[Question]
  [
### Introduction
For the ones who don't know, a palindrome is when a string is equal to the string backwards (with exception to interpunction, spaces, etc.). An example of a palindrome is:
```
abcdcba
```
If you reverse this, you will end up with:
```
abcdcba
```
Which is the same. Therefore, we call this a palindrome. To palindromize things, let's take a look at an example of a string:
```
adbcb
```
This is not a palindrome. To palindromize this, we need to merge the reversed string into the initial string **at the right of the initial string**, leaving both versions intact. The shorter, the better.
The first thing we can try is the following:
```
adbcb
bcbda
^^ ^^
```
Not all characters match, so this is not the right position for the reversed string. We go one step to the right:
```
adbcb
 bcbda
 ^^^^
```
This also doesn't match all characters. We go another step to the right:
```
adbcb
  bcbda
```
This time, **all characters match**. We can *merge* both string *leaving the intact*. The final result is:
```
adbcbda
```
This is the *palindromized string*.
---
### The Task
Given a string (with at least one character) containing only **lowercase letters** (or uppercase, if that fits better), output the **palindromized string**.
---
### Test cases
```
Input     Output
abcb      abcba
hello     hellolleh
bonobo    bonobonob
radar     radar
hex       hexeh
```
This is [code-golf](/questions/tagged/code-golf "show questions tagged 'code-golf'"), so the submission with the least amount of bytes wins!
  
[Answer]
# Pyth (commit b93a874), 11 bytes
```
.VkI_IJ+zbB
```
[Test suite](https://pyth.herokuapp.com/?code=.VkI_IJ%2BzbB&test_suite=1&test_suite_input=abcb%0Abonobo%0Aradar%0Ahex&debug=0)
This code exploits a bug in the current version of Pyth, commit [b93a874](https://github.com/isaacg1/pyth/commit/b93a8740ed847dadfeab62e1b01db815d0d88775). The bug is that `_IJ+zb` is parsed as if it was `q_J+zbJ+zb`, which is equivalent to `_I+zb+zb`, when it should (by the design intention of Pyth) be parsed as `q_J+zbJ`, which is equivalent to `_I+zb`. This allows me to save a byte - after the bug is fixed, the correct code will be `.VkI_IJ+zbJB`. I'll explain that code instead.
Basically, the code brute forces over all possible strings until it finds the shortest string that can be appended to the input to form a palindrome, and outputs the combined string.
```
.VkI_IJ+zbJB
                z = input()
.Vk             For b in possible strings ordered by length,
       +zb      Add z and b,
      J         Store it in J,
    _I          Check if the result is a palindrome,
   I            If so,
          J     Print J (This line doesn't actually exist, gets added by the bug.
          B     Break.
```
[Answer]
## Python, 46 bytes
```
f=lambda s:s*(s==s[::-1])or s[0]+f(s[1:])+s[0]
```
If the string is a palindrome, return it. Otherwise, sandwich the first letter around the recursive result for the remainder of the string.
Example breakdown:
```
f(bonobo)
b  f(onobo) b
b o f(nobo) o b 
b o n f(obo) n o b
b o n obo n o b
```
[Answer]
## Haskell, 36 bytes
```
f s|s==reverse s=s|h:t<-s=h:f t++[h]
```
More readably:
```
f s
 |s==reverse s = s
 |(h:t)<-s     = h:(f t)++[h]
```
If the string is a palindrome, return it. Otherwise, sandwich the first letter around the recursive result for the tail of the string.
The string `s` is split into `h:t` in the second guard, obviating a filler `1>0` for this case. This is shorter than doing `s@(h:t)` for the input.
[Answer]
# Jelly, ~~11~~ 10 bytes
```
ṫỤfU$Ḣœ^;U
```
[Try it online!](http://jelly.tryitonline.net/#code=4bmr4bukZlUk4biixZNeO1U&input=&args=aGVsbG8)
### How it works
```
ṫỤfU$Ḣœ^;U  Main link. Argument: s (string)
 Ụ          Yield all indices of s, sorted by their corr. character values.
ṫ           Tail; for each index n, remove all characters before thr nth.
            This yields the list of suffixes of s, sorted by their first character,
            then (in descending order) by length.
    $       Combine the two links to the left into a chain:
   U        Upend; reverse all suffixes.
  f         Filter; only keep suffixes that are also reversed suffixes.
            This gives the list of all palindromic suffixes. Since all of them
            start with the same letter, they are sorted by length.
     Ḣ      Head; select the first, longest palindromic suffix.
      œ^    Multiset symmetric difference; chop the selected suffix from s.
         U  Upend; yield s, reversed.
        ;   Concatenate the results to the left and to the right.
```
[Answer]
# Pyth - ~~16~~ 12 bytes
*4 bytes saved thanks to @FryAmTheEggman.*
FGITW, much golfing possible.
```
h_I#+R_Q+k._
```
[Test Suite](http://pyth.herokuapp.com/?code=h_I%23%2BR_Q%2Bk._&input=%22adbcb%22&test_suite=1&test_suite_input=%22abcb%22%0A%22hello%22%0A%22bonobo%22%0A%22radar%22%0A%22hex%22&debug=0).
[Answer]
# [Brachylog](https://github.com/JCumin/Brachylog), ~~16~~ ~~6~~ 5 bytes (Non-competing)
```
:Ac.r
```
[Try it online!](http://brachylog.tryitonline.net/#code=OkFjLnI&input=ImJvbm9ibyI&args=Wg)
When I posted my initial answer, it was still on the old implementation in Java. Since I have reprogrammed everything in Prolog, it now works as it should have in the first place.
### Explanation
```
(?):Ac.        Output is the concatenation of Input with another unknown string A
      .r(.)    The reverse of the Output is the Output
```
Backpropagation makes it so that the first valid value for `A` it will find will be the shortest that you can concatenate to Input to make it a palindrome.
### Alternate solution, 5 bytes
```
~@[.r
```
This is roughly the same as the above answer, except that instead of stating "Output is the concatenation of the Input with a string `A`", we state that "Output is a string for which the Input is a prefix of the Output".
[Answer]
## JavaScript (ES6), 92 bytes
```
(s,a=[...s],r=a.reverse().join``)=>s.slice(0,a.findIndex((_,i)=>r.startsWith(s.slice(i))))+r
```
Computes and slices away the overlap between the original string and its reversal.
[Answer]
# Retina, ~~29~~ 25
```
$
¶$_
O^#r`.\G
(.+)¶\1
$1
```
[Try it online!](http://retina.tryitonline.net/#code=JArCtiRfCk9eI3JgLlxHCiguKynCtlwxCiQx&input=Ym9ub2Jv)
Big thanks to [Martin](https://codegolf.stackexchange.com/users/8478/martin-b%C3%BCttner) for 11 bytes saved!
This just creates a reversed copy of the string and smooshes them together. The only really fancy part of this is the reversing method: `O^#r`.\G`, which is done by using sort mode. We sort the letters of the second string (the ones that aren't newlines and are consecutive from the end of the string, thanks to the `\G`) by their numeric value, which, since there are no numbers, is 0. Then we reverse the order of the results of this stable sort with the `^` option. All credit for the fancy use of `\G` belongs to Martin :)
[Answer]
# CJam, 18
```
q__,,{1$>_W%=}#<W%
```
[Try it online](http://cjam.aditsu.net/#code=q__%2C%2C%7B1%24%3E_W%25%3D%7D%23%3CW%25&input=bonobo)
**Explanation:**
```
q         read the input
__        make 2 copies
,,        convert the last one to a range [0 … length-1]
{…}#      find the first index that satisfies the condition:
  1$>     copy the input string and take the suffix from that position
  _W%=    duplicate, reverse and compare (palindrome check)
<         take the prefix before the found index
W%        reverse that prefix
          at the end, the stack contains the input string and that reversed prefix
```
[Answer]
## Lua, ~~89~~ 88 Bytes
I beat the Javascript! \o/
**Saved 1 byte thanks to @LeakyNun ^^**
It's a full program, takes its input as command-line argument.
```
i=1s=...r=s:reverse()while s:sub(i)~=r:sub(0,#r-i+1)do i=i+1 end print(s..r:sub(#r-i+2))
```
## ungolfed
```
i=1                             -- initialise i at 1 as string are 1-indexed in lua
s=...                           -- use s as a shorthand for the first argument
r=s:reverse()                   -- reverse the string s and save it into r
while(s:sub(i)~=r:sub(0,#r-i+1))-- iterate while the last i characters of s
do                              -- aren't equals to the first i characters of r
  i=i+1                         -- increment the number of character to skip
end
print(s..r:sub(#r-i+2))         -- output the merged string
```
[Answer]
# Prolog, 43 bytes
```
a(S):-append(S,_,U),reverse(U,U),writef(U).
```
This expects a codes string as input, e.g. on SWI-Prolog 7: `a(`hello`).`
### Explanation
This is basically a port of my Brachylog answer.
```
a(S) :-               % S is the input string as a list of codes
    append(S,_,U),    % U is a list of codes resulting in appending an unknown list to S
    reverse(U,U),     % The reverse of U is U
    writef(U).        % Write U to STDOUT as a list of codes
```
[Answer]
# Octave, ~~78~~ 75 bytes
Saved 3 bytes thanks to Eʀɪᴋ ᴛʜᴇ Gᴏʟғᴇʀ!
```
function p=L(s)d=0;while~all(diag(s==rot90(s),d++))p=[s fliplr(s(1:d))];end
```
ideone still fails for named functions, but [here](http://ideone.com/JSDPVJ) is a test run of the code as a program.
[Answer]
# Perl, 37 bytes
Based on xnor's answer.
Includes +2 for `-lp`
Run with input on STDIN, e.g.
```
palindromize.pl <<< bonobo
```
`palindromize.pl`:
```
#!/usr/bin/perl -lp
s/.//,do$0,$_=$&.$_.$&if$_!~reverse
```
[Answer]
# [Vyxal](https://github.com/Vyxal/Vyxal), 2 bytes
```
Ṙ⋎
```
[Try it Online!](https://vyxal.pythonanywhere.com/#WyIiLCIiLCLhuZjii44iLCIiLCJyYWNlYyJd)
```
 ⋎ # Merge on longest prefix/suffix with...
Ṙ  # Input reversed
```
[Answer]
# [05AB1E](http://github.com/Adriandmen/05AB1E), 18 bytes
Code:
```
Â©gF¹ðN×®«ðñD®åi,q
```
Uses **CP-1252** encoding. [Try it online!](http://05ab1e.tryitonline.net/#code=w4LCqWdGwrnDsE7Dl8KuwqvDsMOxRMKuw6VpLHE&input=Ym9ub2Jv)
[Answer]
## Pyke, 15 bytes
```
D_Dlhm>m+#D_q)e
```
[Try it here!](http://pyke.catbus.co.uk/?code=D_Dlhm%3Em%2B%23D_q%29e&input=radar)
[Answer]
## J, 20 bytes
```
,[|.@{.~(-:|.)\.i.1:
```
This is a monadic verb. [Try it here.](http://tryj.tk) Usage:
```
   f =: ,[|.@{.~(-:|.)\.i.1:
   f 'race'
'racecar'
```
## Explanation
I'm using the fact that the palindromization of **S** is **S + reverse(P)**, where **P** is the shortest prefix of **S** whose removal results in a palindrome.
In J, it's a little clunky to do a search for the first element of an array that satisfies a predicate; hence the indexing.
```
,[|.@{.~(-:|.)\.i.1:  Input is S.
        (    )\.      Map over suffixes of S:
         -:             Does it match
           |.           its reversal? This gives 1 for palindromic suffixes and 0 for others.
                i.1:  Take the first (0-based) index of 1 in that array.
 [   {.~              Take a prefix of S of that length: this is P.
  |.@                 Reverse of P.
,                     Concatenate it to S.
```
[Answer]
## Haskell, 68 bytes
```
import Data.List
f i=[i++r x|x<-inits i,i++r x==x++r i]!!0
r=reverse
```
Usage example: `f "abcb"` -> `"abcba"`.
Search through the `inits` of the input `i` (e.g. `inits "abcb"` -> `["", "a", "ab", "abc", "abcb"]`) until you find one where it's reverse appended to `i` builds a palindrome.
[Answer]
# [MATL](https://esolangs.org/wiki/MATL), ~~17~~ 16 bytes
Loosely inspired in [@aditsu's CJam answer](https://codegolf.stackexchange.com/a/77103/36398).
```
`xGt@q:)PhttP=A~
```
[**Try it online!**](http://matl.tryitonline.net/#code=YHhHdEBxOilQaHR0UD1Bfg&input=J2Jvbm9ibyc)
### Explanation
```
`        % Do...while loop
  x      %   Delete top of stack, which contains a not useful result from the
         %   iteration. Takes input implicitly on first iteration, and deletes it
  G      %   Push input
  t      %   Duplicate
  @q:    %   Generate range [1,...,n-1], where n is iteration index. On the  first
         %   iteration this is an empty array
  )      %   Use that as index into copy of input string: get its first n elements
  Ph     %   Flip and concatenate to input string
  t      %   Duplicate. This will be the final result, or will be deleted at the
         %   beginning of next iteration
  tP     %   Duplicate and flip
  =A~    %   Compare element-wise. Is there some element different? If so, the
         %   result is true. This is the loop condition, so go there will be a 
         %   new iteration. Else the loop is exited with the stack containing
         %   the contatenated string
         % End loop implicitly
         % Display stack contents implicitly
```
[Answer]
# Ruby, 44 bytes
This answer is based on xnor's [Python](https://codegolf.stackexchange.com/a/77116/47581) and [Haskell](https://codegolf.stackexchange.com/a/77115/47581) solutions.
```
f=->s{s.reverse==s ?s:s[0]+f[s[1..-1]]+s[0]}
```
[Answer]
# Oracle SQL 11.2, 195 bytes
```
SELECT MIN(p)KEEP(DENSE_RANK FIRST ORDER BY LENGTH(p))FROM(SELECT:1||SUBSTR(REVERSE(:1),LEVEL+1)p FROM DUAL WHERE SUBSTR(:1,-LEVEL,LEVEL)=SUBSTR(REVERSE(:1),1,LEVEL)CONNECT BY LEVEL<=LENGTH(:1));
```
Un-golfed
```
SELECT MIN(p)KEEP(DENSE_RANK FIRST ORDER BY LENGTH(p))
FROM (
       SELECT :1||SUBSTR(REVERSE(:1),LEVEL+1)p 
       FROM   DUAL 
       WHERE  SUBSTR(:1,-LEVEL,LEVEL)=SUBSTR(REVERSE(:1),1,LEVEL)
       CONNECT BY LEVEL<=LENGTH(:1)
     );
```
[Answer]
## Seriously, 34 bytes
```
╩╜lur`╜╨"Σ╜+;;R=*"£M`MΣ;░p╜;;R=I.
```
The last character is a non-breaking space (ASCII 127 or `0x7F`).
[Try it online!](http://seriously.tryitonline.net/#code=4pWp4pWcbHVyYOKVnOKVqCLOo-KVnCs7O1I9KiLCo01gTc6jO-KWkXDilZw7O1I9SS5_&input=J2FkYmNiJw)
Explanation:
```
╩╜lur`╜╨"Σ╜+;;R=*"£M`MΣ;░p╜;;R=I.<NBSP>
╩                                        push inputs to registers (call the value in register 0 "s" for this explanation)
 ╜lur                                    push range(0, len(s)+1)
     `              `M                   map (for i in a):
      ╜╨                                   push all i-length permutations of s
        "        "£M                       map (for k in perms):
         Σ╜+                                 push s+''.join(k) (call it p)
            ;;R=                             palindrome test
                *                            multiply (push p if palindrome else '')
                      Σ                  summation (flatten lists into list of strings)
                       ;░                filter truthy values
                         p               pop first element (guaranteed to be shortest, call it x)
                          ╜;;R=I         pop x, push s if s is palindromic else x
                                .<NBSP>  print and quit
```
[Answer]
# C#, 202 bytes
I tried.
```
class P{static void Main(string[]a){string s=Console.ReadLine(),o=new string(s.Reverse().ToArray()),w=s;for(int i=0;w!=new string(w.Reverse().ToArray());){w=s.Substring(0,i++)+o;}Console.WriteLine(w);}}
```
Ungolfed:
```
class P
{
    static void Main(string[] a)
    {
        string s = Console.ReadLine(), o = new string(s.Reverse().ToArray()), w = s;
        for(int i = 0; w!=new string(w.Reverse().ToArray());)
        {
            w = s.Substring(0, i++) + o;
        }
        Console.WriteLine(w);
        Console.ReadKey();
    }
}
```
Can anyone provide me with any ideas to group the two calls to .Reverse().ToArray() ? A separate method is more bytes.
[Answer]
# [Jelly](https://github.com/DennisMitchell/jelly), 9 bytes
```
Ṗ;¥ƤUŒḂƇḢ
```
[Try it online!](https://tio.run/##y0rNyan8///hzmnWh5YeWxJ6dNLDHU3H2h/uWPT/cPujpjWR//8rJSYlJynpKChlANXmgxhJ@Xn5SWBWUWJKYhFErgJEJaaA1AIA "Jelly – Try It Online")
## How it works
```
Ṗ;¥ƤUŒḂƇḢ - Main link. Takes a string S on the left
    U     - Reverse s
  ¥       - Group the previous 2 links into a dyad f(p, r):
Ṗ         -   Remove the last element of p
 ;        -   Concatenate the truncated p to r
   Ƥ      - Over each prefix p of s, yield f(p, rev(s))
       Ƈ  - Keep those for which the following is true:
     ŒḂ   -   Is a palindrome?
        Ḣ - Take the first
```
[Answer]
# [K (ngn/k)](https://bitbucket.org/ngn/k), 24 bytes
```
{t@*&{x~|x}'t:x,/:|',\x}
```
[Try it online!](https://tio.run/##y9bNS8/7/z/NqrrEQUutuqKupqJWvcSqQkffqkZdJ6ai9n@auoZSYlJykpK1UkZqTk4@kE7Kz8tPAjGKElMSi8ASFUqa/wE "K (ngn/k) – Try It Online")
Feels like it could be golfed more...
* `,\x` make list of prefixes of input
* `t:x,/:\'` append the reverse of each prefix to the original input, storing in `t`
* `*&{x~|x}'` identify the index of the first item in the list that is a palindrome
* `t@` retrieve that list item and return it from the function
[Answer]
## [QBIC](https://drive.google.com/drive/folders/0B0R1Jgqp8Gg4cVJCZkRkdEthZDQ), 41 bytes
```
;_FA|C=A{a=a+1~C=_fC||_XC\C=A+right$(B,a)
```
Explanation:
```
;_FA|    Read A$ from the cmd line, then flip it to create B$
C=A      Set C$ to be A$
{        Start an infinite DO-loop
a=a+1    Increment a (not to be confused with A$...)
~C=_fC|  If C$ is equal to its own reversed version
|_XC     THEN end, printing C$
\C=A+    ELSE, C$ is reset to the base A$, with
right$(B the right part of its own reversal
,a)      for length a (remember, we increment this each iteration
         DO and IF implicitly closed at EOF
```
[Answer]
# Haskell, 46 bytes
```
f l|l==reverse l=l|(h:t)<-l=l!!0:(f$tail l)++[l!!0]
```
I'm wondering if there's a way to remove the parenthesis in `(f$tail l)++[l!!0]`...
]