## Longest Palindrome

Sunday, October 24, 2010

Greplin issued a programming challenge recently, where the first question involved finding the longest palindrome substring. It was then posted as a challenge to the Programming Praxis blog, and I thought I would contribute a solution in Factor.

First, some vocabularies that we will be using:

```
USING: fry kernel locals make ranges sequences unicode.case
unicode.categories ;
```

As part of the Factor language tutorial, the first
program
many people write in Factor is a word for detecting if something is a
palindrome. The
implementation of `palindrome?`

(extended to support case-insensitive
comparisons using the
unicode
vocabulary) looks like this:

```
: normalize ( str -- str' ) [ Letter? ] filter >lower ;
: palindrome? ( str -- ? ) normalize dup reverse = ;
```

The “obvious” (but not that fast) way to solve the problem is to examine every possible substring, adding to a list if it is a palindrome. The list of palindrome substrings can then be used to answer the question. This is how we’ll implement it.

I thought it would be useful to split the problem into two steps. First, we need a way to enumerate all possible substrings (not including the “empty” substring), applying a quotation to each in turn.

```
:: each-subseq ( ... seq quot: ( ... x -- ... ) -- ... )
seq length [0,b] [
:> from
from seq length (a..b] [
:> to
from to seq subseq quot call( x -- )
] each
] each ;
```

You can try this out in the listener, to see how it works:

```
IN: scratchpad "abc" [ . ] each-subseq
"a"
"ab"
"abc"
"b"
"bc"
"c"
```

Once we have that, it’s pretty easy to build a word to look for palindrome substrings:

```
: palindromes ( str -- seq )
[
[ dup palindrome? [ , ] [ drop ] if ] each-subseq
] { } make ;
```

We can use the `longest`

word that I implemented for my
anagrams post to
find the longest palindrome substring:

```
: longest ( seq -- subseq )
dup 0 [ length max ] reduce '[ length _ = ] filter ;
```

Using this on the 1169-character string from the original challenge, we find 52 unique palindromes of 2 or more characters. The longest palindrome substring I found was a 7-character sequence.