# Longest palindromic substrings

Longest palindromic substrings is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Let given a string s. The goal is to find the longest palindromic substring in s.

## 11l

```F longest_palindrome(s)
V t = Array(‘^’s‘\$’).join(‘#’)
V n = t.len
V p =  * n
V c = 0
V r = 0
L(i) 1 .< n - 1
p[i] = (r > i) & min(r - i, p[2 * c - i]) != 0

L t[i + 1 + p[i]] == t[i - 1 - p[i]]
p[i]++

I i + p[i] > r
(c, r) = (i, i + p[i])

V (max_len, center_index) = max(enumerate(p).map((i, n) -> (n, i)))
R s[(center_index - max_len) I/ 2 .< (center_index + max_len) I/ 2]

L(s) [‘three old rotators’,
‘never reverse’,
‘stable was I ere I saw elbatrosses’,
‘drome’,
‘the abbatial palace’]
print(‘'’s‘' -> '’longest_palindrome(s)‘'’)```
Output:
```'three old rotators' -> 'rotator'
'never reverse' -> 'ever reve'
'stable was I ere I saw elbatrosses' -> 'table was I ere I saw elbat'
'drome' -> 'e'
'the abbatial palace' -> 'abba'
```

## Action!

```BYTE FUNC Palindrome(CHAR ARRAY s)
BYTE l,r

l=1 r=s(0)
WHILE l<r
DO
IF s(l)#s(r) THEN RETURN (0) FI
l==+1 r==-1
OD
RETURN (1)

PROC Find(CHAR ARRAY text,res)
BYTE first,len

len=text(0)
WHILE len>0
DO
FOR first=1 TO text(0)-len+1
DO
SCopyS(res,text,first,first+len-1)
IF Palindrome(res) THEN
RETURN
FI
OD
len==-1
OD
res(0)=0
RETURN

PROC Test(CHAR ARRAY text)
CHAR ARRAY res(100)

Find(text,res)
PrintF("""%S"" -> ""%S""%E",text,res)
RETURN

PROC Main()
Test("three old rotators")
Test("never reverse")
Test("the abbatial palace")
Test("qwertyuiop")
Test("")
RETURN```
Output:
```"three old rotators" -> "rotator"
"never reverse" -> "ever reve"
"the abbatial palace" -> "abba"
"qwertyuiop" -> "q"
"" -> ""
```

## ALGOL 68

Palindromes of length 1 or more are detected, finds the left most palindrome if there are several of the same length.
Treats upper and lower case as distinct and does not require the characters to be letters.

```BEGIN # find the longest palindromic substring of a string #
# returns the length of s #
OP   LENGTH = ( STRING s )INT: ( UPB s + 1 ) - LWB s;
# returns s right-padded with blanks to at least w characters or s if it is already wide enough #
OP   PAD = ( STRING s, INT w )STRING:
BEGIN
STRING result := s;
WHILE LENGTH result < w DO result +:= " " OD;
result
# returns the longest palindromic substring of s #
#         if there are multiple substrings with the longest length, the leftmost is returned #
PROC longest palindromic substring = ( STRING s )STRING:
IF   LENGTH s < 2
THEN s
ELSE
INT lwb s = LWB s;
INT upb s = UPB s;
STRING result := s[ lwb s ];
IF s[ lwb s + 1 ] = s[ lwb s ] THEN
# the first two characters are a palindrome #
result +:= s[ lwb s + 1 ]
FI;
FOR i FROM lwb s + 1 TO upb s - 1 DO
INT  p start := i;
INT  p end   := i + 1;
IF  IF   s[ i - 1 ] = s[ i + 1 ] THEN
# odd length palindrome at i - 1 #
p start -:= 1;
TRUE
ELIF s[ i ] = s[ i + 1 ] THEN
# even length palindrome at i #
TRUE
ELSE FALSE
FI
THEN
# have a palindrome at p start : p end #
# attempt to enlarge the range #
WHILE IF   p start = lwb s OR p end = upb s
THEN FALSE
ELSE s[ p start - 1 ] = s[ p end + 1 ]
FI
DO    # can extend he palindrome #
p start -:= 1;
p end   +:= 1
OD;
IF ( p end + 1 ) - p start > LENGTH result
THEN
# have a longer palindrome #
result := s[ p start : p end ]
FI
FI
OD;
result
FI # longest palindromic substring # ;
# finds the longest palindromic substring of s and checks it is the expacted value #
PROC test = ( STRING s, expected value )VOID:
BEGIN
STRING palindrome = longest palindromic substring( s );
print( ( ( """" + s + """" ) PAD 38, " -> ", ( """" + palindrome + """" ) PAD 36
, IF palindrome = expected value THEN "" ELSE " NOT " + expected value + " ???" FI
, newline
)
)
END # test longest palindromic substring # ;
test( "three old rotators",                 "rotator"                     );
test( "never reverse",                      "ever reve"                   );
test( "stable was I ere I saw elbatrosses", "table was I ere I saw elbat" );
test( "drome",                              "d"                           );
test( "x",                                  "x"                           );
test( "the abbatial palace",                "abba"                        );
test( "",                                   ""                            );
test( "abcc",                               "cc"                          );
test( "abbccc",                             "ccc"                         )
END```
Output:
```"three old rotators"                   -> "rotator"
"never reverse"                        -> "ever reve"
"stable was I ere I saw elbatrosses"   -> "table was I ere I saw elbat"
"drome"                                -> "d"
"x"                                    -> "x"
"the abbatial palace"                  -> "abba"
""                                     -> ""
"abcc"                                 -> "cc"
"abbccc"                               -> "ccc"
```

## Arturo

Translation of: Nim
```palindrome?: function [str]-> str = join reverse split str

lps: function [s][
maxLength: 0
result: new []
loop 0..dec size s 'fst [
loop fst..dec size s 'lst [
candidate: slice s fst lst
if palindrome? candidate [
if? maxLength < size candidate [
result: new @[candidate]
maxLength: size candidate
]
else [
if maxLength = size candidate ->
'result ++ candidate
]
]
]
]

return (maxLength > 1)? -> result
-> []
]

loop ["babaccd", "rotator", "several", "palindrome", "piété", "tantôt", "étêté"] 'str [
palindromes: lps str
print [str "->" (0 < size palindromes)? -> join.with:", " palindromes
-> "X"]
]
```
Output:
```babaccd -> bab, aba
rotator -> rotator
several -> eve
palindrome -> X
piété -> été
tantôt -> tôt
étêté -> étêté```

## AutoHotkey

```LPS(str){
found := [], result := [], maxL := 0
while (StrLen(str) >= 2 && StrLen(str) >= maxL){
s := str
loop {
while (SubStr(s, 1, 1) <> SubStr(s, 0))	; while 1st chr <> last chr
s := SubStr(s, 1, StrLen(s)-1)		; trim last chr
if (StrLen(s) < 2 || StrLen(s) < maxL )
break
if (s = reverse(s)){
found.Push(s)
maxL := maxL < StrLen(s) ? StrLen(s) : maxL
break
}
s := SubStr(s, 1, StrLen(s)-1)			; trim last chr
}
str := SubStr(str, 2)						; trim 1st chr and try again
}
maxL := 0
for i, str in found
maxL := maxL < StrLen(str) ? StrLen(str) : maxL
for i, str in found
if (StrLen(str) = maxL)
result.Push(str)
return result
}
reverse(s){
for i, v in StrSplit(s)
output := v output
return output
}
```
Examples:
```db =
(
three old rotators
never reverse
stable was I ere I saw elbatrosses
drome
x
the abbatial palace
)

for i, line in StrSplit(db, "`n", "`r"){
result := "[""", i := 0
for i, str in LPS(line)
result .= str """, """
output .= line "`t> " Trim(result, """, """) (i?"""":"") "]`n"
}
MsgBox % output
return
```
Output:
```three old rotators			> ["rotator"]
never reverse				> ["ever reve"]
stable was I ere I saw elbatrosses	> ["table was I ere I saw elbat"]
drome					> []
x					> []
the abbatial palace			> ["abba"]
```

## F#

### Manacher Function

```// Manacher Function. Nigel Galloway: October 1st., 2020
let Manacher(s:string) = let oddP,evenP=Array.zeroCreate s.Length,Array.zeroCreate s.Length
let rec fN i g e (l:int[])=match g>=0 && e<s.Length && s.[g]=s.[e] with true->l.[i]<-l.[i]+1; fN i (g-1) (e+1) l |_->()
let rec fGo n g Ʃ=match Ʃ<s.Length with
false->oddP
|_->if Ʃ<=g then oddP.[Ʃ]<-min (oddP.[n+g-Ʃ]) (g-Ʃ)
fN Ʃ (Ʃ-oddP.[Ʃ]-1) (Ʃ+oddP.[Ʃ]+1) oddP
match (Ʃ+oddP.[Ʃ])>g with true->fGo (Ʃ-oddP.[Ʃ]) (Ʃ+oddP.[Ʃ]) (Ʃ+1) |_->fGo n g (Ʃ+1)
let rec fGe n g Ʃ=match Ʃ<s.Length with
false->evenP
|_->if Ʃ<=g then evenP.[Ʃ]<-min (evenP.[n+g-Ʃ]) (g-Ʃ)
fN Ʃ (Ʃ-evenP.[Ʃ]) (Ʃ+evenP.[Ʃ]+1) evenP
match (Ʃ+evenP.[Ʃ])>g with true->fGe (Ʃ-evenP.[Ʃ]+1) (Ʃ+evenP.[Ʃ]) (Ʃ+1) |_->fGe n g (Ʃ+1)
(fGo 0 -1 0,fGe 0 -1 0)
```

```let fN g=if g=[||] then (0,0) else g|>Array.mapi(fun n g->(n,g))|>Array.maxBy snd
let lpss s=let n,g=Manacher s in let n,g=fN n,fN g in if (snd n)*2+1>(snd g)*2 then s.[(fst n)-(snd n)..(fst n)+(snd n)] else s.[(fst g)-(snd g)+1..(fst g)+(snd g)]
let test = ["three old rotators"; "never reverse"; "stable was I ere I saw elbatrosses"; "abracadabra"; "drome"; "the abbatial palace"; ""]
test|>List.iter(fun n->printfn "A longest palindromic substring of \"%s\" is \"%s\"" n (lpss n))
```
Output:
```A longest palindromic substring of "three old rotators" is "rotator"
A longest palindromic substring of "never reverse" is "ever reve"
A longest palindromic substring of "stable was I ere I saw elbatrosses" is "table was I ere I saw elbat"
A longest palindromic substring of "abracadabra" is "aca"
A longest palindromic substring of "drome" is "d"
A longest palindromic substring of "the abbatial palace" is "abba"
A longest palindromic substring of "" is ""
```

## Go

Translation of: Wren
```package main

import (
"fmt"
"sort"
)

func reverse(s string) string {
var r = []rune(s)
for i, j := 0, len(r)-1; i < j; i, j = i+1, j-1 {
r[i], r[j] = r[j], r[i]
}
return string(r)
}

func longestPalSubstring(s string) []string {
var le = len(s)
if le <= 1 {
return []string{s}
}
targetLen := le
var longest []string
i := 0
for {
j := i + targetLen - 1
if j < le {
ss := s[i : j+1]
if reverse(ss) == ss {
longest = append(longest, ss)
}
i++
} else {
if len(longest) > 0 {
return longest
}
i = 0
targetLen--
}
}
return longest
}

func distinct(sa []string) []string {
sort.Strings(sa)
duplicated := make([]bool, len(sa))
for i := 1; i < len(sa); i++ {
if sa[i] == sa[i-1] {
duplicated[i] = true
}
}
var res []string
for i := 0; i < len(sa); i++ {
if !duplicated[i] {
res = append(res, sa[i])
}
}
return res
}

func main() {
strings := []string{"babaccd", "rotator", "reverse", "forever", "several", "palindrome", "abaracadaraba"}
fmt.Println("The palindromic substrings having the longest length are:")
for _, s := range strings {
longest := distinct(longestPalSubstring(s))
fmt.Printf("  %-13s Length %d -> %v\n", s, len(longest), longest)
}
}
```
Output:
```The palindromic substrings having the longest length are:
babaccd       Length 3 -> [aba bab]
rotator       Length 7 -> [rotator]
reverse       Length 5 -> [rever]
forever       Length 5 -> [rever]
several       Length 3 -> [eve]
palindrome    Length 1 -> [a d e i l m n o p r]
```

A list version, written out of curiosity. A faster approach could be made with an indexed datatype.

```-------------- LONGEST PALINDROMIC SUBSTRINGS ------------

longestPalindromes :: String -> ([String], Int)
longestPalindromes [] = ([], 0)
longestPalindromes s = go \$ palindromes s
where
go xs
| null xs = (return <\$> s, 1)
| otherwise = (filter ((w ==) . length) xs, w)
where
w = maximum \$ length <\$> xs

palindromes :: String -> [String]
palindromes = fmap go . palindromicNuclei
where
go (pivot, (xs, ys)) =
let suffix = fmap fst (takeWhile (uncurry (==)) (zip xs ys))
in reverse suffix <> pivot <> suffix

palindromicNuclei :: String -> [(String, (String, String))]
palindromicNuclei =
concatMap go .
init . tail . ((zip . scanl (flip ((<>) . return)) []) <*> scanr (:) [])
where
go (a@(x:_), b@(h:y:ys))
| x == h = [("", (a, b))]
| otherwise =
[ ([h], (a, y : ys))
| x == y ]
go _ = []

--------------------------- TEST -------------------------
main :: IO ()
main =
putStrLn \$
fTable
"Longest palindromic substrings:\n"
show
show
longestPalindromes
[ "three old rotators"
, "never reverse"
, "stable was I ere I saw elbatrosses"
, "drome"
, "the abbatial palace"
, ""
]

------------------------ FORMATTING ----------------------
fTable :: String -> (a -> String) -> (b -> String) -> (a -> b) -> [a] -> String
fTable s xShow fxShow f xs =
unlines \$
s : fmap (((++) . rjust w ' ' . xShow) <*> ((" -> " ++) . fxShow . f)) xs
where
rjust n c = drop . length <*> (replicate n c ++)
w = maximum (length . xShow <\$> xs)
```
Output:
```Longest palindromic substrings:

"three old rotators" -> (["rotator"],7)
"never reverse" -> (["ever reve"],9)
"stable was I ere I saw elbatrosses" -> (["table was I ere I saw elbat"],27)
"drome" -> (["d","r","o","m","e"],1)
"the abbatial palace" -> (["abba"],4)
"" -> ([],0)```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

```def longestPalindromicSubstring:
length as \$len
| if \$len <= 1 then .
else explode as \$s
| {targetLen: \$len, longest: [], i: 0}
| until(.stop;
(.i + .targetLen - 1) as \$j
| if \$j < \$len
then \$s[.i:\$j+1] as \$ss
| if \$ss == (\$ss|reverse) then .longest += [\$ss] else . end
| .i += 1
else
if .longest|length > 0 then .stop=true else . end
| .i = 0
| .targetLen += - 1
end )
| .longest
| map(implode)
| unique
end ;

def strings:
["babaccd", "rotator", "reverse", "forever", "several", "palindrome", "abaracadaraba"];

"The palindromic substrings having the longest length are:",
(strings[]
| longestPalindromicSubstring as \$longest
| "  \(.): length \(\$longest|length) -> \(\$longest)"
)```
Output:
```The palindromic substrings having the longest length are:
babaccd: length 3 -> ["aba","bab"]
rotator: length 7 -> ["rotator"]
reverse: length 5 -> ["rever"]
forever: length 5 -> ["rever"]
several: length 3 -> ["eve"]
palindrome: length 1 -> ["a","d","e","i","l","m","n","o","p","r"]
```

## Julia

```function allpalindromics(s)
list, len = String[], length(s)
for i in 1:len-1, j in i+1:len
substr = s[i:j]
if substr == reverse(substr)
push!(list, substr)
end
end
return list
end

for teststring in ["babaccd", "rotator", "reverse", "forever", "several", "palindrome"]
list = sort!(allpalindromics(teststring), lt = (x, y) -> length(x) < length(y))
println(isempty(list) ? "No palindromes of 2 or more letters found in \"\$teststring." :
"The longest palindromic substring of \$teststring is: \"",
join(list[findall(x -> length(x) == length(list[end]), list)], "\" or \""), "\"")
end
```
Output:
```The longest palindromic substring of babaccd is: "bab" or "aba"
The longest palindromic substring of rotator is: "rotator"
The longest palindromic substring of reverse is: "rever"
The longest palindromic substring of forever is: "rever"
The longest palindromic substring of several is: "eve"
No palindromes of 2 or more letters found in "palindrome."
```

### Manacher algorithm

```function manacher(str)
s =  "^" * join(split(str, ""), "#") * "\\$"
len = length(s)
pals = fill(0, len)
center, right = 1, 1
for i in 2:len-1
pals[i] = right > i && right - i > 0 && pals[2 * center - i] > 0
while s[i + pals[i] + 1] == s[i - pals[i] - 1]
pals[i] += 1
end
if i + pals[i] > right
center, right = i, i + pals[i]
end
end
maxlen, centerindex = findmax(pals)
start = isodd(maxlen) ? (centerindex-maxlen) ÷ 2 + 1 : (centerindex-maxlen) ÷ 2
return str[start:(centerindex+maxlen)÷2]
end

for teststring in ["babaccd", "rotator", "reverse", "forever", "several", "palindrome", "abaracadabra"]
pal = manacher(teststring)
println(length(pal) < 2 ? "No palindromes of 2 or more letters found in \"\$teststring.\"" :
"The longest palindromic substring of \$teststring is: \"\$pal\"")
end
```
Output:
```The longest palindromic substring of babaccd is: "aba"
The longest palindromic substring of rotator is: "rotator"
The longest palindromic substring of reverse is: "rever"
The longest palindromic substring of forever is: "rever"
The longest palindromic substring of several is: "eve"
No palindromes of 2 or more letters found in "palindrome."
The longest palindromic substring of abaracadabra is: "ara"
```

## Mathematica/Wolfram Language

```ClearAll[ExpandSubsequenceTry, LongestPalindromicSubsequence]
ExpandSubsequenceTry[seq_List, beginpos : {a_, b_}] :=
len = Length[seq];
maxbroaden = Min[a - 1, len - b];
Do[
If[! PalindromeQ[Take[seq, {a - j, b + j}]],
last = j - 1;
Break[];
]
,
];
{a - last, b + last}
]
LongestPalindromicSubsequence[l_List] :=
Module[{evenposs, oddposs, subseqs},
evenposs = SequencePosition[l, {x_, x_}];
oddposs = SequencePosition[l, {x_, y_, x_}];
subseqs = Join[evenposs, oddposs];
subseqs = ExpandSubsequenceTry[l, #] & /@ subseqs;
If[Length[subseqs] > 0,
TakeLargestBy[Take[l, #] & /@ subseqs, Length, 1][]
,
{}
]
]
StringJoin@LongestPalindromicSubsequence[Characters["three old rotators"]]
StringJoin@LongestPalindromicSubsequence[Characters["never reverse"]]
StringJoin@LongestPalindromicSubsequence[Characters["stable was I ere I saw elbatrosses"]]
StringJoin@LongestPalindromicSubsequence[Characters["drome"]]
StringJoin@LongestPalindromicSubsequence[Characters["the abbatial palace"]]
```
Output:
```"rotator"
"ever reve"
"table was I ere I saw elbat"
"aca"
""
"abba"```

## Nim

Simple algorithm but working on Unicode code points.

```import sequtils, strutils, unicode

func isPalindrome(s: seq[Rune]): bool =
## Return true if a sequence of runes is a palindrome.
for i in 1..(s.len shr 1):
if s[i - 1] != s[^i]:
return false
result = true

func lps(s: string): seq[string] =
var maxLength = 0
var list: seq[seq[Rune]]
let r = s.toRunes
for first in 0..r.high:
for last in first..r.high:
let candidate = r[first..last]
if candidate.isPalindrome():
if candidate.len > maxLength:
list = @[candidate]
maxLength = candidate.len
elif candidate.len == maxLength:
if maxLength > 1:
result = list.mapIt(\$it)

for str in ["babaccd", "rotator", "several", "palindrome", "piété", "tantôt", "étêté"]:
let result = lps(str)
if result.len == 0:
echo str, " → ", "<no palindromic substring of two of more letters found>"
else:
echo str, " → ", result.join(", ")
```
Output:
```babaccd → bab, aba
rotator → rotator
several → eve
palindrome → <no palindromic substring of two of more letters found>
piété → été
tantôt → tôt
étêté → étêté```

## Perl

The short one - find all palindromes with one regex.

```#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Longest_palindromic_substrings
use warnings;

print "Longest Palindrome For \$_ = @{[ longestpalindrome(\$_) ]}\n"
for qw(babaccd rotator reverse forever several palindrome abaracadabra);

sub longestpalindrome
{
my @best = {"''" => 0};
pop =~ /(.+) .? (??{reverse \$1}) (?{ \$best[length \$&]{\$&}++ }) (*FAIL)/x;
keys %{pop @best};
}
```
Output:
```Longest Palindrome For babaccd = aba bab
Longest Palindrome For rotator = rotator
Longest Palindrome For reverse = rever
Longest Palindrome For forever = rever
Longest Palindrome For several = eve
Longest Palindrome For palindrome = ''
```

The faster one - does the million digits of Pi in under half a second.

```#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Longest_palindromic_substrings
use warnings;

#@ARGV = 'pi.dat'; # uncomment to use this file or add filename to command line

my \$forward = lc do { local \$/; @ARGV ? <> : <DATA> };
\$forward =~ s/\W+//g;

my \$range = 10;
my \$backward = reverse \$forward;
my \$length = length \$forward;
my @best = {"''" => 0};
my \$len;
for my \$i ( 1 .. \$length - 2 )
{
do
{
my \$right = substr \$forward, \$i, \$range;
my \$left = substr \$backward, \$length - \$i, \$range;
( \$right ^ \$left ) =~ /^\0\0+/ and                                # evens
(\$len = 2 * length \$&) >= \$#best and
\$best[ \$len ]{substr \$forward, \$i - length \$&, \$len}++;
( \$right ^ "\0" . \$left ) =~ /^.(\0+)/ and                        # odds
(\$len = 1 + 2 * length \$1) >= \$#best and
\$best[ \$len ]{substr \$forward, \$i - length \$1, \$len}++;
} while \$range < \$#best and \$range = \$#best;
}
print "Longest Palindrome (\$#best) : @{[ keys %{ \$best[-1] } ]}\n";

__DATA__
this data borrowed from raku...

Never odd or even
Was it a car or a cat I saw?
Too bad I hid a boot
I, man, am regal - a German am I
toot
Warsaw was raw
```
Output:
```Longest Palindrome (27) : ootimanamregalagermanamitoo
```

## Phix

Translation of: Raku
```-- demo/rosetta/Longest_palindromic_substrings.exw (plus two older versions)
with javascript_semantics
function longest_palindromes(string s)
--  s = lower/strip_spaces_and_punctuation/utf8_to_utf32, if rqd
integer longest = 2 -- (do not treat length 1 as palindromic)
--  integer longest = 1 -- (do not treat length 0 as palindromic) [works just fine too]
sequence res = {}
for i=1 to length(s) do
for j=0 to iff(i>1 and s[i-1]=s[i]?2:1) do
integer rev = j,
fwd = 1
while rev<i and i+fwd<=length(s) and s[i-rev]=s[i+fwd] do
rev += 1
fwd += 1
end while
string p = s[i-rev+1..i+fwd-1]
integer lp = length(p)
if lp>=longest then
if lp>longest then
longest = lp
res = {p}
elsif not find(p,res) then -- (or just "else")
res = append(res,p)
end if
end if
end for
end for
return res -- (or "sort(res)" or "unique(res)", as needed)
end function

for i=1 to length(tests) do
printf(1,"%s: %v\n",{tests[i],longest_palindromes(tests[i])})
end for
```
Output:
```babaccd: {"bab","aba"}
rotator: {"rotator"}
reverse: {"rever"}
forever: {"rever"}
several: {"eve"}
palindrome: {}
abbbc: {"bbb"}
```

with longest initialised to 1, you get the same except for `palindrome: {"p","a","l","i","n","d","r","o","m","e"}`

## Python

Defines maximal expansions of any two or three character palindromic nuclei in the string.

(This version ignores case but allows non-alphanumerics).

```'''Longest palindromic substrings'''

# longestPalindrome :: String -> ([String], Int)
def longestPalindromes(s):
'''All palindromes of the maximal length
drawn from a case-flattened copy of
the given string, tupled with the
maximal length.
Non-alphanumerics are included here.
'''
k = s.lower()
palindromes = [
palExpansion(k)(ab) for ab
in palindromicNuclei(k)
]
maxLength = max([
len(x) for x in palindromes
]) if palindromes else 1
return (
[
x for x in palindromes if maxLength == len(x)
] if palindromes else list(s),
maxLength
) if s else ([], 0)

# palindromicNuclei :: String -> [(Int, Int)]
def palindromicNuclei(s):
'''Ranges of all the 2 or 3 character
palindromic nuclei in s.
'''
cs = list(s)
return [
# Two-character nuclei.
(i, 1 + i) for (i, (a, b))
in enumerate(zip(cs, cs[1:]))
if a == b
] + [
# Three-character nuclei.
(i, 2 + i) for (i, (a, b, c))
in enumerate(zip(cs, cs[1:], cs[2:]))
if a == c
]

# palExpansion :: String -> (Int, Int) -> String
def palExpansion(s):
'''Full expansion of the palindromic
nucleus with the given range in s.
'''
iEnd = len(s) - 1

def limit(ij):
i, j = ij
return 0 == i or iEnd == j or s[i-1] != s[j+1]

def expansion(ij):
i, j = ij
return (i - 1, 1 + j)

def go(ij):
ab = until(limit)(expansion)(ij)
return s[ab:ab + 1]
return go

# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Longest palindromic substrings'''
print(
fTable(main.__doc__ + ':\n')(repr)(repr)(
longestPalindromes
)([
'three old rotators',
'never reverse',
'stable was I ere I saw elbatrosses',
'drome',
'the abbatial palace',
''
])
)

# ----------------------- GENERIC ------------------------

# until :: (a -> Bool) -> (a -> a) -> a -> a
def until(p):
'''The result of repeatedly applying f until p holds.
The initial seed value is x.
'''
def go(f):
def g(x):
v = x
while not p(v):
v = f(v)
return v
return g
return go

# ---------------------- FORMATTING ----------------------

# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
'''Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
'''
def gox(xShow):
def gofx(fxShow):
def gof(f):
def goxs(xs):
ys = [xShow(x) for x in xs]
w = max(map(len, ys))

def arrowed(x, y):
return y.rjust(w, ' ') + ' -> ' + (
fxShow(f(x))
)
return s + '\n' + '\n'.join(
map(arrowed, xs, ys)
)
return goxs
return gof
return gofx
return gox

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
```Longest palindromic substrings:

'three old rotators' -> (['rotator'], 7)
'never reverse' -> (['ever reve'], 9)
'stable was I ere I saw elbatrosses' -> (['table was i ere i saw elbat'], 27)
'drome' -> (['d', 'r', 'o', 'm', 'e'], 1)
'the abbatial palace' -> (['abba'], 4)
'' -> ([], 0)```

## Raku

Works with: Rakudo version 2020.09

This version regularizes (ignores) case and ignores non alphanumeric characters. It is only concerned with finding the longest palindromic substrings so does not exhaustively find all possible palindromes. If a palindromic substring is found to be part of a longer palindrome, it is not captured separately. Showing the longest 5 palindromic substring groups. Run it with no parameters to operate on the default; pass in a file name to run it against that instead.

```my @chars = ( @*ARGS ?? @*ARGS.IO.slurp !! q:to/BOB/ ) .lc.comb: /\w/;
Lyrics to "Bob" copyright Weird Al Yankovic

I, man, am regal - a German am I
Never odd or even
Too hot to hoot
No lemons, no melon
Too bad I hid a boot
Lisa Bonet ate no basil
Warsaw was raw
Was it a car or a cat I saw?

Rise to vote, sir
Do geese see God?
"Do nine men interpret?" "Nine men," I nod
Rats live on no evil star
Won't lovers revolt now?
Race fast, safe car
Pa's a sap
Ma is as selfless as I am
May a moody baby doom a yam?

Ah, Satan sees Natasha
No devil lived on
Lonely Tylenol
Not a banana baton
No "x" in "Nixon"
O, stone, be not so
O Geronimo, no minor ego
"Naomi," I moan
"A Toyota's a Toyota"
A dog, a panic in a pagoda

Oh no! Don Ho!
Nurse, I spy gypsies - run!
Senile felines
Now I see bees I won
UFO tofu
We panic in a pew
Oozy rat in a sanitary zoo
God! A red nugget! A fat egg under a dog!
Go hang a salami, I'm a lasagna hog!
BOB
#"

my @cpfoa = flat
(1 ..^ @chars).race(:1000batch).map: -> \idx {
my @s;
for 1, 2 {
my int (\$rev, \$fwd) = \$_, 1;
loop {
quietly last if (\$rev > idx) || (@chars[idx - \$rev] ne @chars[idx + \$fwd]);
\$rev = \$rev + 1;
\$fwd = \$fwd + 1;
}
@s.push: @chars[idx - \$rev ^..^ idx + \$fwd].join if \$rev + \$fwd > 2;
last if @chars[idx - 1] ne @chars[idx];
}
next unless +@s;
@s
}

"{.key} ({+.value})\t{.value.unique.sort}".put for @cpfoa.classify( *.chars ).sort( -*.key ).head(5);
```
Output:

Returns the length, (the count) and the list:

```29 (2)	doninemeninterpretninemeninod godarednuggetafateggunderadog
26 (1)	gohangasalamiimalasagnahog
23 (1)	arwontloversrevoltnowra
21 (4)	imanamregalagermanami mayamoodybabydoomayam ootnolemonsnomelontoo oozyratinasanitaryzoo
20 (1)	ratsliveonnoevilstar
```

This isn't intensively optimised but isn't too shabby either. When run against the first million digits of pi: 1000000 digits of pi text file (Pass in the file path/name at the command line) we get:

```13 (1)	9475082805749
12 (1)	450197791054
11 (8)	04778787740 09577577590 21348884312 28112721182 41428782414 49612121694 53850405835 84995859948
10 (9)	0045445400 0136776310 1112552111 3517997153 5783993875 6282662826 7046006407 7264994627 8890770988
9 (98)	019161910 020141020 023181320 036646630 037101730 037585730 065363560 068363860 087191780 091747190 100353001 104848401 111262111 131838131 132161231 156393651 160929061 166717661 182232281 193131391 193505391 207060702 211878112 222737222 223404322 242424242 250171052 258232852 267919762 272636272 302474203 313989313 314151413 314424413 318272813 323212323 330626033 332525233 336474633 355575553 357979753 365949563 398989893 407959704 408616804 448767844 450909054 463202364 469797964 479797974 480363084 489696984 490797094 532121235 546000645 549161945 557040755 559555955 563040365 563828365 598292895 621969126 623707326 636414636 636888636 641949146 650272056 662292266 667252766 681565186 684777486 712383217 720565027 726868627 762727267 769646967 777474777 807161708 819686918 833303338 834363438 858838858 866292668 886181688 895505598 896848698 909565909 918888819 926676629 927202729 929373929 944525449 944848449 953252359 972464279 975595579 979202979 992868299```

in right around 7 seconds on my system.

## REXX

```/*REXX program finds and displays the  longest palindromic string(s) in a given string. */
parse arg s                                      /*obtain optional argument from the CL.*/
if s==''|s==","  then s='babaccd rotator reverse forever several palindrome abaracadaraba'
/* [↑] the case of strings is respected*/
do i=1  for words(s);          x= word(s, i) /*obtain a string to be examined.      */
L= length(x);                  m= 0          /*get the string's length; Set max len.*/
if find(1)  then m= max(m, LL) /*Found a palindrome?  Set M=new length*/
end   /*LL*/
LL= max(1, m)
call find 0                                  /*find all palindromes with length  LL.*/
say ' longest palindromic substrings for string: '        x
say '────────────────────────────────────────────'copies('─', 2 + L)
do n=1  for words(@)                   /*show longest palindromic substrings. */
say '    (length='LL")  "  word(@, n)  /*display a         "      substring.  */
end   /*n*/;       say;    say         /*display a two─blank separation fence.*/
end         /*i*/
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
find: parse arg short                            /*if SHORT==1,  only find 1 palindrome.*/
@=                                         /*initialize palindrome list to a null.*/
do j=1  for L-LL+1;  \$= substr(x, j, LL) /*obtain a possible palindromic substr.*/
if \$\==reverse(\$)  then iterate          /*Not a palindrome?       Then skip it.*/
@= @ \$                                   /*add a palindromic substring to a list*/
if short  then return 1                  /*we have found  one   palindrome.     */
end   /*j*/;   return 0                  /* "   "    "    some  palindrome(s).  */
```
output   when using the default input:
``` longest palindromic substrings for string:  babaccd
─────────────────────────────────────────────────────
(length=3)   bab
(length=3)   aba

longest palindromic substrings for string:  rotator
─────────────────────────────────────────────────────
(length=7)   rotator

longest palindromic substrings for string:  reverse
─────────────────────────────────────────────────────
(length=5)   rever

longest palindromic substrings for string:  forever
─────────────────────────────────────────────────────
(length=5)   rever

longest palindromic substrings for string:  several
─────────────────────────────────────────────────────
(length=3)   eve

longest palindromic substrings for string:  palindrome
────────────────────────────────────────────────────────
(length=1)   p
(length=1)   a
(length=1)   l
(length=1)   i
(length=1)   n
(length=1)   d
(length=1)   r
(length=1)   o
(length=1)   m
(length=1)   e

longest palindromic substrings for string:  abaracadaraba
───────────────────────────────────────────────────────────
(length=3)   aba
(length=3)   ara
(length=3)   aca
(length=3)   ara
(length=3)   aba
```

## Ring

```load "stdlib.ring"

st = "babaccd"
palList = []

for n = 1 to len(st)-1
for m = n+1 to len(st)
sub = substr(st,n,m-n)
if ispalindrome(sub) and len(sub) > 1
ok
next
next

palList = sort(palList,2)
palList = reverse(palList)
resList = []

for n = 2 to len(palList)
if palList = palList[n]
ok
next

see "Input: " + st + nl
see "Longest palindromic substrings:" + nl
see resList```
Output:
```Input: babaccd
Longest palindromic substrings:
bab
aba
```

## Wren

Library: Wren-seq
Library: Wren-fmt

I've assumed that the expression 'substring' includes the string itself and that substrings of length 1 are considered to be palindromic. Also that if there is more than one palindromic substring of the longest length, then all such distinct ones should be returned.

The Phix entry examples have been used.

```import "/seq" for Lst
import "/fmt" for Fmt

var longestPalSubstring = Fn.new { |s|
var len = s.count
if (len <= 1) return [s]
var targetLen = len
var longest = []
var i = 0
while (true) {
var j = i + targetLen - 1
if (j < len) {
var ss = s[i..j]
i = i + 1
} else {
if (longest.count > 0) return longest
i = 0
targetLen = targetLen - 1
}
}
}

var strings = ["babaccd", "rotator", "reverse", "forever", "several", "palindrome", "abaracadaraba"]
System.print("The palindromic substrings having the longest length are:")
for (s in strings) {
var longest = Lst.distinct(longestPalSubstring.call(s))
Fmt.print("  \$-13s Length \$d -> \$n", s, longest.count, longest)
}
```
Output:
```The palindromic substrings having the longest length are:
babaccd       Length 3 -> [bab, aba]
rotator       Length 7 -> [rotator]
reverse       Length 5 -> [rever]
forever       Length 5 -> [rever]
several       Length 3 -> [eve]
palindrome    Length 1 -> [p, a, l, i, n, d, r, o, m, e]