Longest palindromic substrings

From Rosetta Code
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.

Related tasks


Other tasks related to string operations:
Metrics
Counting
Remove/replace
Anagrams/Derangements/shuffling
Find/Search/Determine
Formatting
Song lyrics/poems/Mad Libs/phrases
Tokenize
Sequences



11l

F longest_palindrome(s)
   V t = Array(‘^’s‘$’).join(‘#’)
   V n = t.len
   V p = [0] * 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’,
      ‘abracadabra’,
      ‘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'
'abracadabra' -> 'ada'
'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("abracadabra")
  Test("the abbatial palace")
  Test("qwertyuiop")
  Test("")
RETURN
Output:

Screenshot from Atari 8-bit computer 

"three old rotators" -> "rotator"
"never reverse" -> "ever reve"
"abracadabra" -> "aca"
"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 #
    PRIO PAD = 1;
    OP   PAD = ( STRING s, INT w )STRING:
         BEGIN
            STRING result := s;
            WHILE LENGTH result < w DO result +:= " " OD;
            result
         END # PAD # ;
    # 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( "abracadabra",                        "aca"                         );
    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"
"abracadabra"                          -> "aca"
"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
abracadabra
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"]
abracadabra				> ["aca", "ada"]
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)

The Task

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 ""

FreeBASIC

Function isPalindrome(s As String) As Integer
    For i As Integer = 1 To Len(s) / 2
        If Mid(s, i, 1) <> Mid(s, Len(s) - i + 1, 1) Then Return False
    Next i
    Return True
End Function

Sub LongestPalindrome(s As String)
    Dim As String substr, longest = ""
    Dim As Integer i, j
    For i = 1 To Len(s)
        For j = i To Len(s)
            substr = Mid(s, i, j - i + 1)
            If isPalindrome(substr) Andalso Len(substr) > Len(longest) Then longest = substr
        Next j
    Next i
    
    Print "The longest palindromic substring is/are: "
    For i = 1 To Len(s)
        For j = i To Len(s)
            substr = Mid(s, i, j - i + 1)
            If IsPalindrome(substr) Andalso Len(substr) = Len(longest) Andalso Len(substr) > 2 Then Print substr; "  ";
        Next j
    Next i
    If Len(longest) <= 2 Then Print "<no palindromic substring of two of more letters found>" 
End Sub

Dim s As String
Input "Enter a string: ", s

LongestPalindrome(s)

Sleep

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[0]), 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]
  abaracadaraba Length 3 -> [aba aca ada ara]

Haskell

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"
    , "abracadabra"
    , "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)
                       "abracadabra" -> (["aca","ada"],3)
                             "drome" -> (["d","r","o","m","e"],1)
               "the abbatial palace" -> (["abba"],4)
                                  "" -> ([],0)

jq

Adapted from #Wren

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[0]|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"]
  abaracadaraba: length 3 -> ["aba","aca","ada","ara"]


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_}] := 
 Module[{len, maxbroaden, last},
  len = Length[seq];
  maxbroaden = Min[a - 1, len - b];
  last = maxbroaden;
  Do[
   If[! PalindromeQ[Take[seq, {a - j, b + j}]],
    last = j - 1;
    Break[];
    ]
   ,
   {j, maxbroaden}
   ];
  {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][[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["abracadabra"]]
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:
          list.add candidate
  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. 

use strict;
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 = ''
Longest Palindrome For abaracadabra = aba ara aca ada

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

use strict;
use warnings;
use feature 'bitwise';

#@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
 
constant tests = {"babaccd","rotator","reverse","forever","several","palindrome","abaracadaraba","abbbc"}
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: {}
abaracadaraba: {"aba","ara","aca","ada"}
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[0]:ab[1] + 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',
            'abracadabra',
            '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)
                       'abracadabra' -> (['aca', 'ada'], 3)
                             '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[0] ?? @*ARGS[0].IO.slurp !! q:to/BOB/ ) .lc.comb: /\w/;
    Lyrics to "Bob" copyright Weird Al Yankovic
    https://www.youtube.com/watch?v=JUQDzj6R3p4

    I, man, am regal - a German am I
    Never odd or even
    If I had a hi-fi
    Madam, I'm Adam
    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.*/
                  do LL=2  for L-1               /*start with palindromes of length two.*/
                  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)   ada
    (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
           add(palList,[sub,len(sub)])
        ok
    next
next

palList = sort(palList,2)
palList = reverse(palList)
resList = []
add(resList,palList[1][1])

for n = 2 to len(palList)
    if palList[1][2] = palList[n][2]
       add(resList,palList[n][1])
    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]
            if (ss == ss[-1..0]) longest.add(ss)
            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[0].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]
  abaracadaraba Length 3 -> [aba, ara, aca, ada]
Retrieved from "https://rosettacode.org/wiki/Longest_palindromic_substrings?oldid=354302"