Find The Longest Palindrome In A String

October 15, 2010

Greplin issued a programming challenge recently that required programmers to solve three problems; when completed, Greplin issued an invitation to send them a resume. The first problem required the programmer to find the longest palindrome in the following 1169-character string:


Fourscoreandsevenyearsagoourfaathersbroughtforthonthisconta
inentanewnationconceivedinzLibertyanddedicatedtotheproposit
ionthatallmenarecreatedequalNowweareengagedinagreahtcivilwa
rtestingwhetherthatnaptionoranynartionsoconceivedandsodedic
atedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWeh
avecometodedicpateaportionofthatfieldasafinalrestingplacefo
rthosewhoheregavetheirlivesthatthatnationmightliveItisaltog
etherfangandproperthatweshoulddothisButinalargersensewecann
otdedicatewecannotconsecratewecannothallowthisgroundThebrav
elmenlivinganddeadwhostruggledherehaveconsecrateditfarabove
ourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorl
ongrememberwhatwesayherebutitcanneverforgetwhattheydidhereI
tisforusthelivingrathertobededicatedheretotheulnfinishedwor
kwhichtheywhofoughtherehavethusfarsonoblyadvancedItisrather
forustobeherededicatedtothegreattdafskremainingbeforeusthat
fromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwh
ichtheygavethelastpfullmeasureofdevotionthatweherehighlyres
olvethatthesedeadshallnothavediedinvainthatthisnationunsder
Godshallhaveanewbirthoffreedomandthatgovernmentofthepeopleb
ythepeopleforthepeopleshallnotperishfromtheearth

Your task is to write a function that finds the longest palindrome in a string and apply it to the string given above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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27 Responses to “Find The Longest Palindrome In A String”

  1. Grégory LEOCADIE said

    Could someone delete my previous comment please ?

    I tried the naive way. I don’t know much about palindrome.
    oops my pastebin does not show up. my solution

  2. [...] today’s Programming Praxis exercise, our goal is to write an alogrithm to find the longest palindrome in a [...]

  3. Remco Niemeijer said

    My Haskell solution (see http://bonsaicode.wordpress.com/2010/10/15/programming-praxis-find-the-longest-palindrome-in-a-string/ for a version with comments):

    import qualified Data.ByteString.Char8 as B
    import qualified Data.List.Key as K
    
    longestPalindrome :: B.ByteString -> B.ByteString
    longestPalindrome s = K.maximum B.length
        [p | p <- B.inits =<< B.tails s, p == B.reverse p]
    
  4. programmingpraxis said

    Remco: I also used the O(n^3) algorithm when I solved the challenge; I wrote the code as fast as I can type, it worked the first time, and once I had the answer I moved on to the second level. But after I finished the challenge I went looking for a better way, and Jeuring’s solution was so pretty I had to include it in an exercise.

    By the way, the second level was easy, involving fibonacci numbers, prime checking and integer factorization; I could have stolen code from several of our earlier exercises to solve it quickly, but instead I looked up the prime fibonacci numbers on OEIS and used Dario Alpern’s applet for the factorization. The third level involved generating all possible subsets and testing them for a particular condition, and the brute-force solution took over a minute to run. I’ve since got a much better solution for the third level, but I’m still looking for the “perfect” solution that I can use for an exercise.

    Phil

  5. Bogdan Popa said

    My solution in Python:

    #!/usr/bin/env python
    import sys
    
    def main(args):
    	try:
    		with open(args[1]) as f:
    			stream = f.read()
    	except IndexError:
    		print "usage: pal.py file"
    		return 0
    	except IOError:
    		print "error: could not open file '%s'." % args[1]
    		return 1
    
    	longest = ""
    
    	for i, _ in enumerate(stream):
    		for j, _ in enumerate(stream[i:]):
    			if stream[i:j] == stream[j-1:i-1:-1] and j - i > len(longest):
    				longest = stream[i:j]
    
    	print longest
    
    	return 0
    
    if __name__ == "__main__":
    	sys.exit(main(sys.argv))
    
  6. kbob said

    I took the greplin challenge a few days ago too. Here was
    my solution to problem 1. It’s O(n**2) in the worst case
    but much closer to O(n) for typical input data.

    #!/usr/bin/python
    
    txt = open('gettysburg.txt').read()
    
    longest = ''
    
    def nominate(s):
        global longest
        if len(s) > len(longest):
            longest = s
    
    def explore(i, j):
        """[i..j] is closed interval"""
        while 0 <= i and j < len(txt) and txt[i] == txt[j]:
            i -= 1
            j += 1
        nominate(txt[i+1:j])
        
    
    # Odd-length substrings
    for i in range(1, len(txt) - 1):
        explore(i, i)
    
    # Even-length substrings
    for i in range(1, len(txt)):
        explore(i - 1, i)
    
    print longest
    
  7. http://gist.github.com/629008

    #!/usr/bin/env ruby
    
    def longest_palindrome_in(string)
      palindrome = ""
      0.upto string.length do |outer|
        string.length.downto outer+1 do |inner|
          forward = string.slice(outer..inner)
          if forward.length > palindrome.length && forward.eql?(forward.reverse)
            palindrome = forward
          end
        end
      end
      palindrome
    end
    
    string = DATA.read.gsub "\n", ""
    string.downcase!
    puts longest_palindrome_in string
    
    __END__
    
    Fourscoreandsevenyearsagoourfaathersbroughtforthonthisconta
    inentanewnationconceivedinzLibertyanddedicatedtotheproposit
    ionthatallmenarecreatedequalNowweareengagedinagreahtcivilwa
    rtestingwhetherthatnaptionoranynartionsoconceivedandsodedic
    atedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWeh
    avecometodedicpateaportionofthatfieldasafinalrestingplacefo
    rthosewhoheregavetheirlivesthatthatnationmightliveItisaltog
    etherfangandproperthatweshoulddothisButinalargersensewecann
    otdedicatewecannotconsecratewecannothallowthisgroundThebrav
    elmenlivinganddeadwhostruggledherehaveconsecrateditfarabove
    ourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorl
    ongrememberwhatwesayherebutitcanneverforgetwhattheydidhereI
    tisforusthelivingrathertobededicatedheretotheulnfinishedwor
    kwhichtheywhofoughtherehavethusfarsonoblyadvancedItisrather
    forustobeherededicatedtothegreattdafskremainingbeforeusthat
    fromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwh
    ichtheygavethelastpfullmeasureofdevotionthatweherehighlyres
    olvethatthesedeadshallnothavediedinvainthatthisnationunsder
    Godshallhaveanewbirthoffreedomandthatgovernmentofthepeopleb
    ythepeopleforthepeopleshallnotperishfromtheearth
    
  8. Graham said

    I also did the slow and steady method. O(n^3) isn’t bad for 1169 characters, but it won’t be great for larger data. Small speed up: in my flp() function, starting case is a single character, so we begin by only searching for palindromes of length 2 or greater.

    #!/usr/bin/env python
    # Find the longest palindrome in a given text
    
    def is_pal(s):
        return s == s[::-1]
    
    def flp(s):
        longest, len_longest  = 'g', 1
        for i in xrange(len(s)):
            for j in xrange(2,len(s[i:])):
                sub_s = s[i:i+j+1]
                if is_pal(sub_s) and len(sub_s) > len_longest:
                    longest, len_longest = sub_s, j+1
        return (longest, len_longest)
    
    def main():
        f = open('four_score.txt')
        lines =  ''.join(l for l in f.read().split())
        f.close()
        pal, length = flp(lines)
        print "Length of longest palindrome:\t%s" % length
        print "Longest palindrome:\t%s" % pal
        return
    
    if __name__ == '__main__':
        main()
    
  9. And here’s my go at the O(n^2) solution described in the post, in Ruby:

    #!/usr/bin/env ruby
    
    class PalindromeFinder
      def self.find(string)
        longest = ""
    
        (0...string.length).each do |count|
          palindrome = find_longest_palindrome_at_char string, count
          longest = palindrome if !palindrome.nil? && palindrome.length > longest.length
        end
    
        longest
      end
    
      # Return the longest palindrome in the given string using the character
      # at the position given as the midpoint of the search string.
      def self.find_longest_palindrome_at_char(string, position)
        max_string = string.slice 0..position
        found = nil
        (1..max_string.length/2).each do |count|
          potential = mid max_string, count
          return found unless palindrome? potential
          found = potential
        end
        found
      end
    
      # Return the middle of the given string,
      # counting count characters left and right.
      def self.mid(string, count)
        length    = string.length
        mid       = length / 2
        start_pos = mid - count
        end_pos   = string.length.even? ? mid + (count - 1) : mid + count
    
        puts "ERROR #{string} #{count} #{mid} #{start_pos} #{end_pos}" if start_pos < 0 || end_pos >= length
        string.slice start_pos..end_pos
      end
    
      # Return true if the given string is a palindrome.
      def self.palindrome?(string)
        true if !string.nil? && string.eql?(string.reverse)
      end
    end
    
    string = DATA.read.gsub "\n", ""
    string.downcase!
    puts PalindromeFinder::find string
    
    __END__
    
    Fourscoreandsevenyearsagoourfaathersbroughtforthonthisconta
    inentanewnationconceivedinzLibertyanddedicatedtotheproposit
    ionthatallmenarecreatedequalNowweareengagedinagreahtcivilwa
    rtestingwhetherthatnaptionoranynartionsoconceivedandsodedic
    atedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWeh
    avecometodedicpateaportionofthatfieldasafinalrestingplacefo
    rthosewhoheregavetheirlivesthatthatnationmightliveItisaltog
    etherfangandproperthatweshoulddothisButinalargersensewecann
    otdedicatewecannotconsecratewecannothallowthisgroundThebrav
    elmenlivinganddeadwhostruggledherehaveconsecrateditfarabove
    ourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorl
    ongrememberwhatwesayherebutitcanneverforgetwhattheydidhereI
    tisforusthelivingrathertobededicatedheretotheulnfinishedwor
    kwhichtheywhofoughtherehavethusfarsonoblyadvancedItisrather
    forustobeherededicatedtothegreattdafskremainingbeforeusthat
    fromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwh
    ichtheygavethelastpfullmeasureofdevotionthatweherehighlyres
    olvethatthesedeadshallnothavediedinvainthatthisnationunsder
    Godshallhaveanewbirthoffreedomandthatgovernmentofthepeopleb
    ythepeopleforthepeopleshallnotperishfromtheearth
    
  10. Hurray for leaving debugging code in the post >.<

  11. pradyumna chatterjee said

    txt=”’FourscoreandsevenyearsagoourfaathersbroughtforthonthiscontainentanewnationconceivedinzLibertyanddedicatedtothepropositionthatallmenarecreatedequalNowweareengagedinagreahtcivilwartestingwhetherthatnaptionoranynartionsoconceivedandsodedicatedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWehavecometodedicpateaportionofthatfieldasafinalrestingplaceforthosewhoheregavetheirlivesthatthatnationmightliveItisaltogetherfangandproperthatweshoulddothisButinalargersensewecannotdedicatewecannotconsecratewecannothallowthisgroundThebravelmenlivinganddeadwhostruggledherehaveconsecrateditfaraboveourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorlongrememberwhatwesayherebutitcanneverforgetwhattheydidhereItisforusthelivingrathertobededicatedheretotheulnfinishedworkwhichtheywhofoughtherehavethusfarsonoblyadvancedItisratherforustobeherededicatedtothegreattdafskremainingbeforeusthatfromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwhichtheygavethelastpfullmeasureofdevotionthatweherehighlyresolvethatthesedeadshallnothavediedinvainthatthisnationunsderGodshallhaveanewbirthoffreedomandthatgovernmentofthepeoplebythepeopleforthepeopleshallnotperishfromtheearth”’
    palins=[]
    def palindrome():
    for i in range(len(txt)-1):
    #print “iteration:”+str(i)
    j=len(txt)-1
    while(j>=i):
    #check plaindrome
    temp=txt[i:j]
    last=len(temp)-1
    iters=int(len(temp)/2)
    flag=True
    for n in range(iters):
    if temp[n]!=temp[last-n]:
    flag=False
    break
    if flag==True:
    palins.append(temp)
    j-=1

    def getmax(li):
    longest=”
    for i in li:
    if len(i) > len(longest):
    longest=i
    return (longest,len(longest))

    palindrome()
    print “longest palindrome: %s, size:%d” % getmax(palins)

  12. Dmitry said

    O(n^2) solution in Scheme

    
    ; range
    
    (define make-range cons)
    (define range-from car)
    (define range-to cdr)
    
    (define (range-length r)
      (- (range-to r)
         (range-from r)))
    
    
    ; vector[from, to) -> string
    
    (define (subvector->list v range)
      (define (s->l from to)
        (if (>= from to) 
            (list)
            (cons (vector-ref v from) 
                  (s->l (+ 1 from) to))))
      (s->l (range-from range)
            (range-to range)))
    
    
    ; palindrome stuff
    
    (define (longest-palindrome-range v)
      
      ; v[first] == vector[second]
      (define (pal-pair? first second)
        (if (or (< first 0) (>= second (vector-length v)))
            #f
            (eq? (vector-ref v first) 
                 (vector-ref v second)))) 
      
      ; longest palindrome range for position
      (define (range-for pos)
        (define (range-int from to)
          (if (pal-pair? from to)
              (range-int (- from 1) (+ to 1))
              (make-range (+ from 1) to)))
        
        (let ((odd-p (range-int pos pos))
              (even-p (range-int pos (+ pos 1))))
          (if (> (range-length odd-p) 
                 (range-length even-p))
              odd-p
              even-p)))
      
      ; search
      (define (longest-int from current-answer)
        (if (>= from (vector-length v))
            current-answer
            (let ((candidate (range-for from)))
              (if (> (range-length candidate) 
                     (range-length current-answer))
                  (longest-int (+ 1 from) candidate)
                  (longest-int (+ 1 from) current-answer)))))
      (longest-int 0 (make-range 0 0)))
    
    
    (define (longest-palindrome str) 
      (let* ((v (list->vector (string->list str)))
             (range (longest-palindrome-range v)))
        (list->string (subvector->list v range))))
    
    
    ; usage
    
    (longest-palindrome "problem string")
    
    

    > I’m still looking for the “perfect” solution that I can use for an exercise

    solution based on coin change algorithm gives an answer almost instantly.

  13. lalit mohan said

    Here’s the O(n^2) solution in Matlab:

    function longest_palindrom_quad()
    %O(n^2) solution

    txt = ['Fourscoreandsevenyearsagoourfaathersbroughtforthonthisconta' ...
    'inentanewnationconceivedinzLibertyanddedicatedtotheproposit' ...
    'ionthatallmenarecreatedequalNowweareengagedinagreahtcivilwa' ...
    'rtestingwhetherthatnaptionoranynartionsoconceivedandsodedic' ...
    'atedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWeh' ...
    'avecometodedicpateaportionofthatfieldasafinalrestingplacefo' ...
    'rthosewhoheregavetheirlivesthatthatnationmightliveItisaltog' ...
    'etherfangandproperthatweshoulddothisButinalargersensewecann' ...
    'otdedicatewecannotconsecratewecannothallowthisgroundThebrav' ...
    'elmenlivinganddeadwhostruggledherehaveconsecrateditfarabove' ...
    'ourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorl' ...
    'ongrememberwhatwesayherebutitcanneverforgetwhattheydidhereI' ...
    'tisforusthelivingrathertobededicatedheretotheulnfinishedwor' ...
    'kwhichtheywhofoughtherehavethusfarsonoblyadvancedItisrather' ...
    'forustobeherededicatedtothegreattdafskremainingbeforeusthat' ...
    'fromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwh' ...
    'ichtheygavethelastpfullmeasureofdevotionthatweherehighlyres' ...
    'olvethatthesedeadshallnothavediedinvainthatthisnationunsder' ...
    'Godshallhaveanewbirthoffreedomandthatgovernmentofthepeopleb' ...
    'ythepeopleforthepeopleshallnotperishfromtheearth'];

    n = length(txt);
    palindrom_length = -inf;
    palindrom = [];

    for idx = 1:n
    [odd_found, odd_span] = extend_odd(idx);
    if odd_found
    odd_len = 2*odd_span+1;
    if odd_len > palindrom_length
    palindrom = [idx - odd_span, idx + odd_span];
    palindrom_length = odd_len;
    end
    end
    [even_found, even_span] = extend_even(idx);
    if even_found
    even_len = 2*even_span;
    if even_len > palindrom_length
    palindrom = [idx - (even_span-1), idx + even_span];
    palindrom_length = odd_len;
    end
    end
    end

    disp(['palindrom is ' txt(palindrom(1):palindrom(2)) ]);
    disp(['length is ' num2str(palindrom_length)]);
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    function [odd_found, odd_span] = extend_odd(odd_i)
    flag = false;
    oi = 1;
    while(odd_i – oi >= 1 && odd_i + oi <= n)
    if txt(odd_i – oi) == txt(odd_i + oi)
    flag = true;
    else
    break;
    end
    oi = oi + 1;
    end
    if flag
    odd_found = true;
    odd_span = oi-1;
    else
    odd_found = false;
    odd_span = nan;
    end
    end
    function [even_found, even_span] = extend_even(even_i)
    flag = false;
    oi = 1;
    while(even_i – (oi – 1) <= n && even_i + oi <= n)
    if txt(even_i + oi) == txt(even_i – (oi – 1))
    flag = true;
    else
    break;
    end
    oi = oi + 1;
    end
    if flag
    even_found = true;
    even_span = oi-1;
    else
    even_found = false;
    even_span = nan;
    end
    end
    end

  14. Lars Björnfot said

    Here is a solution in golang. It runs pretty fast, just 0.1 s
    to compile, link, and run, in a Linux inside VirtualBox.
    You can run it on golang.org.
    (It took substantially longer time to write. This is my first program in golang.)

    package main
    
    func main() {
    	input := 
    "Fourscoreandsevenyearsagoourfaathersbroughtforthonthisconta"+
    "inentanewnationconceivedinzLibertyanddedicatedtotheproposit"+
    "ionthatallmenarecreatedequalNowweareengagedinagreahtcivilwa"+
    "rtestingwhetherthatnaptionoranynartionsoconceivedandsodedic"+
    "atedcanlongendureWeareqmetonagreatbattlefiemldoftzhatwarWeh"+
    "avecometodedicpateaportionofthatfieldasafinalrestingplacefo"+
    "rthosewhoheregavetheirlivesthatthatnationmightliveItisaltog"+
    "etherfangandproperthatweshoulddothisButinalargersensewecann"+
    "otdedicatewecannotconsecratewecannothallowthisgroundThebrav"+
    "elmenlivinganddeadwhostruggledherehaveconsecrateditfarabove"+
    "ourpoorponwertoaddordetractTgheworldadswfilllittlenotlenorl"+
    "ongrememberwhatwesayherebutitcanneverforgetwhattheydidhereI"+
    "tisforusthelivingrathertobededicatedheretotheulnfinishedwor"+
    "kwhichtheywhofoughtherehavethusfarsonoblyadvancedItisrather"+
    "forustobeherededicatedtothegreattdafskremainingbeforeusthat"+
    "fromthesehonoreddeadwetakeincreaseddevotiontothatcauseforwh"+
    "ichtheygavethelastpfullmeasureofdevotionthatweherehighlyres"+
    "olvethatthesedeadshallnothavediedinvainthatthisnationunsder"+
    "Godshallhaveanewbirthoffreedomandthatgovernmentofthepeopleb"+
    "ythepeopleforthepeopleshallnotperishfromtheearth"
    	var palin string
    	for i := 0; i < len(input) - 1; i++ {
    		palin = larger(palin, input, i, i)
    		palin = larger(palin, input, i, i+1)
    	}
    	println("Max palin: ", palin)
    }
    func larger(palin string, s string, i int, j int) string {
    	var p = getPalin(s, i, j)
    	if len(p) > len(palin) {
    		return p
    	}
    	return palin
    }
    func getPalin(s string, i int, j int) string {
    	for i >= 0 && j < len(s) && s[i] == s[j] {
    		i--
    		j++
    	}
    	i++            // adjust start index, end index is fine
    	return s[i:j]  // return palindrome
    }
    
  15. [...] Find the Longest Palindrome in a string: [...]

  16. F. Carr said

    Here is a more challenging test-case for your algorithms:

    In the collected works of Shakespeare, there are 3 palindromes of 15 characters each — no Shakespearean palindrome is longer. Two are the phrase “Madam, madam, madam.” which is fairly easy to find. What’s the third?

  17. [...] sure how I came across the Programming Praxis blog, but one of their recent posts caught my eye: find the longest palindrome in a string. Given a string, what is the longest palindrome contained in that string? I thought about it [...]

  18. KNguyen said

    Mine in F#

    
    let isPalindrome (s:string) = 
        List.ofArray (s.ToCharArray()) = List.rev (List.ofArray (s.ToCharArray()))
    
    let rec longest_palin_from_start (s:string) =
        if (isPalindrome s) then s 
        else 
            let length = s.Length
            longest_palin_from_start (s.Substring(0, length-1))
    
    let rec longest_palin_in_string (s:string) = 
        if (s.Length = 1) then s
        else
            let tt = longest_palin_from_start s
            let ttt = longest_palin_in_string (s.Substring(1))
            if (tt.Length > ttt.Length) then tt else ttt
    
  19. KNguyen said

    Mine in F#

    let isPalindrome (s:string) = 
        List.ofArray (s.ToCharArray()) = List.rev (List.ofArray (s.ToCharArray()))
    
    let rec longest_palin_from_start (s:string) =
        if (isPalindrome s) then s 
        else 
            let length = s.Length
            longest_palin_from_start (s.Substring(0, length-1))
    
    let rec longest_palin_in_string (s:string) = 
        if (s.Length = 1) then s
        else
            let tt = longest_palin_from_start s
            let ttt = longest_palin_in_string (s.Substring(1))
            if (tt.Length > ttt.Length) then tt else ttt
    
  20. Lautaro Pecile said
    
    def substrings(s):
        """
        Yields substrings from string s in descending order
        """
        l = len(s)
        for end in xrange(l, 0, -1):
            for start in xrange(l-end+1):
                yield s[start:start + end]
    
    def palindrome(s):
        return s == s[::-1]
    
    def longest_palindrome(s):
        for e in substrings(s):
            if palindrome(e):
                return e
    
  21. zhizhong said

    def longest_palindrome(S):
    longest, n = ”, len(S)
    if n = 0 and j < n:
    if S[i] == S[j]:
    L.append(S[i])
    else:
    break
    i -= 1
    j += 1

    if L:
    return ''.join(L[::-1] + M + L)
    return ''

  22. Robert Grano said

    using System;
    using System.Collections.Generic;
    using System.Linq;
    using System.Text;

    namespace CountPalindrome
    {
    class Program
    {
    static void Main(string[] args)
    {
    Console.WriteLine(“please input a string: “);
    string test = Convert.ToString(Console.ReadLine());
    Console.WriteLine(“the longest palindrome is ” + LongestPalindrome(test));
    Console.ReadLine();
    }
    protected static int LongestPalindrome(string str)
    {
    int i = 0;
    int j = 1;
    int oldJ = 1;
    int intMax = 1;
    int intCount = 0;

    if (str.Length == 0) return 0;
    if (str.Length == 1) return 1;

    int[] intDistance = new int[2] {0,1};

    for( int k = 0; k < intDistance.Length; k++ ){

    j = 1 + intDistance[k];
    oldJ = j;
    intCount = 0;
    i = 0;

    while (j = 0 && j b) return a; return b;
    }

    }
    }

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