# Count of "a"s and "b"s must be equal. Did you get it computer?

In the popular (and essential) computer science book, An Introduction to Formal Languages and Automata by Peter Linz, the following formal language is frequently stated:

mainly because this language can not be processed with finite-state automata. This expression mean "Language L consists all strings of 'a's followed by 'b's, in which the number of 'a's and 'b's are equal and non-zero".

# Challenge

Write a working program/function which gets a string, containing "a"s and "b"s only, as input and returns/outputs a truth value, saying if this string is valid the formal language L.

• Your program cannot use any external computation tools, including network, external programs, etc. Shells are an exception to this rule; Bash, e.g., can use command line utilities.

• Your program must return/output the result in a "logical" way, for example: returning 10 instead of 0, "beep" sound, outputting to stdout etc. More info here.

• Standard code golf rules apply.

This is a . Shortest code in bytes wins. Good luck!

### Truthy test cases

"ab"
"aabb"
"aaabbb"
"aaaabbbb"
"aaaaabbbbb"
"aaaaaabbbbbb"


### Falsy test cases

""
"a"
"b"
"aa"
"ba"
"bb"
"aaa"
"aab"
"aba"
"abb"
"baa"
"bab"
"bba"
"bbb"
"aaaa"
"aaab"
"aaba"
"abaa"
"abab"
"abba"
"abbb"
"baaa"
"baab"
"baba"
"babb"
"bbaa"
"bbab"
"bbba"
"bbbb"


Here is a Stack Snippet to generate both a regular leaderboard and an overview of winners by language.

/* Configuration */

var QUESTION_ID = 85994; // Obtain this from the url
// It will be like https://XYZ.stackexchange.com/questions/QUESTION_ID/... on any question page
var COMMENT_FILTER = "!)Q2B_A2kjfAiU78X(md6BoYk";
var OVERRIDE_USER = 48934; // This should be the user ID of the challenge author.

/* App */

return "https://api.stackexchange.com/2.2/questions/" +  QUESTION_ID + "/answers?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + ANSWER_FILTER;
}

}

jQuery.ajax({
method: "get",
dataType: "jsonp",
crossDomain: true,
success: function (data) {
data.items.forEach(function(a) {
});
comment_page = 1;
}
});
}

jQuery.ajax({
method: "get",
dataType: "jsonp",
crossDomain: true,
success: function (data) {
data.items.forEach(function(c) {
if (c.owner.user_id === OVERRIDE_USER)
});
else process();
}
});
}

var SCORE_REG = /<h\d>\s*([^\n,]*[^\s,]),.*?(\d+)(?=[^\n\d<>]*(?:<(?:s>[^\n<>]*<\/s>|[^\n<>]+>)[^\n\d<>]*)*<\/h\d>)/;

function getAuthorName(a) {
return a.owner.display_name;
}

function process() {
var valid = [];

var body = a.body;
if(OVERRIDE_REG.test(c.body))
body = '<h1>' + c.body.replace(OVERRIDE_REG, '') + '</h1>';
});

var match = body.match(SCORE_REG);
if (match)
valid.push({
user: getAuthorName(a),
size: +match[2],
language: match[1],
});

});

valid.sort(function (a, b) {
var aB = a.size,
bB = b.size;
return aB - bB
});

var languages = {};
var place = 1;
var lastSize = null;
var lastPlace = 1;
valid.forEach(function (a) {
if (a.size != lastSize)
lastPlace = place;
lastSize = a.size;
++place;

.replace("{{NAME}}", a.user)
.replace("{{LANGUAGE}}", a.language)
.replace("{{SIZE}}", a.size)

var lang = a.language;
if (/<a/.test(lang)) lang = jQuery(lang).text();

languages[lang] = languages[lang] || {lang: a.language, user: a.user, size: a.size, link: a.link};
});

var langs = [];
for (var lang in languages)
if (languages.hasOwnProperty(lang))
langs.push(languages[lang]);

langs.sort(function (a, b) {
if (a.lang > b.lang) return 1;
if (a.lang < b.lang) return -1;
return 0;
});

for (var i = 0; i < langs.length; ++i)
{
var language = jQuery("#language-template").html();
var lang = langs[i];
language = language.replace("{{LANGUAGE}}", lang.lang)
.replace("{{NAME}}", lang.user)
.replace("{{SIZE}}", lang.size)
language = jQuery(language);
jQuery("#languages").append(language);
}

}
body { text-align: left !important}

width: 290px;
float: left;
}

#language-list {
width: 290px;
float: left;
}

font-weight: bold;
}

table td {
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr>

</tbody>
</table>
</div>
<div id="language-list">
<h2>Winners by Language</h2>
<table class="language-list">
<tr><td>Language</td><td>User</td><td>Score</td></tr>
<tbody id="languages">

</tbody>
</table>
</div>
<table style="display: none">
</tbody>
</table>
<table style="display: none">
<tbody id="language-template">
</tbody>
</table>

• Can the input be empty? (You're saying it's not part of the language, but not whether it's an input we need to consider.) Jul 20 '16 at 20:04
• What if our language doesn't have truthy or falsy? Would empty string == truthy and non-empty string == falsy be acceptable? Jul 20 '16 at 20:20
• Nice challenge, but I think the title could be a little less ambiguous (i.e. a mention of a^n b^n or similar, rather than just the number of as equalling the number of bs) Jul 21 '16 at 12:28
• @Sp3000 I choosed this title because it looked fun . I may change it later to sth else ...
– user55673
Jul 21 '16 at 13:27
• I'm a little surprised that in 50+ answers I'm the only one to use a paser generator. To be sure it's not strictly competitive on length, but the problem posed is one of parsing a simple but non-trivial language. I'd very much like to see answers in other compiler-compiler syntaxes because I am not widely familiar with the choices. Jul 22 '16 at 22:47

# MATL, 5 4 bytes

tSP-


Prints a non-empty array of 1s if the string belongs to L, and an empty array or an array with 0s (both falsy) otherwise.

Thanks to @LuisMendo for golfing off 1 byte!

Try it online!

### How it works

t      Push a copy of the implicitly read input.
S     Sort the copy.
P    Reverse the sorted copy.
-   Take the difference of the code point of the corresponding characters
of the sorted string and the original.

• My second (working) MATL answer. :) Jul 21 '16 at 0:49
• Strange definition of truthy and falsy: 'aabb' gives -1 -1 1 1 is truthy. 'aaabb' gives -1 -1 0 1 1 and is falsy Jul 25 '16 at 8:02
• @Etoplay A non-empty array with all its values nonzero is truthy. It's the definition used in Matlab and Octave Jul 25 '16 at 12:36

## Python 3, 32 bytes

eval(input().translate(")("*50))


Outputs via exit code: Error for false, no error for True.

The string is evaluated as Python code, replacing parens ( for a and ) for b. Only expressions of the form a^n b^n become well-formed expressions of parentheses like ((())), evaluating to the tuple ().

Any mismatched parens give an error, as will multiple groups like (()()), since there's no separator. The empty string also fails (it would succeed on exec).

The conversion ( -> a, ) -> b is done using str.translate, which replaces characters as indicated by a string that serves as a conversion table. Given the 100-length string ")("*50, the tables maps the first 100 ASCII values as

... Z[\]^_abc
... )()()()()(


which takes ( -> a, ) -> b. In Python 2, conversions for all 256 ASCII values must be provided, requiring "ab"*128, one byte longer; thanks to isaacg for pointing this out.

• Ok, that's clever.
– TLW
Jul 21 '16 at 2:03
• What does the *128 do? Jul 22 '16 at 22:17
• 128 can be replaced by 50 (or 99 for that matter) to save a byte. Jul 22 '16 at 23:40
• @Eʀɪᴋ ᴛʜᴇ Gᴏʟғᴇʀ: I think it´s a quantifier. But I don´t really know Python and have not found any documentation on that yet. Jul 23 '16 at 3:02
• @isaacg Thanks, I wasn't aware that changed for Python 3.
– xnor
Jul 23 '16 at 6:43

## Retina, 12 bytes

Credits to FryAmTheEggman who found this solution independently.

+a;?b
;
^;$ Prints 1 for valid input and 0 otherwise. Try it online! (The first line enables a linefeed-separated test suite.) ### Explanation Balancing groups require expensive syntax, so instead I'm trying to reduce a valid input to a simple form. Stage 1 +a;?b ;  The + tells Retina to repeat this stage in a loop until the output stops changing. It matches either ab or a;b and replaces it with ;. Let's consider a few cases: • If the as and the bs in the string aren't balanced in the same way that ( and ) normally need to be, some a or b will remain in the string, since ba, or b;a can't be resolved and a single a or b on its own can't either. To get rid of all the as and the bs there has to be one corresponding b to the right of each a. • If the a and the b aren't all nested (e.g. if we have something like abab or aabaabbb) then we'll end up with multiple ; (and potentially some as and bs) because the first iteration will find multiple abs to insert them and further iterations will preserve the number of ; in the string. Hence, if and only if the input is of the form anbn, we'll end up with a single ; in the string. Stage 2: ^;$


Check whether the resulting string contains nothing but a single semicolon. (When I say "check" I actually mean, "count the number of matches of the given regex, but since that regex can match at most once due to the anchors, this gives either 0 or 1.)

f s=s==[c|c<-"ab",'a'<-s]&&s>""


The list comprehension [c|c<-"ab",'a'<-s] makes a string of one 'a' for each 'a' in s, followed by one 'b' for each 'a' in s. It avoids counting by matching on a constant and producing an output for each match.

This string is checked to be equal to the original string, and the original string is checked to be non-empty.

• This is lovely. I often forget how useful it is that Haskell orders the elements of a list comprehension in a consistent and very specific way. Jul 21 '16 at 19:31
• Much nicer than my best attempt (f=g.span id.map(=='a');g(a,b)=or a&&b==(not<$>a)) . Well done. Jul 22 '16 at 21:04 • Wow, I didn't know one could match on a constant in a list comprehension! Jul 24 '16 at 7:41 ## Grime, 12 bytes A=\aA?\b eA  Try it online! ## Explanation The first line defines a nonterminal A, which matches one letter a, possibly the nonterminal A, and then one letter b. The second line matches the entire input (e) against the nonterminal A. ## 8-byte noncompeting version e\a_?\b  After writing the first version of this answer, I updated Grime to consider _ as the name of the top-level expression. This solution is equivalent to the above, but avoids repeating the label A. • Why didn't you do it in J? Jul 20 '16 at 19:38 • @LeakyNun I just wanted to show off Grime. :P Jul 20 '16 at 19:39 • You built this language? Jul 20 '16 at 19:40 • @LeakyNun Yes. Development is slow, but ongoing. Jul 20 '16 at 19:41 # Brachylog, 23 19 bytes @2L,?lye:"ab"rz:jaL  Try it online! ### Explanation @2L, Split the input in two, the list containing the two halves is L ?lye Take a number I between 0 and the length of the input :"ab"rz Zip the string "ab" with that number, resulting in [["a":I]:["b":I]] :jaL Apply juxtapose with that zip as input and L as output i.e. "a" concatenated I times to itself makes the first string of L and "b" concatenated I times to itself makes the second string of L  • Congratulations on getting on tryitonline.net! Jul 20 '16 at 20:01 # 05AB1E, 9 bytes Code: .M{J¹ÔQ0r  Explanation: .M # Get the most frequent element from the input. If the count is equal, this results into ['a', 'b'] or ['b', 'a']. { # Sort this list, which should result into ['a', 'b']. J # Join this list. Ô # Connected uniquified. E.g. "aaabbb" -> "ab" and "aabbaa" -> "aba". Q # Check if both strings are equal. 0r # (Print 0 if the input is empty).  The last two bytes can be discarded if the input is guaranteed to be non-empty. Uses the CP-1252 encoding. Try it online!. • What happens with empty input? Jul 20 '16 at 19:54 • Look for non-zero in the post; it’s in there :) – Lynn Jul 20 '16 at 20:01 • @Lynn Doesn't the spec only say no-zero for a valid language though? Not about input. Jul 20 '16 at 20:02 • True. Thought wrong there. But you can still do .M{J¹ÔQ0r for yours. Jul 20 '16 at 20:17 • @Emigna Thanks, I have edited the post. Jul 20 '16 at 20:20 # Jelly, 6 bytes Ṣ=Ṛ¬Pȧ  Prints the string itself if it belongs to L or is empty, and 0 otherwise. ### How it works Ṣ=Ṛ¬Pȧ Main link. Argument: s (string) Ṣ Yield s, sorted. Ṛ Yield s, reversed. = Compare each character of sorted s with each character of reversed s. ¬ Take the logical NOT of each resulting Boolean. P Take the product of the resulting Booleans. This will yield 1 if s ∊ L or s == "", and 0 otherwise. ȧ Take the logical AND with s. This will replace 1 with s. Since an empty string is falsy in Jelly, the result is still correct if s == "".  ## Alternate version, 4 bytes (non-competing) ṢnṚȦ  Prints 1 or 0. Try it online! or verify all test cases. ### How it works ṢnṚȦ Main link. Argument: s (string) Ṣ Yield s, sorted. Ṛ Yield s, reversed. n Compare each character of the results, returning 1 iff they're not equal. Ȧ All (Octave-style truthy); return 1 if the list is non-empty and all numbers are non-zero, 0 in all other cases.  # J, 17 bytes #<.(-:'ab'#~-:@#)  This works correctly for giving falsey for the empty string. Error is falsey. Old versions: -:'ab'#~-:@# 2&#-:'ab'#~# NB. thanks to miles  ## Proof and explanation The main verb is a fork consisting of these three verbs: # <. (-:'ab'#~-:@#)  This means, "The lesser of (<.) the length (#) and the result of the right tine ((-:'ab'#~-:@#))". The right tine is a 4-train, consisting of: (-:) ('ab') (#~) (-:@#)  Let k represent our input. Then, this is equivalent to: k -: ('ab' #~ -:@#) k  -: is the match operator, so the leading -: tests for invariance under the monadic fork 'ab' #~ -:@#. Since the left tine of the fork is a verb, it becomes a constant function. So, the fork is equivalent to: 'ab' #~ (-:@# k)  The right tine of the fork halves (-:) the length (#) of k. Observe #:  1 # 'ab' 'ab' 2 # 'ab' 'aabb' 3 # 'ab' 'aaabbb' 'ab' #~ 3 'aaabbb'  Now, this is k only on valid inputs, so we are done here. # errors for odd-length strings, which never satisfies the language, so there we are also done. Combined with the lesser of the length and this, the empty string, which is not a part of our language, yields its length, 0, and we are done with it all. • I modified it into 2&#-:'ab'#~# which should let you avoid the error and just output 0 instead while still using 12 bytes. Jul 20 '16 at 21:33 • @miles Fascinating! I never thought about it like that. Jul 20 '16 at 21:39 • Does this handle the empty string? Jul 21 '16 at 11:24 • @Zgarb fixed it! Jul 21 '16 at 19:30 # Bison/YACC 60 (or 29) bytes (Well, the compilation for a YACC program is a couple of steps so might want to include some for that. See below for details.) %% l:c'\n'; c:'a''b'|'a'c'b'; %% yylex(){return getchar();}  The function should be fairly obvious if you know to interpret it in terms of a formal grammar. The parser accepts either ab or an a followed by any acceptable sequence followed by a b. This implementation relies on a compiler that accepts K&R semantics to lose a few characters. It's wordier than I would like with the need to define yylex and to call getchar. Compile with $ yacc equal.yacc
$gcc -m64 --std=c89 y.tab.c -o equal -L/usr/local/opt/bison/lib/ -ly  (most of the options to gcc are specific to my system and shouldn't count against the byte count; you might want to count -std=c89 which adds 8 to the value listed). Run with $ echo "aabb" | ./equal


or equivalent.

The truth value is returned to the the OS and errors also report syntax error to the command line. If I can count only the part of the code that defines the parsing function (that is neglect the second %% and all that follows) I get a count of 29 bytes.

# JavaScript, 5455 44

s=>s&&s.match(^a{${l=s.length/2}}b{${l}}$)  Builds a simple regex based on the length of the string and tests it. For a length 4 string (aabb) the regex looks like: ^a{2}b{2}$

Returns a truthy or falsey value.

11 bytes saved thanks to Neil.

f=s=>s&&s.match(^a{${l=s.length/2}}b{${l}}$) // true console.log(f('ab'), !!f('ab')) console.log(f('aabb'), !!f('aabb')) console.log(f('aaaaabbbbb'), !!f('aaaaabbbbb')) // false console.log(f('a'), !!f('a')) console.log(f('b'), !!f('b')) console.log(f('ba'), !!f('ba')) console.log(f('aaab'), !!f('aaab')) console.log(f('ababab'), !!f('ababab')) console.log(f('c'), !!f('c')) console.log(f('abc'), !!f('abc')) console.log(f(''), !!f('')) • The f= can be omitted. Jul 20 '16 at 19:53 • Is a function expression a valid submission, or must it actually be, ahem, functional? Jul 20 '16 at 19:54 • A function is a valid submission. Jul 20 '16 at 19:56 • @TimmyD It used to return true, but now it returns false. Jul 20 '16 at 20:06 • s=>s.match(^a{${s.length/2}}b+$)? – l4m2 May 30 '18 at 4:36 ## Perl 5.10, 35 17 bytes (with -n flag) say/^(a(?1)?b)$/


Ensures that the string starts with as and then recurses on bs. It matches only if both lengths are equal.

Thanks to Martin Ender for halving the byte count and teaching me a little about recursion in regexes :D

It returns the whole string if it matches, and nothing if not.

Try it here!

• Closest I can manage including the non-empty test case is 18 bytes: $_&&=y/a//==y/b// (requires -p), without the empty you could drop the && for 16! So close... Jul 21 '16 at 9:08 • So I can do another 17 bytes: echo -n 'aaabbb'|perl -pe '$_+=y/a//==y/b//' but I can't shift another byte... Might have to give up on this! Jul 22 '16 at 15:33
• Just realised that this could be done in 7 bytes using that regex as -F/^(a(?1)?b)$/: tio.run/##LYw9CoVADIT7nMNCCxGLV/pTeQwlAQtBdFHPb9yZPFgyk518k9Zr/… Apr 17 '20 at 10:51 ## C, 57 53 Bytes t;x(char*s){t+=*s%2*2;return--t?*s&&x(s+1):*s*!1[s];}  Old 57 bytes long solution: t;x(char*s){*s&1&&(t+=2);return--t?*s&&x(s+1):*s&&!1[s];}  Compiled with gcc v. 4.8.2 @Ubuntu Thanks ugoren for tips! Try it on Ideone! • Since I'm new here and can't comment on other answers yet, I just want to point out that 62b solution from @Josh gives false positive on strings like "aaabab". Jul 22 '16 at 15:47 • Change (t+=2) to t++++ for -1 byte. Jul 25 '16 at 13:20 • @owacoder t++++ is not a valid C code. Jul 25 '16 at 14:21 • Save some with t+=*s%2*2 and :*s*!1[s] Jul 31 '16 at 14:18 • Very clever answer! It does unfortunately fail on input "ba" : ideone.com/yxixG2 – Josh Aug 8 '16 at 15:07 # Retina, 22 bytes Another shorter answer in the same language just came... ^(a)+(?<-1>b)+(?(1)c)$


Try it online!

This is a showcase of the balancing groups in regex, which is explained fully by Martin Ender.

As my explanation would not come close to half of it, I'll just link to it and not attempt to explain, as that would be detrimental to the glory of his explanation.

# Befunge-93, 67 bytes

0v@.<  0<@.!-$< >0\v +>~:0!#^_:"a" -#^_$ 1
~+1_^#!-"b" _ ^#0: <


Try it here! Might explain how it works later. Might also try to golf it just a tad bit more, just for kicks.

# MATL, 9 bytes

vHI$e!d1=  Try it online! The output array is truthy if it is non-empty and all its entries are nonzero. Otherwise it's falsy. Here are some examples. v % concatenate the stack. Since it's empty, pushes the empty array, [] H % push 2 I$    % specify three inputs for next function
e     % reshape(input, [], 2): this takes the input implicitly and reshapes it in 2
% columns in column major order. If the input has odd length a zero is padded at
% the end. For input 'aaabbb' this gives the 2D char array ['ab;'ab';'ab']
!     % transpose. This gives ['aaa;'bbb']
d     % difference along each column
1=    % test if all elements are 1. If so, that means the first tow contains 'a' and
% the second 'b'. Implicitly display

• That's some convenient definition of truthy. (I knew about the non-zero requirement, but not about the non-empty one.) Jul 21 '16 at 0:34

# x86 machine code, 29 27 bytes

Hexdump:

33 c0 40 41 80 79 ff 61 74 f8 48 41 80 79 fe 62
74 f8 0a 41 fe f7 d8 1b c0 40 c3


Assembly code:

    xor eax, eax;
loop1:
inc eax;
inc ecx;
cmp byte ptr [ecx-1], 'a';
je loop1;

loop2:
dec eax;
inc ecx;
cmp byte ptr [ecx-2], 'b';
je loop2;

or al, [ecx-2];
neg eax;
sbb eax, eax;
inc eax;
done:
ret;


Iterates over the a bytes in the beginning, then over the following 'b' bytes. The first loop increases a counter, and the second loop decreases it. Afterwards, does a bitwise OR between the following conditions:

1. If the counter is not 0 at the end, the string doesn't match
2. If the byte that follows the sequence of bs is not 0, the string also doesn't match

Then, it has to "invert" the truth value in eax - set it to 0 if it was not 0, and vice versa. It turns out that the shortest code to do that is the following 5-byte code, which I stole from the output of my C++ compiler for result = (result == 0):

    neg eax;      // negate eax; set C flag to 1 if it was nonzero
sbb eax, eax; // subtract eax and the C flag from eax
inc eax;      // increase eax

• I think you can improve your negation. Try: neg eax to set the carry flag as before, cmc to invert the carry flag and salc to set AL to FFh or 0 depending on whether the carry flag is set or not. Saves 2 bytes, although does end up with an 8-bit result rather than 32-bit. Jul 22 '16 at 21:40
• The same thing using string ops, with ESI pointing to the input string, and returning the result in AL (uses SETcc, requires 386+): xor eax,eax | xor ecx,ecx | l1: inc ecx | lodsb | cmp al, 'a' | jz l1 | dec esi | l2: lodsb | cmp al,'b' | loopz l2 | or eax,ecx | setz al | ret Jul 26 '16 at 21:26
• @ninjalj You should post that in an answer - it's sufficiently different from mine, and I suspect is significantly shorter! Jul 26 '16 at 22:02

# Ruby, 24 bytes

eval(gets.tr'ab','[]')*1


(This is just xnor's brilliant idea in Ruby form. My other answer is a solution I actually came up with myself.)

The program takes the input, transforms a and b to [ and ] respectively, and evaluates it.

Valid input will form a nested array, and nothing happens. An unbalanced expression will make the program crash. In Ruby empty input is evaluated as nil, which will crash because nil has not defined a * method.

# Sed, 38 + 2 = 40 bytes

s/.*/c&d/;:x;s/ca(.*)bd/c\1d/;tx;/cd/p


A non empty string output is truthy

Finite state automata can not do this, you say? What about finite state automata with loops. :P

Run with r and n flags.

### Explanation

s/.*/c&d/        #Wrap the input in 'c' and 'd' (used as markers)
:x               #Define a label named 'x'
s/ca(.*)bd/c\1d/ #Deletes 'a's preceded by 'c's and equivalently for 'b's and 'd's. This shifts the markers to the center
/cd/p            #If the markers are next to one another, print the string

• Nice approach. Thanks for the breakdown. Jul 25 '16 at 3:28

# JavaScript, 44 42

Crossed out 44 is still regular 44 ;(

f=s=>(z=s.match^a(.+)b$)?f(z[1]):s=="ab"  Works by recursively stripping off the outer a and b and recursively using the inner value selected but .+. When there's no match on ^a.+b$ left, then the final result is whether the remaining string is the exact value ab.

Test cases:

console.log(["ab","aabb","aaabbb","aaaabbbb","aaaaabbbbb","aaaaaabbbbbb"].every(f) == true)
console.log(["","a","b","aa","ba","bb","aaa","aab","aba","abb","baa","bab","bba","bbb","aaaa","aaab","aaba","abaa","abab","abba","abbb","baaa","baab","baba","babb","bbaa","bbab","bbba","bbbb"].some(f) == false)


# ANTLR, 31 bytes

grammar A;r:'ab'|'a'r'b'|r'\n';


Uses the same concept as @dmckee's YACC answer, just slightly more golfed.

To test, follow the steps in ANTLR's Getting Started tutorial. Then, put the above code into a file named A.g4 and run these commands:

$antlr A.g4$ javac A*.java


Then test by giving input on STDIN to grun A r like so:

$echo "aaabbb" | grun A r  If the input is valid, nothing will be output; if it is invalid, grun will give an error (either token recognition error, extraneous input, mismatched input, or no viable alternative). Example usage: $ echo "aabb" | grun A r

## Alternate, 35 bytes

$args-match'^(a)+(?<-1>b)+(?(1)c)$'


This uses the regex from Leaky's answer, based on .NET balancing groups, just encapsulated in the PowerShell -match operator. Returns the string for truthy, or empty string for falsey.

• In the alternate version you should evaluate -match against $args[0], otherwise -match will work as a filter Jul 24 '16 at 18:18 • @MathiasR.Jessen In production code, yes, but we can golf the [0] here because we're only given one input and we only need one truthy/falsey value as output. Since an empty string is falsey and a non-empty string is truthy, we can filter against the array and either get the input string back or nothing back, which satisfies the challenge requirements. Jul 25 '16 at 12:30 # Pyth - 13 bytes &zqzS*/lz2"ab  Explained:  qz #is input equal to "ab #the string "ab" * #multiplied by /lz2 #length of input / 2 S #and sorted? &z #(implicitly) print if the above is true and z is not empty  • You can use a string as input and then make it &qS*/lQ2"ab Jul 20 '16 at 20:25 • @LeakyNun thanks for the tip! Can you explain how/why that works? This is my first time ever using Pyth Jul 20 '16 at 20:46 • For example, +4 will expand to +4Q (implicit filling of arguments) Jul 21 '16 at 4:07 ## Haskell, 39 bytes p x=elem x$scanl(\s _->'a':s++"b")"ab"x


Usage example: p "aabb" -> True.

scanl(\s _->'a':s++"b")"ab"x build a list of all ["ab", "aabb", "aaabbb", ...] with a total of (length x) elements. elem checks if x is in this list.

# Python, 43 40 Bytes

lambda s:''<s==len(s)/2*"a"+len(s)/2*"b"


connsidered the obvious solution thanks to Leaky Nun

other idea, 45 bytes:

lambda s:s and list(s)==sorted(len(s)/2*"ab")


-4 bytes by using len/2 (i get an error when the half comes last)

now gives false for the empty string

-3 bytes thanks to xnor

• Yes, lambdas don't have to be named. Jul 20 '16 at 19:51
• lambda s:list(s)==sorted("ab"*len(s)//2) (Python 3) Jul 20 '16 at 19:52
• lambda s:s=="a"*len(s)//2+"b"*len(s)//2 (Python 3) Jul 20 '16 at 19:52
• yeah, I realized that while posting it. lol, the obvious solution is shorter in Python 2: Jul 20 '16 at 19:57
• You can do ''< instead of s and` to rule out the empty case.
– xnor
Jul 20 '16 at 22:54