 ], [ 1, 2, 3, 4, 5 ], [ 4, 17, 9, 23, 1, 14 ], ); foreach my $test ( @tests ) { my $raRes = allSums( $test ) or do { warn qq{$test: Not an array ref.\n}; say q{-} x 25; next; }; print Data::Dumper ->new( [ $test, $raRes ], [ qw{ test raRes }] ) ->Indent( 1 ) ->Dumpxs(); say q{-} x 25; } sub allSums { my $raNumbers = shift; return 0 unless ref( $raNumbers ) eq q{ARRAY}; my $raSums = [ [], [], ]; my $nElems = scalar @{ $raNumbers }; if ( $nElems < 3 ) { return $raSums; } foreach my $sumsOf ( 2 .. $nElems - 1 ) { my $nZeros = $nElems - $sumsOf; my $rcNext = permutary( $nZeros, $sumsOf ); while ( my $str = $rcNext->() ) { my @posns; push @posns, pos $str while $str =~ m{(?=1)}g; unshift @{ $raSums->[ $sumsOf ] }, { join( q{+}, @{ $raNumbers }[ @posns ] ), sum @{ $raNumbers }[ @posns ] }; } } return $raSums; } sub permutary { no warnings qw{ portable }; my ( $numZeros, $numOnes ) = @_; my $format = q{%0} . ( $numZeros + $numOnes ) . q{b}; my $start = oct( q{0b} . q{1} x $numOnes ); my $limit = oct( q{0b} . q{1} x $numOnes . q{0} x $numZeros ); return sub { return undef if $start > $limit; my $binStr = sprintf $format, $start; die qq{Error: $binStr not $numOnes ones\n} unless $numOnes == $binStr =~ tr{1}{}; my $jump = 0; if ( $binStr =~ m{(1+)$} ) { $jump = 2 ** ( length($1) - 1 ); } elsif ( $binStr =~ m{(1+)(0+)$} ) { $jump = 2 ** ( length($1) - 1 ) + 1; $jump += 2 ** $_ for 1 .. length( $2 ) - 1; } else { die qq{Error: $binStr seems malformed\n}; } $start += $jump; return $binStr; }; }

The results:-

5: Not an array ref. ------------------------- $test = [ 1 ]; $raRes = [ [], [] ]; ------------------------- $test = [ 1, 2 ]; $raRes = [ [], [] ]; ------------------------- $test = [ 1, 2, 3 ]; $raRes = [ [], [], [ { '1+2' => 3 }, { '1+3' => 4 }, { '2+3' => 5 } ] ]; ------------------------- $test = [ 1, 2, 3, 4 ]; $raRes = [ [], [], [ { '1+2' => 3 }, { '1+3' => 4 }, { '1+4' => 5 }, { '2+3' => 5 }, { '2+4' => 6 }, { '3+4' => 7 } ], [ { '1+2+3' => 6 }, { '1+2+4' => 7 }, { '1+3+4' => 8 }, { '2+3+4' => 9 } ] ]; ------------------------- $test = [ 1, 2, 3, 4, 5 ]; $raRes = [ [], [], [ { '1+2' => 3 }, { '1+3' => 4 }, { '1+4' => 5 }, { '1+5' => 6 }, { '2+3' => 5 }, { '2+4' => 6 }, { '2+5' => 7 }, { '3+4' => 7 }, { '3+5' => 8 }, { '4+5' => 9 } ], [ { '1+2+3' => 6 }, { '1+2+4' => 7 }, { '1+2+5' => 8 }, { '1+3+4' => 8 }, { '1+3+5' => 9 }, { '1+4+5' => 10 }, { '2+3+4' => 9 }, { '2+3+5' => 10 }, { '2+4+5' => 11 }, { '3+4+5' => 12 } ], [ { '1+2+3+4' => 10 }, { '1+2+3+5' => 11 }, { '1+2+4+5' => 12 }, { '1+3+4+5' => 13 }, { '2+3+4+5' => 14 } ] ]; ------------------------- $test = [ 4, 17, 9, 23, 1, 14 ]; $raRes = [ [], [], [ { '4+17' => 21 }, { '4+9' => 13 }, { '4+23' => 27 }, { '4+1' => 5 }, { '4+14' => 18 }, { '17+9' => 26 }, { '17+23' => 40 }, { '17+1' => 18 }, { '17+14' => 31 }, { '9+23' => 32 }, { '9+1' => 10 }, { '9+14' => 23 }, { '23+1' => 24 }, { '23+14' => 37 }, { '1+14' => 15 } ], [ { '4+17+9' => 30 }, { '4+17+23' => 44 }, { '4+17+1' => 22 }, { '4+17+14' => 35 }, { '4+9+23' => 36 }, { '4+9+1' => 14 }, { '4+9+14' => 27 }, { '4+23+1' => 28 }, { '4+23+14' => 41 }, { '4+1+14' => 19 }, { '17+9+23' => 49 }, { '17+9+1' => 27 }, { '17+9+14' => 40 }, { '17+23+1' => 41 }, { '17+23+14' => 54 }, { '17+1+14' => 32 }, { '9+23+1' => 33 }, { '9+23+14' => 46 }, { '9+1+14' => 24 }, { '23+1+14' => 38 } ], [ { '4+17+9+23' => 53 }, { '4+17+9+1' => 31 }, { '4+17+9+14' => 44 }, { '4+17+23+1' => 45 }, { '4+17+23+14' => 58 }, { '4+17+1+14' => 36 }, { '4+9+23+1' => 37 }, { '4+9+23+14' => 50 }, { '4+9+1+14' => 28 }, { '4+23+1+14' => 42 }, { '17+9+23+1' => 50 }, { '17+9+23+14' => 63 }, { '17+9+1+14' => 41 }, { '17+23+1+14' => 55 }, { '9+23+1+14' => 47 } ], [ { '4+17+9+23+1' => 54 }, { '4+17+9+23+14' => 67 }, { '4+17+9+1+14' => 45 }, { '4+17+23+1+14' => 59 }, { '4+9+23+1+14' => 51 }, { '17+9+23+1+14' => 64 } ] ]; -------------------------

I hope this is of interest.

Cheers,

JohnGG


In reply to Re: Sum of N elements in an M element array by johngg
in thread Sum of N elements in an M element array by abhay180

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