$ cat 652805.pl
#!/usr/bin/perl -w
#
# Generate all possible subsequences of sequence 1
#
use strict;
use warnings;

# Sequence 1
my @seq_1 = ('a', 'b', 'c', 'd', 'e');

# Count of all possible subsequences
my $s1_max = 2 ** @seq_1;
print "Number of possible subsequences: ", $s1_max,"\n";

# To get each possible subsequence, use a binary number
# as a mask to tell you which digits to print
for my $seq (0 .. $s1_max-1) {
        print "Sequence ", $seq, ": ";
        my $bit = 0;
        while ($bit < @seq_1) {
                print $seq_1[$bit], " " if 2**$bit & $seq;
                ++$bit;
        }
        print "\n";
}
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...roboticus

"Sequence" means that you cannot skip characters in your string.

What you are describing would be a contiguous sequence. Otherwise known as a 'substring'. Skipping characters is permitted, it is their relative positions that makes it a sequence.

Contrast LC subsequence with LC substring.

For the subsequence problem, the characters in the solution must

• appear in both strings. (common)
• appear in the same relative ordering in both strings and the solution. (sequence).
• Be longer than any other set of characters that complies with the above two conditions. (longest)

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CountZero

A program should be light and agile, its subroutines connected like a string of pearls. The spirit and intent of the program should be retained throughout. There should be neither too little or too much, neither needless loops nor useless variables, neither lack of structure nor overwhelming rigidity." - The Tao of Programming, 4.1 - Geoffrey James

Hrm. I wouldn't call that a sequence, but ok. You problem is still a function of length and nothing more.

It's the sum of 2 ^ (remaining length), from 1 to length. Since we can have any character on or off (essentially).

So you have something length 5, for example. That'd be 1 * 2^0 + 2 * 2 ^1 + 3 * 2^2 + 4 * 2 ^ 3 + 5 * 2 ^4. Just looking at that sequence should give you a good idea of how to right a loop around it.