Finding "sub-palindromes" 2: subsequences.

Question

The same task as Finding "sub-palindromes" but instead of finding substrings you must find subsequences that are not substrings.

eg1:

input: "12131331"
output: 
"11", "33", "111", "121", "131", "313", "333", "1111", "1331", "11311", "13331"
or 
"11", "33", "111", "333", "1111", "11311", "13331"

eg2:

input: "3333"
output: 
"33", "333"
or
(null)

• Input is a string of printable ascii characters.
• Output is a list of unique strings.
• If a subsequence also appears as a substring it may be omitted.
• Shortest code wins.

Answer 1

Haskell (119)

import Data.List
main=interact f
f a=show.nub.filter(\x->(not$isInfixOf a x)&&x==reverse x&&length x>1)$subsequences a

Isn't too difficult with a builtin subsequences and nub... :)

Answer 2

Golfscript (95)

);.{{(\a\:x;.{[x]\+}%+}:b;{.!{[$]}{b}if}:a;.a{..-1%=&},\{,}{(;}/{{,}{);}/}%{+}*-.&{`}%", "*}and

I haven't really tried to golf this further, it's just a combination of left overs.

The question is inconsistent. My program prints all palindromic subsequences that are not substrings. Hope this is OK.

Example 1:

echo "12131331" | ruby golfscript.rb subseq_not_substr.gs
"11", "111", "13331", "13131", "1111", "11311"

Example 2:

echo "3333" | ruby golfscript.rb subseq_not_substr.gs

Empty String Example:

echo "" | ruby golfscript.rb subseq_not_substr.gs

With uglier output formatting, eg [11 111 13331 13131 1111 11311], it could be made a bit shorter.

Answer 3

GolfScript, 39 characters

:^1/[""]\{`{1$\+}+%}/.&{..-1%=^@?0<&},`

Examples:

> "12131331"
["11" "333" "111" "13331" "13131" "1111" "11311"]

> "3333"
[]

Basic blocks of the code:

# Save input in variable
:^

# Build all possible subsequences of the input
1/[""]\{`{1$\+}+%}/

# Filter unique ones
.&

# Filter relevant palindromes
{.
  .-1%=   # check if palindrome
  ^@?0<   # check if sequence is no substring
  &       # and operation on both
},

# Format output
`